A Measurement of the Michel Parameters ρ and ƞ in Leptonic Tau Decays Citation Chadha, Mandeepa (1998) A Measurement of the Michel Parameters ρ and ƞ in Leptonic Tau Decays. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/xkhh-jq80. https://resolver.caltech.edu/CaltechTHESIS:09022025-221121899 Abstract This thesis describes a precise measurement of the Michel parameters ρ and ƞ using the leptonic tau decays recorded by the CLEO II detector. These measurements can be used to provide limits on the non-(V - A) contributions to the Lorentz structure of the charged weak interactions in tau decays. The electronic decay of the tau lepton, τ → evv, is used to measure the spectral shape Michel parameter: ρ ε = 0.732 ± 0.014 ± 0.009, where the first error is statistical and the second systematic. This measurement is extracted from the electron energy spectrum; the energy spectrum is insensitive to the low energy spectral shape Michel parameter ƞ ε , and thus insensitive to the presence of scalar couplings. The muonic decay mode of the tau lepton, τ → µvv, is used to measure both the spectral shape Michel parameters: ρ µ = 0.747 ± 0.048 ± 0.044 and ƞ µ = 0.010 ± 0.149 ± 0.171 simultaneously. Once again, the first errors are statistical and the second systematic. The two parameters are strongly correlated; the correlation coefficient C ρƞ is 0.949. Assuming lepton universality of the vector-like couplings, the two leptonic decay modes are simultaneously analyzed to improve the measurement of the ƞ parameter. Since the electron mode is insensitive to the ƞ parameter, we can measure ρ very precisely using the electron mode. This measurement can now be used to constrain the ρ measurement in the muon analysis, and thus obtain: ρ εµ = 0.735 ± 0.013 ± 0.008 and ƞ εµ = -0.015 ± 0.061 ± 0.062, where the first errors a.re statistical and the second systematic. The correlation coefficient is now reduced to 0.615. These measurements are all more precise than previous measuren1ents; some are more precise than previous world average measurements. No indications for any deviations from the Minimal Standard Model have been found. This measurement of the ƞ parameter provides a lower limit on the charged Higgs mass in the Minimal Supersymmetric Standard Model: m H± > (0.97 x tan β) GeV at the 90% confidence level. This limit is not very interesting unless tan β is very large. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: (Physics) Degree Grantor: California Institute of Technology Division: Physics, Mathematics and Astronomy Major Option: Physics Thesis Availability: Public (worldwide access) Research Advisor(s): Barish, Barry C. Thesis Committee: Barish, Barry C. (chair) Hughes, Emlyn Willard Preskill, John P. Weinstein, Alan Jay Defense Date: 23 September 1997 Record Number: CaltechTHESIS:09022025-221121899 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:09022025-221121899 DOI: 10.7907/xkhh-jq80 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 17661 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 12 Sep 2025 10:33 Last Modified: 12 Sep 2025 11:36 Thesis Files PDF - Final Version See Usage Policy. 68MB Repository Staff Only: item control page

A Measurement of the Michel Parameters p and r; in Leptonic Tau Decays Thesis by )VIandeepa Chadha In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy Californi a Institute of Technology Pa.sa.clena., California 1998 (Submitted September 23, 1997) .. ]] @ 199 8 Ma.ndeepa. Cha.clha. All Ri ghts Reserved lll This is my letter to the world, Tha.t never wrote to me, The simple news tha.t nature told , vVith simple majesty. -Emily Dickinson JV Acknowledgements A 'Nork many yea.rs in the ma.king, I dedicate this thesis to Ta.run who's held my hand through the la.st four! I cannot thank enough the many people who helped in many ways a.long the way. First of all, I would like to thank Barry Barish and Rysza.rd Stroynowski for providing the motivation for this analysis. Next, I'd like to thank Alan ·w einstein for picking up where they left off, and for his patience and guidance, without which this thesis would not have been possible. I'd also like to thank .Jon Urheim and Mauritius Schmicltler for many discussions and arguments; Doug Cowen for teaching me to like Ithaca; and Bill Ross for providing all those la.ughs. I would also like to thank my undergraduate professors , R. C. Verma and M. P. Gupta, for introducing me to the wonderful world of High Energy Physics. La.st but not the lea.st, I'd like to thank my parents who provided the strength and encouragement long-distance over the airwaves , and Micha.el Rogers for playing the parent whenever I needed one nearby. I might not be great at expressing my feelings, but I do appreciate all that you all have clone for me! V Abstract This thesis describes a precise measurement of the Michel parameters p and 17 using the leptonic tau decays recorded by the CLEO II detector. These measurements can be used to provide limits on the non-(V - A) contributions to the Lorentz structure of the charged weak interactions in tau decays. The electronic decay of the tau lepton , T ----+ eIJv , is used to measure the spectral shape Mi chel parameter: Pe = 0. 732 ± 0.01 4 ± 0.009 , where the first error is statistical and the second systemati c. This measurement is extracted from the electron energy spectrum; the energy spect rum is insensiti ve to t he low energy spectral shape Michel para.meter 17e , and thus insensiti ve to the presence of scalar couplings. The muoni c decay mode of the tau lepton, T ----+ p11 v , is used to measure both the spectral shape Michel parameters: P J.1 0.747 ± 0.048 ± 0.044 and 171-, 0.010 ± 0.149 ± 0.171 simultaneously. Once again , the first errors are statisti cal and the second systemati c. The two parameters a.re strongly correlated ; the correlation coefficient Cp,1 is 0.949 . Assuming lepton uni versality of the vector-like couplings, the two leptonic decay modes a.re simultaneously analyzed to improve the measurement of the 17 para.meter. Since the electron mode is insensitive to the 17 para.meter, we can measure p very precisely using t he electron mode . This measurement can now be used to constrain VJ the p measurement in the muon a.na.lysis , and thus obtain: and Pe11. 0. 7:35 ± 0.01:3 ± 0.008 17eJI. -0.01 5 ± 0.061 ± 0.062 , where the first errors a.re sta.tist ica.l and the second systematic. The correlation coefficient is now redu ced to 0.615. These measurements a.re a.11 more precise than previous measuren1ents; some a.re more precise than previous world average measurements. No indi cations for any deviations from the Minimal Standard Model have been found . This measurement of the 17 para.meter provides a lower limit on the charged Higgs mass in the Minimal Supersymmetric Standard Model: rnH ± > (0.97 x tan /3 ) Ge\! at the 90 % confidence level. This limit is not very interesting unless tan fJ is very large. V il Contents Acknowledgements IV Abstract V 1 Introduction and Overview 1 2 The Standard Model of Particle Physics 5 2.1 Elementary Particles 5 2.2 Fundamental Forces . 7 2.3 Weak Interactions and the (V - A) Theory . 8 2.4 The Tau Lepton . . . . . . . . . . . . . . 10 2.4. l The Discovery of the Tau Lepton 10 2.4.2 Ta.u Production . . . . 12 2.4.3 Theory of Ta.u Decays 19 2.5 Michel Para.meters . . .. 26 2.6 Heli city Ba.sis Probabilities 33 2.7 Beyond the Standard Model 39 2.7.l Charged Higgs 39 2. 7.2 Right-Handed liV' Bosons 40 2.7.3 Anomalous Electri c a.nd l\fagnetic Couplings 40 2.7.4 Massive Neutrinos L! l 3 The CLEO Experiment at CESR 42 :3 .1 CES R . . . . . . . . 42 3.2 T he CLEO Detector 44 3.2.1 Beam Pipe .. 47 3.2.2 Central Tracking System 47 Vlll 3.3 3.4 4 Time of Flight . . . . . 3.2.4 Electromagnetic Calorimeter . 57 3.2.5 Superconducting Solenoidal Magnet 60 3.2.6 Muon Chambers 60 3.2.7 Trigger and Data Acquisition 62 Simulation of Physics Processes and Detector Response 6:3 3.3.1 Event Generation . . 64 3.3.2 Detector Simulation 66 Future Upgrades to CESR and CLEO . 67 Data Analysis 68 4.1 Event Reconstruction . 68 4.1.1 Tracking 69 4.1.2 Crystal Calorimeter Clustering 70 4.1.3 Track-Cluster Matching 71 4.1.4 Muon Identification . 72 4.1.5 Electron Identification 7:3 4.1.6 Reconstruction of 1r 0 --+ , ,, Decays 74 4.2 5 :3.2.3 Event Selection 75 4.2.1 TAUSh:lVI 75 4.2.2 Event Topology 76 4.2 .:3 Cuts to Minimize Backgrounds 78 Backgrounds 79 5.l T Background 80 5.1.1 Fake Leptons 80 5. 1.2 Feed Across Into Tag T --+ lrn° 11r Mode 85 Non-T Backgrounds . . . . . . . . . . . . . . . 90 5.2.1 Cosmic Rays, Beam Gas and Beam \i\fall Events 90 ,5.2.2 Two Photon Physics 92 5.2.:3 Bhabha Events . .. 94 5.2 JX 5.2.4 Hadronic Backgrounds 96 6 Yields and Branching Ratios 97 7 Experimental Technique 101 7.1 Reconstruction of the Pseudo Rest Frame. 104 7.2 Low Momentum Muons 108 8 9 Fitting and Results 111 8.1 Fit Functions .. 111 8.2 Electron Mode Results 115 8.3 Muon Mode Results 118 8.4 Invoking Lepton Universality. 122 Determining Systematic Errors 125 9.1 Sources of Error . . . . . . . . . 9.2 How Well Does the Fit Technique ·w ork? 126 9.3 Trigger . . . . . . . . . 127 9.4 Electron Identification 132 9.5 Muon Identification . 136 9.6 Backgrounds . . . . 139 9.6.1 Fake Muons 1:39 9.6.2 Fake Electrons 14:3 9.6.3 Feed-down into Tag Mode 1L15 9.7 Beam Energy Corrections 146 9.8 Tau Flight Direction Estimation in Pseudo Rest Frame Analysis 147 9.9 Radiative Processes 149 9.10 Spin Correlations . 9.11 Geometric Acceptance 158 9.12 Monte Carlo Statistics 160 9.13 Bin Migration and Resolution 161 9.14 Are There Any Anomalous Effects in the Data? 163 X 9.15 'rhe Tau Neutrino . . . . 165 9.16 Total Systemati c Errors 166 10 Summary and Conclusions 167 10.1 Results . . . . . . . . 167 10.2 Future Improvements 169 10.3 Interpretation of the Results 170 10.4 Conclusion . . . . . . . . . . 172 A Some Mathematics 173 A.1 Solving the Cova.ria.nt Integral Io:;3 173 A.2 Ca.lcula.ting the Limits of Integration 174 B Muon Fake Rates 176 C The Spin Sensitive Variable w 179 D SVD Development 181 D.1 Silicon Vertex Detector Mechanical Assembly 183 D ·) The CLEO II.5 SVD Data. Acquisition 184 D.2.1 SCI Crates . 187 D.3 Schema.tics . . . . . 190 D.4 Printed Circuit Boards 197 Bibliography 198 Xl List of Figures 2.1 Lowest order radiative corrections . 24 2.2 Dalitz plots for the three body final state. 26 2.3 90% C.L. limits on couplings in the fl sector. 35 2.4 90% C.L. limits on couplings in the T sector. 37 2.5 Allowed region in p - r; parameter space. . . :38 3.1 A schematic view of the Cornell Electron Storage Ring, CESR. 43 3.2 A schematic view of the side view of t he CLEO II detector. 45 :3.3 A schematic end-view of the CLEO II detector. 46 3.4 The vertex detector (VD). . . . . . . . . . . . . 49 3.5 Cross section of the precision tracking layers and the vertex detector. 50 :3 .6 Main drift chamber cell structure. . . . . . . . . . . . . . 52 3.7 dE/ dx in the drift chamber versus the track momentum. 54 3.8 1/ f3 versus track momentum in the barrel time of flight counters. . 56 3.9 Cross section of the muon chamber proportional tubes . 61 3.10 Cross section of one muon chamber superlayer. 62 4.1 Reconstructed 1r 0 . 74 5.1 All potentia.l background sources. 79 5.2 TVIomentum dependence of the fake electron probability. 81 5.3 Distribution of the total shower energy associated with a track. 5.4 Effects of the shower energy requirement on the muon and hadron spectra. 83 5.5 Fake fl spectra.. 84 5.6 Energy distributions of the single highest energy unused shower in the barrel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 Xll 5.7 Energy distributions of the single highest energy unused shower in the encl cap. 88 5.8 cos a plots for the two most significant feed-clown modes. 89 5.9 ZVPTX distribution . . . . . . . . . . . . . . . . . . . . . 91 5. 10 Distributions of the visible Pt and the visible energy scaled to the beam energy.. . . . . . . 92 5.11 0min distribution. 9;3 5.12 E/p distribution of the hadronic track. 95 5.1:3 T he charged weighted polar angle di stribution. 95 6.1 The electronic and muonic branching ratios. . 100 7.1 Rest fram e scaled momentum di st ributions for different p values . 101 7.2 Rest fr ame scaled momentum distributions for different TJ values . 102 7.:3 Laboratory frame momentum spectra.. 103 7.4 Event topology. . 105 7.5 cos a distribution. 107 7.6 Pseudo res t frame spectra. 108 7.7 P seudo rest fram e spectrum for the J)p. < l.5Ge\! /c muons. 109 8.1 The electron pseudo rest frame energy spectrum. 115 8.2 The electron laboratory fram e momentum spectrum . 116 8.3 The background subtracted muon pseudo rest frame energy spectrum. 118 8.4 The background subtracted muon laboratory frarne momentum spectrun1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 8.5 The lo- error ellipses obtained on analyzing the muon mode. 121 8.6 The lo- error ellipses obtained on analyzing the muon and electron modes simultaneously. 124 9.1 Tracking p and TJ in the allowed parameter space. 126 9.2 Distribution of the trigger lines . . . . . . . . . . 128 9.:3 Momentum dependence of the trigger efficiency. 128 Xlll 9.4 Momentum dependence of the tracking component of the ELTRACK line. 1:30 9.5 Moment um dependence of the neutral component of the ELTRA CK line. 130 9.6 The electron identification efficiency measured in the data. 134 9.7 Muon ident ification efficiency measured in the dat a. . . . . 136 9.8 Muon parameter error ellipses obtained before and after the fake muon subtraction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.9 140 Error ellipses obtained before and after the fake muon subtraction in the combined mode analysis. . . . . . . . . . . . . . . . . . . . . . . . 141 9.10 Error ellipses obtained on neglecting the low momentum background subtraction. . . . . . . . 142 9.11 Another Bhabha search. 144 9.12 Error ellipses obtained on neglecting the beam energy corrections. 147 9.13 Res ults obtained as a fun ction of cos a. 148 9.14 Opt imization of the cos a constraint. 149 . 9.1.5 The energy spectrum of all unused shmvers in the lepton hemisphere . 151 9.16 Ivii chel parameters as a fun ction of t he normalization of the radiation in te :M onte Carlo samples. . . . . . . . . 152 9.17 Distribution of the polarimetric variable. 154 9.18 Pola.rimetric variable data distribution normalized to the Monte Carlo distribution . . . . . . . . . . . . . . . . . . . . 155 9.19 Distributions of the charged pion momentum. 1.56 9.20 Distribution of the 7r 0 energy. . 156 9.21 cos 0 distributions for all tracks. 159 9.22 lVIichel parameters as a function of the acceptance. 160 9.2:3 Momentum dependence of the difference between the generated and reconstructed moment um . . . . . . . . . . . . . 162 9.24 Data. set dependence of two Michel parameters. 16:3 9.25 Are the Michel parameters charge dependent? . 164 9.26 Position in the de tector and the Michel parameters. 165 XIV 10.1 Comparing results with previous measurements. 168 10.2 New 90% C.L. limits on couplings in the T sector. 170 B.1 Nlomentum dependence of DPTHMU ... 177 B.2 l\!Iomentum dependent fake muon rates .. 178 D.1 Schema.tic end (top) and side (bottom) views of the CLEO II..5 Silicon Vertex Detector. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 D.2 A schema.tic of the silicon vertex detector data. acquisition system. 185 D.3 The SCI crate. 187 D.4 The SCI Controller Boa.rd. 188 D.5 The SCI I/0 Boa.rd. 189 D.6 The SCI Controller Boa.rd schematic. 19:3 D.7 The JV-side SCI 1/0 Boa.rd schema.tic. 196 xv List of Tables 2.1 Lepton properties. 6 2.2 Quark Properties .. 6 2.3 Fundamenta.l forces .. 7 2.4 Bilinear covariants . . 9 2.5 Michel parameter predictions for different couplings .. 30 2.6 Current status of measurements of the Michel parameters. 32 3.1 Tau decay modes simulated in TA UOLA .. . . . . . . . . . 65 4.1 Luminosity break-down for the different data sets considered in this ana.lysis. . . . . . . . .. . .. . 75 5.1 Feed-clown and feed-up modes . . 85 9.1 Definition of the ELTRACE: trigger line. 129 9.2 Trigger systematic errors. 1:31 9.3 SEID efficiency a.s a function of the momentum and cos 0. . 133 9.4 Run dependent correction factors for the electron identification effic1enc1es. . . . . . . . . . . . . . . 133 9.5 Angular distribution of electrons. 134 9.6 Electron identification systematic errors . 135 9.7 Angular distribution of muons ... .. 1:37 9.8 Muon identification systematic errors. 1:38 9.9 Fake muon systematic errors. 14:3 9.10 Fake electron systematic errors . 144 9.11 Systematic error contributions from feed -clown background modes . 146 9.12 Radiation photons in the Monte Carlo samples. 150 9.1:3 Radiation systematic error. . . . . . . . . . . . . 152 XVI 9.14 Spin correlations systematic errors. . . . . . . . . . . . . . . . . . 158 9.15 Systematic errors resulting from the finite l\fonte Carlo statist ics. 161 9.16 Bin Migration systematic errors. 162 9.17 All significant sources of errors. 166 10.1 Final result s. 167 D.l Components on two boards. 197 1 Chapter 1 Introduction and Overview Elementary particle physics * is the science that studies the fundamental building blocks of matter and their interactions. The Standard Model describes the interactions between these particles , and has been extremely successful [l]. It is the starting point for any investigation of modern particle physics, and provides the fundamental hypotheses which form the framework on which many extended theories are based. Over the last twenty-five years, many tests of the Standard Model have been carried out with increasing precision, but no lasting significant discrepancy has been established. Despite the many successes, which started with the observations of neutral currents [2 , 3] in 1973, and including both the observations of the HI and zo bosons [4 , 5] in 1983, and the recent discovery of the top quark [6, 7] in 1995, there remain several basic unanswered questions: • Are the quarks , leptons , and gauge bosons truly elementary? • vVhy are there so many "elementary particles"? • Why do they have their observed pattern of masses? • \,\!hat is the origin of mass? Is it the Higgs mechanism? • What is the origin of CP violation? • \,\!hat is the "true" theory of everything? The Standard Model requires numerous input parameters obtained from experiment, and does not satisfactorily connect electroweak interactions with quantum chromodynamics or gravity. Further, the Standard Model contains known flaws , revealed at very high energy, making it an unsatisfying final theory. In spite of the fact that *The term physics is derived from the Greek word 'physis' , whi ch means t he enclevour of seeing th e essential nature of all things . 2 the Standard Model accounts for a vast array of experimental data, it is far from the "final" theory. While the ultimate goal of high energy physics is to understand the underlying principles that govern our ph_ysical universe, the immediate goals are to test the Standard Model and to probe for nevv phenomena beyond. The analysis described in this thesis addresses both these immediate goals. We present a high precision measurement of the Michel parameters p and T/ measured in leptonic decays of the tau. These parameters have been precisely measured in muon decay, and have been found to be consistent with Standard Model VV-boson exchange, i.e., with the V - A structure hypothesis. The tau lepton, with its two leptonic decays T- --+ ll-v,,.vT and T- --+ CvevT , gives us a unique opportunity to study the universality of the charged leptonic weak interaction. Are these two decay modes just duplicates of the muon decay modeµ- --+ e-Vell 7 , governed by the same type of weak interaction, i.e., ii -A? The current precision of experimental measurements of the Michel parameters in the tau sector are an order of magnitude weaker than corresponding measurements in the muon sector, where, in spite of the good experimental precision reached, an overall ana.lysis with all possible weak couplings leaves much room for decay contributions in addition to those from the standard Hi boson. The higher tau mass makes leptonic tau decays ( compared to muon decay) more sensitive to physics beyond the Standard l\/Iodel. Scalar couplings, induced by charged Higgs bosons, for example, would be proportional to the mass of the charged lepton, and thus this effect would show up in the muonic decay of the tau lepton with a factor ~ 10 7 larger than in the electronic decay of the muon! The much higher mass of the tau lepton is therefore a strong motivation to search for deviations of the Michel parameters from their V - A predictions in tau decays. The thesis is organized in chapters and appendices as follovvs: 'vVe begin in Chapter 2 with a brief overview of the current understanding of the Standard Model of particle physics. This chapter concentrates on the physics of tau leptons at electron-positron colliders in general, and on their vveak decays in particular. The Michel parameters, the focus of this thesis, are discussed here in 3 detail. Chapter 3 describes the measurement device and experimental setup. i. e., the CLEO II detector at the CESR e+C collider. This chapter also contains a brief overview of the Monte Carlo simulations consi sting of the event generat ion and t he detector simulation processes. CESR is constantly upgraded to achieve higher luminosities, and the detector is periodically upgraded both to handle this increased luminosity, and to improve its detection capabilities . The collaboration installed a. silicon vertex microstrip detector in the fall of 1995. The author has worked on the mechanical support system for this device, as well as the new data acquisition system required for it. Details of this work are outlined in Appendix D. Chapter 4 describes the event reconstruction procedure. We li st the selection cri teria. used to obtain the event samples used in the analysis , and then proceed to describe in some detail some of the more interesting/unusual requirements. Chapter 5 describes in some detail all the potentia.l sources of background s. Each of the significant background sources is minimized using several specia.l cuts and the surviving backgrounds are well understood. The two event samples used to measure the Michel parameters can also be used to measure the two leptoni c branching ratios of the tau lepton. Chapter 6 describes t he results obtained for B(T----+ C v el/7 ) and B(T----+ µ-v µVr ). No attempt is ma.de to minimize the systematic errors since these branching ratios have already been well measured at CLEO [8]. Chapter 7 describes the special reference frame utilized in this thesis to achieve maximum sensitivity to the Michel parameters st udied. This "pseudo" rest frame technique, fir st pioneered by t he ARGUS Collaboration [9] is essential in t he 17 measurements. Chapter 8 discusses the fit procedure employed to obtain the measurements of the Michel para.meters. It also includes all the res ult s obtained using this fit procedure. Chapter 9 describes in great detail the work clone to ens ure that all t he systematic errors were minimized and well understood. This work was important to achieve t he level of precision desired in this analysis . 4 Chapter 10 summarizes the work presented 111 this document , and discusses its significance. Future improvements on the results presented here are briefly described. Four appendices to this thesis are attached. Some of the mathematical integrals used in Chapter 2 are detail ed in Appendix A.l. Appendix B describes in detail the determination of muon fake rates in the muon chambers in the CLEO II detector. This study is performed using the data, and its results are used to calibrate the fake rates in the Monte Carlo genera.tor. A precise knowledge of these fake rates is essential to obtain the level of precision achieved in this thesis. Appendix C defines the spin sensitive variable w, used to test the Monte Carlo simulation of the spin-spin correlations that exist between the two T leptons in e+e----+ ,+,-. Appendix D describes the author 's involvement in hardware projects which primarily revolved a.round the new silicon vertex detector. The analysis presented here does not include any data collected after the installation of this new detector component. 5 Chapter 2 The Standard Model of Particle Physics The Standard Model of particle physics describes our knowledge of what composes the material universe, and what interactions occur among these constituents. This chapter fir st gives a bri ef overview of the elementary particles and their interactions , followed by a brief description of the formalism of the Standard Model. It then concentrates on the T lepton and its interactions and defines the Mi chel parameters, the focu s of this thesis . 2 .1 Elementary Particles In our current understanding , matter everywhere is composed of only a fev-1 fund amental building blocks: six kinds of leptons and six kinds of quarks. These spin 1/2 fermions are considered funda.m enta.l for two reasons. They and their antiparticles make up all matter, and ea.ch of these fermions is no t decomposable . At the current experimental level of 10- 16 m, no compositeness has been observed. Bot h leptons and quarks a.re smaller than this level, and are many orders of magnit ude smaller than the a.tom (approximately 10- 10 111). The best known lepton is the electron ( C) , the negatively charged particle found in the outermost portion of all atoms. There also exist two heavier versions of the electron : the muon (/L-) and the tau (,-). Aside from their larger masses (so that they can decay into lighter particles ), t hese two leptons are identical in many respects to the electron. Ea.ch of the three leptons is associated with a massless neutral particle (three more leptons) called the neutrino (11e , 11, 1, ll r )- The tau-neutrino llr is the onl y lepton which has not yet been directly observed experimentally. The six leptons are grouped into three doublets, or generations , a.s shown in Table 2.1, where we li st some 6 of the properties of the various leptons. Lepton Charge (e) Mass (MeV/c 2 ) Lifetime (sec ) -1 0 -1 0 -1 0 0.511 < 15 X 10- 6 stable ( > 4.:3 x l 023 years) stable 2.197 X 10- 6 stable (291.0 ± 1.5) X 10- 15 stable e fl /Jp. T 105.7 < 0.17 1777.0 ± 0.3 < 2"1 Table 2.1: Properties of the six leptons. For the neutrino masses, the current 90% confidence level upper limits from experiment are listed . The different generations are enclosed by the double lines. The six quarks can also be grouped into three generations with progressively larger mass as shown in Table 2.2, where we li st some of the quark properties . The v and cl quarks are the constituents of the proton and neutron in the nuclei of atoms. Quark Charge (e) Mass (Ge\! /c 2 ) cl - 1/3 2/3 -1/3 2/3 -1/3 2/:3 ~ 0.004 ~ 0.007 ~ 0.3 ~ 1.3 Zl s C b t ~ 4.8 ~ 174 ]3 s C B T -1 /2 +1/2 0 0 0 0 0 0 -1 0 0 0 0 0 0 +1 0 0 0 0 0 0 -1 0 0 0 0 0 0 +1 Table 2.2: Properties of the six quarks. The symbol 13 denotes the third component of isospin; S, C, B, and T denote strangeness, cha.rm, bottom (or beauty), and top (or truth) respectively. The quark masses are all model dependent. The double lines enclose the different generations. I 7 2.2 Fundamental Forces The interactions between all matter a.re governed by four fundam ental forces : the strong, electromagnetic, weak and gravitational forces. These forces a.re all mediated by the gauge bosons. The different kinds of interactions , their media.tors, and some of their properties a.re listed in Table 2.3. Force Relative Strength Range (m) Boson Strong Electromagnetic Weak 1 10- 2 10-13 < 10-1-5 00 gluon (g) photon (, ) < 10-18 w± Gravitational 10-38 zo 00 graviton ( G) Charge (e) Spin Mass (Ge\! /c 2 ) 0 0 ±1 0 0 l 1 1 1 2 0 0 80 .2 91.2 0 Table 2.3: The four fundam ental forces and their media.tors. The forces a.re listed in ord er of decreasing strengths; the li sted strengths a.re evaluated a.t a di stance scale of 10- 1 5 m and serve onl y a.s a. rough comparison. Gluons mediate the strong interactions between any two quarks, photons carry the electromagnetic forc e between any two quarks or charged leptons, the l;l/ ± and zo boson s mediate t he weak interactions within one and between two families of fermions, and finally the graviton carri es the gravitational forc e between any two particles with mass. The gravitational forc e is far too weak to be detected at the level of particle mass scales. The photons and t he H/ ±, zo bosons have been experimen tally observed. .Jet structure in certain ha.droni c events ( e+ C ---+ qqg) [10] provides indirect evi dence for the existence of gluons. The photon s and gluons a.re stable, and the massive Ml and Z bosons decay into lighter particles in approximately 10- 27 s. Gravitons a.re no t observable at experimentally achievable energies. 8 2.3 Weak Interactions and the (V - A) Theory Although all hadrons a.nd leptons pa.rticipa.te in wea.k interactions , these interactions can only be observed in circumstances vvhere the much fast er strong or electromagnetic decays a.re forbidden by conservation laws. The lifetimes for wea.k decays with energy << mw, mz depend on the phase-space factors , as well as the weak coupli ng constant G F, but a.re long compared with typical lifetimes for the electromagnetic decays ( ~ 10- 19 s) or strong decays (~ 10- 23 s). The weak cross sections are correspondingly small. \iVea.k forces are produced by the "weak charge"; electric charge produces the electromagnetic forces and color produces the strong forces. All quarks and leptons are carriers of this weak charge. Leptons have no color and thus cannot participate in st rong interactions. The electrically neutral neutrinos cannot participate in electromagnetic decays either, thus ma.king them unique . There are two kinds of weak interactions: elect rically charged (mediated by the l1V± bosons ) and electrically neutral (mediated by the zo boson). Both the leptonic decay s of the tau lepton st udi ed in this thesis T- --+ c- v e 1J, , where C is ei ther the muon or the electron, a.re examples of the charged weak interact ion. 'vVeak interactions were first observed in the slow process of nuclear ,8-deca.y, or, in terms of quark constituents , d--+ u + e- + v, . This example of the charged weak interaction is mediated by the exchange of a virtual J;l/ ± boson, but since the momentum transfer involved is sma.11, i.e., q2 << rniv , the interaction is effectively point-like and can be described by the four-fermion coupling G = g2/m?v, the Fermi constant* . Fermi first postulated this contact interaction in *y characterizes th e coup ling strength of the fe rmionic current to the H' boson. 9 193-5, and developed his theory of ,8-decay in analogy with the theory of electromag- netic decays. He suggested the matrix element: ea k ] w eak G' [ L; G7' ]w baryon le))ton = 7 1, 'p!\i. '11-'n l e2 in analogy with J\,1 ex: 2q ( 2.1) Jb a1"1Jon ft epton • . The coupling constant G replaces e 2/ q2 . Since weak currents are assumed to interact at a point , the propagator of the exchanged photon in electromagnetic interactions , 1/ q2 is replaced by 1/ ( miv - q2 ), and since q2 ~ mi1 at low energies characteristic of tau decays , it plays no role. Fermi's choice of a vector-vector form of the weak amplitude Jvl was satisfactory (prior to the discovery of parity violation in 1956) in describing nuclear ,8-decay, but a priori, there is no reason to use only vectors. The Lorentz invariant amplitude Jvl can be constructed using all other possible bilinear covariants li sted in Table 2.4. The matrix element can now be written as : C, [J,p 011/'n] [{ e0 14'u ] , (2.2) i=S,V.T ,P,A where C; a.re the appropriate coefficients. The different forms for the opera.tor 0 , a.re named according to the transformation properties of the weak currents under rotations and space inversions: scalar (S), vector (V), tensor (T) , pseudoscala.r (P) , and axial vector (A) . 0 ,. Scalar Vector Tensor Axial vector Pseudoscalar Parity No. of components 4,4, 1h·//. 1/• 1/>cr,w 1/ > 1/ '"(5 , ·//. 1/> 1L•-y5 1j, 1 4 6 4 1 + (Space) (Space) Table 2.4: Exhaustive list of possible bilinear quantities with definite properties under Lorentz transformations. 10 After a careful analysis of nuclear /3 decay, p decay, a.nd parity violation , Fermi arri ved at the conclusion that the decay was dominated by ( V -A) interactions. Using lepton uni versality, T decays mu st be dominated by ( 1· - A) al so. In this thesis , we search for small deviations from this ( V - A ) theory. 2.4 The Tau Lepton The tau is the third heavy lepton. Today, many of the properties of the t a.u lepton a.re precisely known [11 , 12]. In thi s section , we present a brief account of the discovery of thi s particle, follow ed by a.n account of its production m echani sm , vvith an emphasi s on its production in e+ e- annihilation. Finally, a bri ef summary of the t heorv of leptoni c tau decays is presented. 2.4.1 The Discovery of the Tau Lepton The possibility of a third , heavier, sequential lepton was investi gated in detail by Y. S. Tsai [13] in 1971. He predi cted decay correlations and branching fractions de- pendent on t he lepton 's mass . The fir st experimental confirmation of its exi stence took place in 197.S in annihilations of e+e- into tau pairs. These observat ions were ma.de by M. L. Perl et al. [1 4] using the Mark I detector a.t the SP E AR storage ring at the Stanford Linear Accelerator Center (SLAC). They observed 24 events cont ainin g an electron and a muon , and no other visible charged or neutral par ticles . The a.copl anar tracks did no t fulfill energy and moment um conservation requirements, im pl ying the presence of undetected part icles in the event . T he li st of possibl e candidates for the undetec ted part icles is compri sed of charged particles or photons that escaped the 2.6 1r steradi an accept ance, and particles no t easil y detectable like neutrinos, J\'f meson s a nd neutron s. The Dali tz di stributions for these events did no t exhibit an y significant structure at a particular mi ssing mass value, impl ying that there were at lea.st t wo mi ssing particles in ea.ch event. T hi s suggested that the particles were not the charged particles or photons that escaped detection. 11 To interpret this observation, MARI~ I ha.cl to collect more data. The next analysis [1.5] included 105 such events . The almost collinear angle between the two tracks suggested that t he origin must be from the production of a pair of nevv particles, and the inclusi ve moment um spectrum indi cated that each of these new part icles decayed into a.t lea.st three bodi es . Systemat ic elimination of other possibilities suggested that the undetected particles were neutrinos. Finally, t he observed p{·oduction cross section suggested that the mass of the heavy particle was in the range 1.6 to 2.0 Ge V / c2 . All these observations were consistent with t he creation of a pair of heavy leptons (later named the T) , each of which decayed into a charged lepton and two neutrinos: T ----+ ( JJ D, where C was either an electron or a. muon. A follo wing experiment [16] confirmed that the production occurred below the threshold for open charm meson production, thus eliminating any possibility that these new observations were associated with purely leptoni c decays of the charm quark. Today, many of t he properties of the tau lepton are precisely known , and· are summari zed in t he following sections. They are consistent wit h the Standard Model CV - A) interaction t heory, but permit small departures, wh ich are t he subj ect of this t hesis. 12 2.4.2 Tau Production This subsection describes the different way s tau leptons can be created. The leptoni c tau decays, analyzed in this thesis, utili ze tau pairs produ ced in e+e- annihilations obser ved by the CLEO II detector. Tau leptons can also be produ ced in photoproduction and electroprodu ction reactions, in pz3 collisions, in t he decay of heavy quarks, and in interactions such as V r + N ---+ T + N '. e+C Annihilation e 't The squ ared matrix element for the process e+c ---+ ,+, - is given by: e4 -L/11/LT q4 e 1w ' where t he two leptonic tensors a.re given by: and L:v ( 2.:3) where p 1 , p2 , p3 a.nd p4 represent the four-v ectors of the e- , e+, , - a.n cl ,+ respecti vely. low , averaging over t he ini t ial elect ron and positron spins, and summing over t he 13 final tau spins, we get: l 2 Tr [(p2 - m) ,"' (P1 + m) ,v] l 2 Tr [(p4 - hf);,, (/J3 + Af) 1·v] (2.4) where rn is the mass of the electron and positron, and JI!! is the mass of the tau leptons. Neglecting the masses of the electron and positron , and using the trace relation: (2.5) the Jeptonic tensor L~v simpli fies to: (2.6) Next , using the fact that the trace of an odd number of gamma ma.trices vanishes , and that Tr (%1'u) = 4 g p.v, in addition to the above trace relation , the other leptonic tensor L :v simplifies to: (2.7) Thus, 4 (IMl 2) = 8 e4 [( P2 • p,!)(p1 • p3) + (P2 • p3 )(p1 • p4) + (p2 • JJ1)AI 2] . (2.8) CJ Now , assummg that the electron and the positron have energy E, and that their momenta are parallel to the +z and - :: axis respectively, t he four- vectors for the electron and positron are: Pl = ( E , 0, 0, JJ) P2 = ( E , 0, 0, -jJ) , (2.9) 14 and the four-vectors for the produced ta.us are: (2.10) In terms of the polar angle f) and azimuth angle ¢, IPI sin 0 sin ¢ , Pv IPI cos 0 . and A (2.11) Now , defining /3 = lfl /E, and using s = q2 = (JJi + P 2 ) 2 = 4E2 , we get: (p1 • p3) = is (1 - fJ cos 0) (JJ1 • p,i) = =i-" ( 1 + fJcos 0) s - and (!Ji· p2 ) 2 (2.12) Substituting the result s ob tained in Equation 2.12 into Equ ation 2.8, we get: The differential cross section is given by: cla- 1 2 elf!= F (IA11 )clLips, (2.1 4 ) where th e f-lux , F = 4p1 fa= 4p 2 fa , and the two body phase space, clL-ips = ~ JJ~cm . 47r~ 4 v s (2.1 5 ) Thus , in e+e- annihilat ion, tau pairs are produced with a different ial cross section , claclO ·) o: - - _ • (3 • (2 4 :::i · 2 /3 2 sm 0) , (2.16) 15 where 0 is t he angle between the T+ and e+, p 3/ p 1 = /3 = v / c is the tau velocity, and o = e 2 / 271 is the fin e structure constant. The integrated cross section can now be expressed as : + - o-o( e e ........, T + T 2 ) 2 471 0 3 - /3 = - - . /3 · - - 3s 2 (2.17) At high center of mass energies, where /3 = l , the integrated cross section simplifies to: + _ _+ __ 4710 2 _ 86.86 nb Ge\/ o-o ( e e . . . . , , T ) - -- _ 3s 2 ------ s (2 .1 8) with o = 1/137.036 and (n.c)2 = 389386 nb GeV 2 . Photoproduction and Electroproduction Tau pairs can be produ ced in t he following photoproduction [1 7] and electroprod uction reactions: (2.19) where N is th e target proton or nucleus, and N ' represents the final hadroni c state. Particle Decays to T and IJr These particle decay modes incl ude the decays of the heavy l;\/ and Z bosons, as well as t he semi-leptoni c decays of t he heavy band c quarks. l1V decays: the decay modes, H'+ . . . . , T+ + /J r and 1v- . . . . , T- + vr , have been observed by the UAl [1 8], UA2 [1 9], and CDF [20] experiments. Aside fro m being used to identify the l;\/ bosons [21], these decays are used to st ud y the TY T IJ, vertex 16 at Js = m w. Using the ratio of the branching fractions of the leptonic decays, B(T+' - - T-V , ) B(W----+ Cve ) ' (2.20) the ratio of the charged current couplings gr/ge can be deduced , and used as a test of universality. The average of the three m easurements mentioned above is: Jg,/ ge = 1.00 ± 0.04 , in agreement with Standard Model expectations. The width for z 0 decay into lepton pairs is given by: (2.21) where n(rn z ) '.: : :'. 1/127 is the QED fin e structure constant evaluated at the Z 0 mass, -1 + 4 sin 2 0i,v Ll sin 01v cos 0w ' V/' = - - - - - - and -1 Cl f = . 4 Sll1 0M: COS 0w ' (mw) = 0.23:3 ± 0.001 ·m.z 2 Sill- 01+· • ? = 1- where rnw and rn, z a.re the masses of the f;l/ ± and zo bosons respectively. The uni versality of the lepton coupling impli es equality of the partial widths for the decay of the zo to e+ C, fl+ fl- and r+r- pairs. Further, t he Standard Model predicts that the T 's from the decay of the zo ---+ r+ T- a.re polari zed as a direct consequence of parity violations in the weak neutral current. Pure leptonic decays of the D± and D;- , (2.22) 17 where f is the T lepton, have not been observed . These modes have a decay wid th given by: (2.23) where .fo,D, are the weak decay constants of the D and Ds, and take into account the strong interaction dynamics of eel and cs annihilation insid e the meson. Theory estimates their size to be 150 to 250 Me V , but they must be measured thro ugh these decay processes . The rn ~ term lea.els to the tau mode having larger rate than t he electron and m uon modes, and thus the decay to the tau mode provides the best way to measure the weak decay constants . The theory of leptonic decays of the B mesons , (2.24) is analogous to that for D decays (see Equation 2.23) , but the smaller values of , ~,b and , ,,~b supp ress the decay widths. Tau Production in Hadron Collisions Taus can be produced in p + N Collisions , the largest contribu tion to the rate is expected to be from the decay mode Ds ---+ T + V7 , where the Ds is created in the reaction: p + N ---+ Ds + ... , (2.25) and N is a nucleon or a nucleus. These collisions can be from an external proton beam on a fixed target or from a circu lating proton beam on a gas jet target . Tau leptons can also be produced in a proton-proton collider (pfj ---+ T;T/ -x) , where t he produced HI boson subsequently decays in to the tau lepton. 18 Heavy ion collisions [22, 23] can also result in the production of tau pairs: the virtual photons emitted in the colli sion of a pair of heavy ions can produce a T+T- pair ·when the ions a.re at energies mu ch greater than the ta.u mass . Neutrino production Tau leptons can be produced in a new generation of accelerator experiments searching for neutrino oscillations, first sugges ted [24] many yea.rs back in a.na.logy with the oscillations of neutral 1{ 0 mesons. Th e CHORUS a.nd NO!VIAD experiments were con ceived to detect the appearance of th e ta.u neutrino in a. rat her pure CERN muon neutrino beam following the hypotheti cal fl avor oscillation phenomenon. The charged current interac tion , res ul ts in t he produ ct ion of the t au lepton when t he neut rino energy is suffi cient ly a.hove t he tau produ ction t hreshold. Other experiments , such a.s the short baseline E-80:3 and th e MI NOS long baseline neutrino oscillation experiments a.t F N AL , also hope to observe neutrino osci llations by observing the t a.u lepton produced when t he tau neut rino interacts. Th e reaction shown in Equat ion 2.27 ( a.nd related reactions ) can help determine the overall Lorentz struct ure ; see Section 2.6 for details. 19 2.4.3 Theory of Tau Decays The decay of the charged tau lepton probes the weak charged current sector at a mass scale characterized by the mass of the tau m 7 .. while the produ ct ion of T+Tpa.irs at e+ e- colliders probes the neu tral current sector at the higher energy scale characteri zed by m z . The leptonic decays of the charged tau lepton to a lighter charged lepton C ( C = e, p) are purely weak in nature, and the Standard Model (V-A) four fermion coupling scheme, described in Section 2.3 , can be used for the calculation of the leptoni c tau decay, where p,, Pe, p 1 , P2 are the four-mom entum of the tau , daughter charged lepton. 17c and // 7 respectively, and S 7 , St, s 1 , and s 2 are their polarization four-vectors. e 't Pr = Pv + Pv + Pc and q = Pr - Pv = Pc + Pu Using t he Feynman rules in the (V - A) theory. the matrix elem ent is given by: - iJ\,1 Since , max q2 = m~ = 4.8 x 10- 4 mf,i• « m?1, , t he H/ boson propagator can be taken 20 to the q2 ---, 0 limit , i gµv / m?1r , leading to: (2 .29) 4 g Now, 4 64 m ,i,v L'w Jl1µ.v ' [un 1' ( 1 - ,'5 )uT] [uT '°(' ( 1 - , 5 )u 2] where Lµv -Tr [P2 1 11 (PT - mr:frl,v (1 - , 5 )] -P2o(PT - mTsT) ;3Tr [, 0 1 /1 , f3 , ,v ( 1 - , •5 l] [·un/1 (1 - y 5 )v1] [fi11'v (1 - , 5 )ut] and Nl1w -Tr [(pc - rne:fe )1µ P11'v (1 - 1 5 )] - (pc - m.ese)°"pfTr hcr1'1, 10/v (l - , 5 )] (2.:30) Thus, substit uting for the lepton ic tensors Lµ,, and lv11,.v, and using the trace relations : (2 .31) Equation 2.30 can be written as: g4 - cl mw ])2 • (pc - m esc) P1 ' (pT - rnTsT) 32 G} ])2 • (pl' - rn.esc) ])1 • (Pr - mTsT) , ,·) = g 4/(3'>~rri.w 4 ) •ts use cl . wl1ere G'P The differential transition probability is given by: df l -') - ~rnT :32 G} P2 • (Pt - ·1n esc) P1 • (p, - mrsr) cl 3 p1 (21r)32E1 (2.32) 21 Integrat ing over the neutrinos, (2.:34) with the covariant integral (2.35) Using the result obtained in Appendix A.l, the differential transition probability can be written as: elf In the rest frame of the parent tau lepton, the four-mom entum vectors p, = (rn, , 0), Pc = (Ee, P e), q = (m, - Ee, -pt) , and t he four-spin vector .s, = (0, s, ), where s is a unit vector den oting the three-spin in the tau rest frame. The daughter charged le pton 's four-spin can be calculated using a Lorentz transformation to a new fram e in which the lepton has a three-momentum P e, and p,, . s,, .Seo 'l rl C , Sc St • Pc • se rnc(Et +m t ) + - - - - - pe Making appropriate substitutions iu Equation 2.36 , the different ial decay width: elf 2 d3 1i G F •Pt { 2 ') 2 -: .:..11 )( )".) -n,., E·•c (mr + E7• - 2mrEe - Pc ) 3 [(Ee - Pt • s e )mr + m,(p c - m esc - fracpc • s c Ee+ m ePt ) ·Sr] Pc • sc , [( Ec - Pt · s c )(mr - Ee)+ (p c - ni cse - - - - p r ) · Sr] Ee + m,, • } • (2.:38) 22 Neglecting the daughter lepton's mass m e m the first approxiniation , Pt = E e 11 , where 11 is a unit vector in the direction of the charged daughter lepton's motion in the tau rest frame. N mv, i3 c2 PEe {(rn;-2m,Ee)[Etm,(1-11 ·St) +1nrEc 11 -sr(l-11 -st )] 327r)·mr' c elf ;('TF5 l +2(rn; - mrEc - rn.rl1 • Sr) [Ee(l - 1.1 • Sc )(mr - Ee)+ Ez(l - 11 . Sc l] /3 GT,2 3(~7r)· mr e ,2 7r G Tp 2 . ') . clOepe clEe Eern 7 ( 1 - 11 ·Se) [(3rnr - 4Ee) + (mr - 4Ee)11 ·Sr] . 5 F c Pe ·) -:--1r 95 - E m;Ee(l - 11 • se ) (3mr - 4Ee ) + (mr - 4Ee )11 • Sr A A [ A A ] A 3( ~7r) rnr (2.39) The maximum va.lues for the charged daughter lepton's energy and momentum are obtained when the two neutrinos are emitted in one direction , and the lepton e is emitted in the opposite direction: (2.40) and For mt = 0, the maximum lepton energy E e,ma,r = mr/2 , and defining E = Ee/ Ee,ma,r , the entire lepton 's energy range is spanned by the interva.l O < E < 1. Now, E e = E mr/2, and choosing the tau spin a.xis along the 11 • Sr +.: direction in polar coordinates, = cos 0. The differential decay rate can now be written as: f G}m·~[-- 2 ·. -][ l-2s e][l-11-s" ]/-sin0cl0cl¢ . .) 3 2c ( 3 - 2c ) 1 + _ ') c COS ·) Cc , l 9 ~1r ~ 41r 3 ~._ (2.41) where n(s) = 2s 2(:3 - 2t) is the normalized lepton energy spectrum vvith an energy dependence corresponding to a l\!Iichel parameter [25] p = 3/4. Since we do not measure any spins in this analysis, and since the net tau polarization at CLEO is zero, we can sum over the daughter lepton spin and average over the tau spin, to obtain: r•2 elf .s up1n, [2t 2 (:3 - 2t )] cit . 19271" 3 (2.42) 23 The final integrat ion over the charged lepton momentum yields: (2.43) For ,- --+ p-v,1 11r , the lepton mass rn,, cannot be neglected and (2.44) The phase space factor [13], F(x) = 0.9726 for muons. Another factor F(rnv)rn.7 ), of the same functional form as F( x), would apply in case of a. heavy tau neutrino in , --+ 11 ev; for , --+ 11pv the factor is more comp li cated if both 11r a.ncl up are considered heavy. Since ni(11e ) « rn.(117 ), the present limit on the tau neutrino mass, ni(u,) < 24 Me\! implies that 1 - F(nlv)m.r) < 1.5 x 10- 3 _ 1 The non-local structure of the HI propagator results in an additional multiplicative correction factor [26] given by: :3 rn: ) Fw = ( l + ~-2-' o rnw ~ 1.0003 . (2.45) The QED radiative corrections to first order to this decay width a.re given by the multiplicative factor: Frac1 a( mr) = .l - - ( r. 2 - -25• ) , 21r 4 (2.46) and a.re calcu lated [27 , 28] assuming t he ( V - A) theory as a. starting point. The diagrams which contribute to order a a.re shown in Figure 2.1. Radiative decays or bremsstrahlung ( cl , e) is very important for the low energy part of the spectrum, while the virtual photon diagrams (a , b, c) are relatively more important at higher energies. The numerical values above a.re calculated using world average results [29] for all particle masses. The running coupling constant of QED [28] at the , mass is a( mr) = 1/13:3.29 incorporating virtua.l photon corrections a.s well a.s the emission of 24 v, (a) (b) (c) e v, (c) (d) Figure 2.1: Lowest order radiati ve corrections. real photons and light fermion pairs . T he differential transition probability can also be writ ten in terms of the Dalit z [:30] plot vari ables E e and E1 = E 11e as: dI' = ~ IJvt l clP 83 ' 2 1,/.T where clPS'3 = ~ d EedE1 , and :32r.· IM 2 = M G}(Pr • P1 )(p2 • J)c) . 1 (2 .47) In the tau rest fram e, mrE1 , Pz • Pe 1 2 2 2 2 . (1nr + rn 1 - m 2 - m e - 2m,E1 ) , 2 and assun1ing m 1 = m2 = m e = 0, (2. 48 ) 25 a para.bola. in E 1 with zeros at E 1 = 0 and E 1 = Ei110'" = 1nr/2. Defining E = E/ Ema 1 •. where Ep101 • = Et 01• = mr/2, the differential decay rate: (2.49) and the decay rate: (2. 50) where the li1i.1its of integration are calculated in Appendix A.2. Now , performing the integration over the anti-neutrino scaled energy s 1 , we get: c/ f = G2 .s 1 'Fmr clEl' - E 2 (3 - 2 Et ) 3 1671" 6 e • ' (2.51) which is the famous p = 3/4 Michel spectrum for the Standard Model (\/ - A) coupling. If the coupling were ( V + A) instead of ( V - fl), the matrix element in Equation 2.47 would be replaced by: (2.52) which results in a para.bola in Ee instead on E 1 , as found before. The corresponding differential decay rate can be written as: (2.53) and the integration over E 1 results in: (2 .54) which corresponds to the p = 0, ( V + A) spectrum. Figure 2.2 shows plots in the EfETie plane for both th e ( V - A) (l eft) and the 26 (V + A) couplings. The non-uniformity in the plot is directly proportional to IMl 2 . (V -A) (V + A) Figure 2.2: Dalitz plots for the three body final state T- --+ c --,;l' 11T assuming the (V - A) (left ) a.nd the (\/+ A) (right) interaction. The final integration over the lepton Csea.led energy in both Equation 2.51 ( V -A) a.nd Equation 2.54 ( V + A) results in the same decay rate obtained earli er in this sect ion (Equation 2.43) independent of the type of coupling considered: (2.55) 2.5 Michel Parameters Instead of the Sta.nda.rd Model matrix element in Equation 2.29 , one can use a more general matrix element for the decay T- --+ e- v l' 11T: j v{ where the O; a.re the usual Dirac matrices shown in Table 2.4 , and the index i runs through 8, V, T, A a.nd P. The 10 complex coupling constants (20 real parameters ) C; 27 and C[ must be determined by experiment . However , the overall phase is arbitrary, and so 19 real para.meters remain to be determined . The matrix element in Equation 2.56 can now be written in the helicity projection form as: M (2 .57) i = S . V.T ,\1,>- r=R .L vvhere i labels the type of interaction: scalar, vector, tensor, and Ac, ,\, = R, L indi cate a right- or left- handed chirality of the daughter lepton and the parent tau respectively. The corresponding 10 complex parameters t g\ 1 ,\r a.re linearly related to the C'; and C[ parameters in Equation 2.56, and are to be determined by experiments . The differential transition probability summed over the fina.l charged lepton espin for the decay of the tau is now found to be: G}m~ [ . l+h(x) ( ·L"'( :t - .l ) + -4 p ( ti:r ' - 6 ) + .-.~417 . m c(l:t)) . -1927r 3 1 + 417(rne/rn,) :3 17?.r x 4 , ex g(x)) ] sin0cl0dcp 2 +t cos 0 ( 4(1 - :r) + :--8(ti:r: - 6) + - - - - - - x ch 2 3 21r :t 41r (2.58) where :r = Ee/ Ema,, is the sea.led lepton energy in the T rest frame. The maximum kinematically allowed energy in the Trest frame is given by Ema:i- = (m; + mz)/2mT. The angle between the tau spin direction and the charged daughter lepton is denoted by 0, and h(x) and g(x) a.re radiative corrections to O( cx/1r). The Michel parameters [25, 31] denoted by p, 17, t and 8 are combinations of the complex coupling constants g\ 1 _\ T (or Ci and Cf) a.s shown later. The terms in p and 8 give zero when integrated over the whole spectrum and these quantities characterize the shape of the isotropic and anisotropic spectra. at the highenergy encl. The 17 parameter characterizes the low-encl of the isotropic spectrum. The terms in t average out for unpolari zed taus. tThe giR and gIL coup lings are not lin early independent of th e other coupling constants a.nd a re exclud ed. 28 The Michel parameters can be written as: p l- ~ [1grR1 2+ 2 1g~L 1 + 21grR1 2 2 + 21ghLl + R (gzRgrR + 97'1L97~r)] 4:~ [2ICA 12+21c:41 2+ 2ICv 12 + 21c~ 12 + 4R( c ,~Cv + c:;c{,) 2 2 2 +ICPl + 1c~1 + ICs l + 1c~1 2] ' Tl !R( 6giR9[R + 6g½L9hr, + 97'1R9li + 97'1L9YR + 9iR9~L + 9iL91R) ') ~ R( c;,c.4 - t '> 5 1 2l4i [1 9RR c;;c~ + C5Cv - c~~c~.) , I9LL ', 12 + I9LR 5 12 ', 12+ 4 (1 9RR V 12 V 12 V 2 V 2) - I9rn - l9LL + 3lgRLI - 3l9LRI -20 (lgL/ - l9hLi2) + 16 R (g¾Lgj[i - 9LRSg;,1)] ! [R( C;,c~ + lb : [ (19hRl -4 (l9hLl CsC~) -4R(C;c:4 + CtC\,) + 8R(C_ ~c~. + CtC~)] ' 2 2 2 2 + l9ZRl - lghLi2) + 4 (19~Rl - l9YLi2) - l9iLl - l9[Ri2) + 4 R (9hL9RI - 9LRSg;,~)] 2 2~ [R( c;,c~ + c .;c~) + 2R( c;1c:4 + c;.c{. J + 2R( c ,~c\. + etc~ l] , with a.nd B IC:s1 2 + 1c~1 2+ ICPl 2 + 1c~1 2 + 4ICv 12 + 4IC{,12 + 4IC' A 12 +4IC:4 12 +6ICrl 2 + 6IC~l 2 • (2.,59) Redefining the coupling constant G'p a.llows one to choose the normalization pa.ram- 29 eter : A= B = 16. The Fermi Coupling constant is now given by [32]: ,2 1 3 l l (\) :J~7r' - GTp - - Tf -.- (2.60) l + 417 m e,/ m.c ' m 'l, where Tf is the lifetime of the mother lepton C, m e, its mass and me,, the mass of the charged daughter lepton. ry is the low energy spectrum para.meter and is important in the muonic decay of the T. Higher order corrections have been neglected here. In the Standard Model, the weak interaction proceeds via. the ( V - A) coupling, so that the only non-zero coupling constant is grL = 1 (or C.4 = Cv = 1, c:4 = C{; = -1 and all others zero ). Thus, substituting in Equation 2.59, 'Ne find the Standard Model Michel parameters a.re: 17=0 , t=-1 , t f5 = - :3 4 , and A = B = l6 . Now, substituting these values for the Michel para.meters in Equat ion 2.58, we find that this equat ion red uces to the original transition probability expression in Equation 2.41. Integrating Equation 2.58, and including the lead ing order corrections, the width can be written as: ') G2pni~", [ 1 - 8m-e2 - 8m~ 1n f m,,, m.f rn,,, 3• rn:'), ___ -T + 417 + 4AI - -T + 80" • T + ___ 19 •)~7r 3 rn;'7 mT2 m., mT m.;·7 or-; 1n ·711 - - o(mT) (1r 2 _ 25) ] 21r 4 ( 2 _61 ) where 17 is one of the Michel para.meters defined above, and l'° [ s s* s s* ·) v 1.' * ·) v v* ] '.tn 9irn.9LR + 9RR9RL - ~9LL9LR - ~9RR9RI, O" 1~ [-6gl°Lg~f - 6grLgrR + 9%R9rR + g~Lgr£ + gzRg1R + gzLg~2l (2.62) Neglecting neutrino masses and higher order terms in Equation 2.61 , we find that the 30 ratio of leptoni c branching ratios: g,, ) 2 ( [l + 477(m,,/mT )] 9e (2.63) where f( xµ ) = 0.9726 , and g,,/Ye = 1.0012 ± 0.0016 , can also be used to measure the 77 parameter. Table 2. 5 li sts other possible valu es of the Mi chel parameters. We note that t he parameter value depends on the produ ct of the couplings at the two vertices in the interaction. In thi s thesi s, we can use the available experimental information about the daughter C vertex to infer information about the T vertex . The coupling at the C vertex is known to be ( V - A) to a precision that is more than an order of magnitude better than the corresponding precision on the T vertex couplings (see Table 2.6). Coupling T X C (V - A) x (V - A) (V+A) x (V+A) V X \/ A x A (l, . -A) x (V+A) (V + A) x (V - A) V x (V-A) A x (V-A) Parameters LL RR LR RL (l'° -rA) x (V-rA) ( \/ - A) x ( l·· - A) .. . . . . + E2 ( \ / + A) X ( \/ + A ) -, J'J ) X ( ,':,-, - p) .. . + t_2 ( ,':,- ... + E2 ( 8 + p ) X ( ,5' + p) .. . + E 2 8 X 8 ... + E: 2 T X T LL p 17 3/4 3/4 3/8 :3/ 8 0 0 3/8 3/8 0 0 0 0 0 0 0 0 t -1 +l 0 0 -3 +3 -2 +2 ~ [l + C!';.2)2] 0 -1+,.2 27' 304 0 0 2E2 -1 30 4 +3 /4 3(/ -1 :3t / -! -¾(l - 2E2 ) 3/-1 3/ 4 3/4 3/4 ¾(l - 2E2 ) !R '-=-j ·) !RE/8 ' ~ 0 -1 2 E /2 - l c: 2 /16-1 - 1 + ./'E 2 tb -3/4 +:3 / Ll 0 0 0 0 -3/8 +:3/8 Table 2. 5: Mich el parameter predi ctions for different couplings . For entri es with admixtures we ass ume E « 1. The f in th e T x T admi xture term is f = + 8, +3 , -2 for LR, (LR+ RL ), RL . 31 If p = :3/4 (see Equation 2. ,5 9) , we can exclude t he mixing of right-handed and left-handed currents (g~L and glR) if there are no simultaneous sca.lar and tensor couplings. However, V + A cannot be excluded , and the pure right-handed coupling, g1R , is a.lways possible. Such interactions are expected to be mediated by a heavy right-handed HI R boson which exi sts in some simple extension s of the Standard Model and are briefl y described in Sect ion 2.7. A non-zero 77 m eas urement shows there are a.t least hvo different couplings with opposite chira.lities for the charged leptons whi ch would result in parity violation. If we now ass ume (V - A) (glL) to be dominant , then the second coupling would be a Higgs type coupling gJrn with the right-handed tau and daughter lepton (see Equation 2.59). The presence of this scalar coupling would result in an interference between the amplitude mediated by the Standard l\!Iodel l,1/ boson and t he new scalar boson. The effects of this interference would be seen in the differential decay ra.te of the leptonic tau decay and the low energy part of the momentum spectrum of the charged daughter lepton. T he change in t he low energy spect rum is parameterized by a non- zero m easurement of the 17 para.meter. Table 2.6 li st s the current stat us of m easurements of t he Michel parameters in both the muon and tau sectors. All the tau sector measurements shown here assurne lepton uni versali ty in the vector-like couplings. 32 Experiment Para.meter Value Decays 0. 732 ± 0.0:34 ± 0.020 0.751 ± 0.0:39 ± 0.027 0.794 ± 0.039 ± 0.031 0. 71 ± 0.09 ± 0.05 0.742 ± 0.027 0.0:3 ± 0.18 ± 0.12 -0.04 ± 0.15 ± 0.10 0.25 ± 0.17 ± 0.11 -0.0 1 ± 0.14 0.98 ± 0.11 ± 0.05 1.18 ± 0.1 5 ± 0.08 0.94 ± 0.21 ± 0.07 1.0:3 ± 0. :36 ± 0.05 1.03 ± 0.12 0.65 ± 0.10 ± 0.05 0.88 ± 0.11 ± 0.07 0.81 ± 0.1 4 ± 0.06 0. 84 ± 0.27 ± 0.05 0.76 ± 0.11 p Decays 0. 7518 ± 0.0026 -0.007 ± 0.01 3 1.003 ± 0.008 0.7c19 ± 0.004 Standard Model T ARGUS [3:3] ALEPH [34] 1 3 [35] SLD [:36] average [37] ARGUS [9] ALEPH [34] 1:3 [35] average [37] ARGUS [:3:3] ALEPH [34] 13 [35] SLD [36] average [37] ARGUS [33] ALEPH [:34] 1 3 [:35] SLD [:36] average [37] average [:38] average [38] average [38] average [38] p 17 ~ ~8 p 17 ~ 8 Table 2.6: Current stat us of measurements of the :tvlichel para.meters. 0.75 0 1 0.75 0.75 0 1 0.75 3:3 2.6 Helicity Basis Probabilities In order to determine the coupling constants g\ 1 \T uniquely from experimental measurements, it is convenient to introdu ce [39] the probabilities Q ,\ c,\r (A i' , Ar = R, L) for t he decay of a. Ar-handed tau into an Ac-handed daughter lepton C +. These probabilities a.re given in terms of the coupling constants by: (2.64) vvhere 6.\ 1.\T = 1 for Ae =Arand 6 ,\ e,\r = 0 for Ae -f. Ar. These probabilities a.re related to the Michel parameters p , 17, (, and 8 as shown below: (2.65) where the parameters ( (longi t udina.l polarization of the daughter lepton) , and e' (angular dependence of the longitudinal polarization) have not been measured in T decays . In the Standard l\ilodel ( = e' = l, Now, defining P1~ as the probability that a. right-handed tau lepton decays into a daughter charged lepton (, and P/4 as t he probability that the tau lepton decays into a right-handed daughter charged lepton C, we get: +The corresponding para.m eters in muon decay can be obtain ed by replacing th e r by th e µ. a nd by replacing th e daughter lepton f by th e f in this ent ire section. 34 1 - (1 - () (2.66) 2 For fl decay, where precise measurements of the polari zations of both the daughter and the parent lepton have been performed , there exist upper bounds on Q RR, Q LR and Q RL , and a lower bound on Q LL · T hese bounds imply corresponding bounds on the 8 couplings , l9nRI, l9nL I and lg2RI , where n includes S', V , and T § couplings . It is not possibl e to deduce an upper limi t for l9LLI from normal muon decay without detect ing the neutrinos. One cannot tell if s 9LL = O 9LL v , l = s or 9LL ') = ~- 9LvL O = · (2.67) A meas urement of the cross section of t he inverse muon decay 11" e- --+ f.l-Ve [40, 39] normali zed to t he (V - A) prediction can be used to resolve thi s am bigui ty. Thi s normali zed cross section S can be written as : where h is the heli city of the IJ,,., and is known very precisely from pion decay experiments: h = - l [41]. Thus S gives information about fiv e coupling constants (gIL , g¼L , 9LR , gIR , and gJm), all of whi ch couple to the left-handed 11"' The influence of four of t hese constants on S is found to be negligible with t he upper limi ts deri ved from normal muon decay. On e now obtains (2.69) § jg~R I is excluded s in ce it is not lin ea rl y ind epend ent. 3Ei which yields a lower limit for gfL , and through the normali zation requirement , one gets an upper li m it for the remaining gfL : 5 12 < 4( 1-S). I9LL (2.70) Thus t he weak interaction can be completely determined in muon decay using the no rmal and inverse decay. The present 90 % confidence level bounds on the couplings in t he muon sector a.re shown in Figure 2.3. The outer circles di splay the mathematical limits for the 9\, ,\, in the complex plane, the inner circles show the areas still allowed by experiments. For glL , which has been chosen to be real, one gets t he small line close t o glL = l. These limit s confirm that the bulk of theµ decay transition amplit udes are consistent with the Standard Model ( V - A ) type. Figure 2.:3: 90 % confidence level experimental li mi ts for the normalized fl -decay couplings ft.\, = [/\e_\ jNn, where Nn = m ax( lg~e-\, 1) = 2, l, 1/J:3 for n = S, V , T. 36 The experimental analysis in the tau lepton sector is necessarily different from the one applied to the muon sector, because of the much shorter tau lifetime. Effects of a finit e tau neutrino mass mvr on the couplings 9t.\T a.re m;,)m; [42]. With the present experimental limit of 24 Me V / c2 , any possible effect is ::; 0. 2 x 10- 3 . The polarization dependent Michel para.meters ~ and b in muon decays a.re measured using m eas urements of the decay a.symmetry of the positrons from muon decay. This a.symmetry is measured by stopping polarized muons and detecting the decay positrons as a. function of the emission angle relati ve to the muon polari zation. In tau decays a.t CESR energi es (far below the Z 0 ), it is not possible, a.t present, to prepare polari zed tau leptons, thus rendering the above mentioned analysis impossible. One can, however, get information a.bout the tau spin polarization by making use of the spin correlation of the two tau leptons [13]. These spin correlations have now been exploited by several experiments (ARGUS [33], 13 [35], and CLEO [44]) to measure the polarization dependent Michel parameters in tau decays. Another possibility is to use the polarization in production (and decay ) at the zo resonance (LEP) , enhanced when the electron beam is polarized (SLC). The Michel parameters ( and C require a. measurement of the polarization of the charged daughter lepton emitted in the tau decay. Thi s polari zation has never been m easured . In principle, this could be done for the ,- -+ p - v,,JJT decay by stopping the muons and detecting their decay products [43]. As explained earli er, one requires either the measurement of the inverse decay I/T c - -+ , - De , or the measurement of the correlations between one of the neutrinos and the fl - or ,- for the muoni c decay to di stinguish between the l i L and the gyL couplings. Neither of these meas urement s exist to-date, and thus the limits on the relevant couplings in the tau sector a.re much 'Nea.ker than th e corresponding limits in t he muon sector. 37 The present 90 % confidence level bounds on the couplings in the tau sector a.re shown in Figure 2.4. The outer circles display the mathematical limits for the g\ 1 .\ r in the complex plane, and the inner circles show the areas still allowed by experiments. Vve note that these limits are much weaker , but consistent with the corresponding limits obtained in the muon sector. s. +i ~ -~ - 9 LR +1 -1 - 1 +1 _,// -; -; -; -; -; -; -; -; -1 -; - 1 Figure 2. 4: 90 % confidence level experimental limits for the norma.lized T-d eca.y couplings r/<.\r 9'.\ 1 .\)Nn, where N 11 max(lg\\.\J) = 2, 1, 1/J:3 for n = 8, 1\ T. The Particle Data Group [37] world average results for the Michel para.meters a.re used to calculate these limits. = = In this thesis , we do not exploit the a.fore-mentioned spin correlations. Since the beams a.re unpolarized , and left- and right-handed tau leptons a.re produced in equal amounts at CLEO beam energies, there is no net polarization (in contrast to LEP, where there is net polarization at the zo pole). The cos 0 term in Equation 2.58 averages to zero, and one is sensitive only to the spectra.I shape Michel parameters , p and 17. The allowed range for the para.meters p and 17 is shown in Figure 2.5. The solid lines enclose the allowed region in parameter space; the clotted lines enclose the a.llowecl region when we assume that there are no tensor couplings. \Ne note that a 38 m easurem ent of p > 3/4 indicates the presence of tensor couplings . .0 .4 p .8 1.2 Figure 2. 5: Limits for t he Michel param eters p and T/ a.re defined by the solid lines . The clotted line encloses the allowed region in the absence of tensor couplings. The Standard Model prediction is denoted by the dot. The a.symmetry para.meters ~ and 15 a.re not measured in this thesis. These para.meters can be measured at CLEO by exploiting the correlations between the spins of the two ta.u leptons. T he decay of one tau in the event is used as a spin analyzer, from which one can infer information on the spin direction of the other tau. The details of thi s CLEO analysis to m eas ure the a.symmetry parameters a.re di scussed in reference [44]. :39 2.7 Beyond the Standard Model The st udy of the tau lepton provides a particularly clean laboratory in the hunt for new physics beyond the Standard Model. Strong interaction effect s are absent in the leptonic tau decays studied in this t hesis. In this section , we bri efl y describe some of the physics beyond the Standard Model, and a precise measurement of the Mi chel parameters can be used to constrain this new physics. 2. 7 .1 C barged Higgs Comparing Figures 2.:3 and 2.4 , we find that t he limits on non-standard couplings obtained from the tau Michel parameters leave large holes in which new physics might hide. Tau res ult s becorne much more interesting if specific models are considered. Examples of such models are those which predict t he presence of charged Hi ggs bosons lead ing to mass dependent scalar couplings [45]. One possible scalar candidate is the scalar charged Higgs of the Two Higgs Doublet Model [46]. In this model , the Michel parameter 17 is related to the mass of the charged Hi ggs: 2 :) 17 1nrm 1,tan f-, 2m7-r (2.71) where fJ is t he ratio of the vac uum expectat ion value of the neutral components of the two Higgs doublets and m H denotes the mass of t he charged Higgs which mediates the decay. Since the charged Higgs is a scalar particle, this effect corresponds to the spin flip of the daughter charged lepton ; the effect scales with t he mass of the da ughter lepton and is strongly suppressed in the electron spectrum. 40 2. 7 .2 Right-Handed T,V' Bosons The presence of a. Hl ' boson [47] whi ch co uples to ri ght-handed fermions would resul t in the mixing of mass eigen states thus distorting the daughter lepton spectrum , res ul ting in the Michel parameters: p :3 (rnf + m~) 2 + (mf - ni~) 2 cos 2 2( rn1 + m~ 8 4 m .1 4 4 m .2 . " 4 cos 2c, (2.72) m1 +m2 where m 1 and m 2 are the masses of the H11 and ltf/2 bosons respectively, and ( is the mixing angl e between the vVi~ and H'R states. 2. 7.3 Anon1alous Electric and Magnetic Couplings Constraints on t he universali ty of the charged and neutral current interact ions, as well as the shape of the daughter elect ron and muon energy spectrum , provide t he st rongest bound s on anomalou s, CP conser ving, ,JJ\;1/ dipole moment type couplings. The presence of non-zero anomalous couplings produces a di stortion in the final state charged lepton spectrum whi ch in general cannot be ex pressed as shifts in t he Michel param eters . The 1i chel spectru m ass umes t he absence of deri vative couplings which arise as a res ult of anomalous moments. To lowest order, t he normali zed lepton energy spect rum in t he tau rest fr ame can be wri tten as [48]: 1 elf ) . . - = ;1·-[6 - 4.r + 1,· (4;1· - :3)] , r cfr ,vhere 1,· correspond s to the anomalous dipol e complex fo rm factor, an d :r = Ee/ Ema.r 41 Cornparing with the conventional Michel spectrum (ignore polarization terms in Equation 2.58), we see that t he effect of h'. on the normalized spectrum to this order is the same as Sbp/3. Using the current world average value bp = p - 0.750 = -0.021 ± 0.027 [37], we obtain K = -0.021 ± 0.072. A more precise measurement of the p parameter in this ana.lysis should improve this constraint on h'.. 2. 7.4 Massive Neutrinos The presence of a massive Dirac neutrino would permit right-handed couplings and would thus result in changes to the Michel parameters. The p parameter would be slightly less than :3/4 [49]. Mixing between this new massive neutrino and the tau neutrino would also distort the spectrum in a manner not characterized by the Michel parameters. 42 Chapter 3 The CLEO Experiment at CESR In this chapter, we provide a. description of the apparatus that was used to generate ( CESR) and collect (CLEO) the sample of leptonic tau decays used to determine the Michel para.meters measured in this thesis. We also provide details a.bout the l\fonte Carlo simulation packages used to simulate the processes studied . 3.1 CESR The Cornell electron storage ring CESR serves both the CLEO experiment and the Cornell high energy synchrotron source CHESS. The form er studies the electron positron colli sions while the latter focuses the synchrotron radiation emitted by the beams to st udy a variety of topics. CESR is located inside a. 768 111 circumference tunnel approximately 10 meters underground. The tunnel, on the Cornell University camp us in Ithaca., New York, collides elect rons against positrons with center of mass energies in the range of 9 to 12 Ge V , the region of the Y resonan ces . The ma.in components of CESR a.re shown schematically in Figure 3.1. Electrons a.re stripped from a. metal cathode plate and accelerated by high voltage fields inside a.n elect ron "gun" producing a. high intensity electron beam. The positrons a.re produced by directing 50 Me V energy electrons on to a. thin tungsten target. Thi s lea.els to the QED pair production reaction: (t - +nucleus)---+ (e+c Cnucleus). These particles a.re injected into the linear accelerator (LIN AC), which boosts their energy to approximately 150 Me V. Next, the particles a.re transferred to the 768 111 circumference synchro tron , located a.long the inner tunnel wall. Magnets separate the electrons and positrons, a.nd the electrons (positrons) travel in counterclockwise (clockwise) circular orbits in a. vacuum chamber. A periodic arrangement of dipole, quadrupole, and sexta.pole magnets keep them in orbit, confined within small well defined bunches in the :1· and y dimensions. In less tha.n 8 ms (co rresponding to less WEST TRANSFER LINE EAST TRANSFER LINE LINAC CLEO II • Positron Bunch - Clockwise e Electron Bunch - Counter Clockwise Figure 3.1: A schema.tic view of the Cornell Electron Storage Ring , CESR. than 3200 revolutions ), the particles reach an energy of 5.3 GeV. The acceleration is achieved by four 2 m long radio frequency (RF) cavities. Electrons (positrons) a.re then transferred into the storage ring through the eas t (west ) transfer lines into one of seven different bunches *, evenly spaced about in the ring. The counter rota.ting bunches of electrons and positrons are kept apart by a series of electrostatic separators to prevent collisions at all but one point in the ring. This is achieved by deflecting th e beams hori zontally in a novel beam orbit known as the pretzel orbit. Thus parasitic collisions are prevented , to ensure a long beam life *The present configurat ion utilizes 9 x 2 bun ches . 44 time. The particles lose about 1 Me V energy per orbit clue to synchro t ron radiation. Thi s lost energy is replaced by 500 iVIH z RF cavities putting out -500 KW. The extremely good vacuum ( 10- s Torr) in the storage ring , a.long with the opti cs configuration , allow stored beams to be maint ained for several hours. T he elec tron and positron beams are fo cused at the interaction point by a seri es of strong quadrupole magnets. The fin al set of quadrupole fo cusing m agnet s a.re permanent sumerium cobalt m agnets that surround the beam pipe part of t he ,,va.y inside the CLE O II detector. The beams a.re fo cused to a small cross section: 0" 1 - ~10 pm (verti cal) , O" y ~100 f-lm (horizontall y ), and O" z ~l cm (length). T he small cross section is essential for increasing the particle flux a.t th e interaction point , t hus increasing t he rate of e+e- colli sions. T he rate at whi ch t he electrons and posit rons collide is t he product of t he instantaneou s lu m inosity of the ma.chi ne times t he cross sect ion . The instantaneous luminosity of t he collicler is gi ven by N 1 N2-fn A where N 1 and N 2 a.re t he number of parti cles per bunch , n is t he number of bunches, f is t he revolution frequency per bunch , and A is t he cross sectional area of t he region where t he bunches cross . Ea.ch bunch is compri sed of N 1 '.:::' N 2 '.:::' 10 11 particles and t here a.re n = 7 bunches. T he revolu tion frequency, f ~ 400 kH z and A = 4 iT0" -0" y = 1 1.25 x 10- 4 cm 2 , resulting in a ty pi cal lum inosity of 2.25 x 10 32 cm- 2 seC 1 (now higher). CESR is current ly the world' s highest luminosity collicler. 3.2 The CLEO Detector CLEO II is a general purpose solenoid al rnagnet spectrometer and calorimeter with excellent particle and shower energy detect ion capabilities. The origina.l CLEO detect or ,va.s completed in 1979 and started recording data t hat year. A series of upgrades 45 including improved time of flight detectors . muon detectors , and vast ly improved electromagnetic calorimetry over the next 10 yea.rs resulted in the CLEO II detector which began operating in 1989 . The upgraded detector, designed for optimum performance near the i (4S) resonance (center of mass energy of 10 ..58 Ge V ) is shown in Figures :3.2 and 3.3 and is descr ibed in cl eta.il in [50]. Muon Chambers Outer Iron Inner Iron Return Iron Magnetic Coil Barrel Crystals ~~~~~~~~~~~~~~~~~4----_j Time of Flight Central Drift Chamber -t-----;r"-- Endcap Crystals E==~~~~~~~~~!E~~~====~~~--,.L-- Endcap Time of Flight Beam Pipe Figure 3.2: A schema.t ic view of the side view of the CLEO II detector. In t he CLEO coordinate system, the direction of the positron beam through the 46 detector defines the .: a.xis, the y a.xis points vertically up , a.nd the :r a.xis is selected such that it defines a. right-handed coordinate system (southward and a.way from the center of the ring). In polar coordinates the xy plane defines the r¢ plane and the third coordinate, 0, is the angle ma.de by a. given vector with respect to the z a.xis. z =~l_s_o_.o_c_m_ _~_ _ _z _ ~ Muon Chambers Outer Iron Endcap Crystals "-."'- Magnetic Coil Barrel Crystals Inner Iron Time of Flight CD LA and VD am Pipe Endcap Time of Flight Endcap Muon Chambers z= 280.0 cm z = 120.0 cm Figure 3.:3: A schema.tic end- view of the CLEO II detector. In the fall of 1995, the detector was upgraded to CLEO II. 5. Since the measurements described in this thesis do not use any of the data collected ,vith the upgraded 47 detector , the details of the upgrad e a.re not described here. In the subsections that follow , we bri efl y describe the detector components of the CLEO II detector , in order of their radial dis tance from the interaction point. 3.2.1 Bea111 Pipe The 33 cm lon g beryllium beam pipe wi t h a :3.5 cm inner radi us separates the vacuum of the storage ring from the other detector components. The walls of the pip e a.re design ed to be a.s thin as possible to reduce both scattering a.nd energy loss by parti cles passing through it, while still providing mechanical stabili ty against the stresses introdu ced by 1 atmosphere of pressure. The 0.5 mm thi ck pipe is lined with a 1 pm layer of ni ckel a.nd a 20 1tm layer of silver, corresponding to 0.44% of a radiation length. The coating is designed to absorb synchrotron radiation photons. 3.2.2 Central Tracking Syste111 The three innermost devices a.re proportional wire chambers. Th ey measure the trajectory of charged particles and perform measurements of specifi c ionizat ion loss as the charged particl es traverse t he third chamber. All three chambers share the same ga.s mixture t of 50% argon a.nd 50% ethane. vVhen particles travel through the gas volu me , they ioni ze the gas atoms, thu s leaving a tra.il of electrons and ions. All three chambers collec t and amplify this ioni zation on anode wires . The cathodes and the a.nodes establish an elect ric field causing the electrons to drift toward the closest anode. There, they gai11 energy in the electric field of t he a.node wire resulting in secondary ioni zation. An avalanche is created , resulting in a.n electronic pulse which is registered as a. "hit" if it is passes a t hreshold in the readout electronics. The particle traj ec tori es through these devices are helical because of the 1.5T solenoidal magnetic field. The fi eld a.long t he ::: a.xis bends the charged parti cles in tT he gas in t he PTL was sw itched to DM E (di m eth y l eth er) in April 1992, resu lting in a n improvem ent in t he s patial resolution o n th e positi o n m easurem ents from 100 µ.m to 50 µ.m. T he ma.in drift chamb er gas was also swit ched t o helium isobu ta.ne in 1995 . 48 the r¢ plane by the Lorentz force. The clockwise or counterclockwi se bending of the track depends on the charge of the particle. The radius of curvat ure is a measure of its momentum Pt transverse to the beam axis; Pt = 0.03BR , where Bis the magnet ic fie ld strength in Tesla and R is the radius of curvature in meters. The tracking devi ces measure the curvature, H = 1/(2R), and thus Pt· There is no bending in the r:: plane; the polar angle 0 combined with the Pt measurement provides a measurement of the magnitude of the momentum . The drift cham bers have an acceptance that is homogeneous over azimuth, a.nd covers the polar angle range cos 01 < 0.98. However , track reconstruction efficiency I and resolutiolls a.re poorer for cos 01 > 0. 71 ( angles below 45° and above 13.5°) because I the track ex its in :: res ulting in a. red uction in the number of layers. A brief description of ea.ch of the three drift chambers is given below. Precision Tracking Layers The Precision Tracking Layers or the PTL is the innermost drift chamb er lying closest to the beam pipe and extending from a radius of 4.5 cm to 7.5 cm . The chamber's relatively small cell size and proximity to the interaction point allows us to separate primary from secondary vertices. It is 0. 5 rn long and consists of 384 polycarbonate tubes arranged in 6 concentri c layers with 64 cells/layer. Ea.ch of the tubes is held at ground providing a field cage for a single axially aligned sense wire which runs through its center. The a.no de wires a.re 15 µm gold plated tungsten. The walls of the tubes a.re ma.de of cond uctive a.luminized mylar and serve as the cathode. The cells in two consec utive layers are staggered by 1/2 cell to help in resolving the ambiguity induced by the fact that the di stance between the ioni zing particle and wire does not determin e on which side of the wire tlie particle passed. No longitudinal( :: coordinate) direction measurements a.re ma.de with this chamber, since the sense wires all run paralle l to the chamber. No attempt is ma.de to instrument charge division read out. 49 Vertex Detector The oldest component of the CLEO II detector , the vertex detector (VD) , started being used as the second (intermediate ) drift chamber when the PLT was installed. It extends from a radius of 8.1 cm to 16.4 cm and is 0.9 111 long (see Figure 3.4). A total of 800 sense wires and 2272 field wires are arranged to form 10 layers of small hexagonal cells, with :3 field wires for each sense ,,vire. All wires a.re axial , the inner five layers have 64 cells per layer, and the outer fi ve layers have 96 cells per layer. The cells a.re staggered from layer to layer as shown in Figure 3.5 , to resolve the ambiguity in the sign of the drift di stance ( left or right of the wire). Filament Tube lnncr Cathode Strips Outer Cathode Strips Figure 3.4: The vertex detector (VD). On the inside of the first layer and the outside of the tenth layer , segmented cathode strips con1plete the remaining field shaping. The signals induced on these cathode strips a.re also read out to provide::: measurements. Th e segmentation, shmvn in Figure 3.4, is 5.85 (6.85) 111111 a.long the beam direct ion on the inner (outer) cathode surface. The image charge of avalanche at the wire is spread over approximately t hree pa.els of the cathode. Both inner and outer cathode surfaces a.re di vid ed into eight azimuthal sections to reduce confusion of cathode signals correlated to different sense wires. 50 - - - - - : . Outer Cathode Strips + . + • +! + •....• ! + . • . + . + •! + • + ... I + + • . • • +·. + . +·+·. · • • • ! + . •+ . + • + •! + + '. +! + 16.4cm.,,,\· Jc' \\Jc' \,: "" Jr + • + .• •• +· .• +·. .\' ·+l \·.+ .. ;._.... +· . . •··!vo \'< . • J( • ~ • + • ~ •...•• ! • Jr • • • • • + •• Jr • • Jr • )( • + \ · .,.· \ \ \. \ • Field Wire + Sense Wire + •• _+.: . • ' ,...+•_+_ · .1 •• + . + + Jr • Jr.+ • • • • • i i '.~ · ) ( · _ . · · + • + · i \ • ~ + • Jr • -: Inner Cathode Strips "·\ 8.1 cm/ . . . )(. • • \ • . • • . . ! PTL I 4.5 cm ,, '. i .,,---i Be Beampipe '-< ii 3.5 cm"' \ \ \ i ' • \ I I • ' \• 'I \\ i o.o cm +Interaction Point Fi gure :3. 5: Cross section of t he precision t racking layers and t he vertex detector. To provide further m easurements in the axi al direction , the sense wires are m ade of a ni ckel- chromium alloy with abou t three t imes t he resisti vity of gold plated tungsten and are instrumented for charge di vision m easurem ents . Comparing the relati ve ampli t ude of signals observed at opposite end s of each sense wire provides z coordinate track information , a.nd t he:: coordi nate where t he t rack passes neares t each sense wire is measured with a. resolu t ion of 1. 7 cm . The fi eld wires a.re made of alumi nium . The ga.s in the vertex detector is maintained a.t 20 psi absolute pressure to provide higher gain and shorte r drift times. 51 Central Drift chamber The outer drift chamber (DR) 1s the pnmary tracking chamber of the CLEO II detector. It covers the region from a radius of 17.8 cm to 94.7 cm, with an active length of 189 cm. It is used primarily to measure charged particle moment um vectors at the vertex, and for particle identification. The momentum transverse to the beam axis, the radial di stance of closest approach of the track extrapolation to the beam lin e, the Pt, and the azimuthal direction c/>, are measured with 40 axial (parallel to the beam axis) wire layers. Longitudinal measurements , polar angle and the longitudinal distance from the center of the interaction region to the extrapolation of the track to the beam axis ( z coordinate) , are measured with 11 small angle stereo wire layers and 2 layers of segmented cathode readouts. The pitched stereo wires are spaced every fourth layer . A total of 12240 sense wires and 36240 field wires a.re arranged in 51 layers of cells, with three field wires for each sense wire as illustrated in Figure 3.6. The 20 1-,tm di ameter gold plated tungsten sense wires are arranged in square cells, staggered by 1/2 cell from layer to layer. The number of sense wi res per layer increases with radius so as to keep the cell sizes uniform; there are 96 wires in t he innermost layer and 384 wires in the outermost layer. The sense wi res are readout at only one end and thus has no instrumentation for charge di vision. As in the VD , the inner and outer surfaces of the chamber have segmented cathode surfaces which shape the field cage. They also provide :; measurements from the indu ced signals. The segmentation of the cathode surfaces is a.bout 1 cm along the beam direction. The cathode is divid ed into 16 (8) azimu t hal sections in the inner (outer) cathode, ea.c h covering 6 (48) wires, to reduce confusion of cathode signals correlated to different sense wires. The drift chamber runs at atmospheri c press ure. 52 sssss:sssssssssssssssssssssssssssssss DR Outer Shell DR Outer Cathode Strips • Field Wires o Stereo Sense Wires • Axial Sense Wires . o . o • 0 •• , O ,o·O•O•O•O·o • 0 . . . . • • • • • • . . ,' ~ \~. \ : __ \ ~~~ ~ ~: ~;: : _o: o • 12 ~ ': • 11 • 10 ~ ~ DR inner Cathodes DR Inner Shell VD Outer Shell F igure 3.6: Main drift chamber cell st ru ct m e. Momentum and Angular Resolution The resolution of the tracking system can be parameterized as: 2 2 53opt ) ( BL2Jn + (0.0540 ) BL (3.2) where the first term is a result of individual measurement errors in drift dis tances, and the second term a.rises clue to t he distortion of the track from a true helix by multiple scattering. B is the magnetic field strength in tesla, o is the accuracy of the individual position measurements in the drift chambers in meters, Pt is the transverse momentum in Ge V / c, L is the length over which the measurements a.re made in meters, n is the number of position measurements , and t is the thickness of the obstructing material in the chambers in radiation lengths. For the CLEO II tracking chambers, B = 1.5T, L = 0.85 m , n = 49, s = 150 /Jm, a.ncl t = 0.025 radiation lengths. Equation 3.2 now becomes (0.00llpt) 2 + (0.0067) 2 (3.3) and lea.els to Dpt= 47 Me\! /c at a Pt= 5.28 Ge\! /c . This is lower than the resolution of 64 Me V / c measured by a sample of e+ c -, p+ fl- a.t 5.28 Ge V / c beam energy. The angular resolution is measured to be 84> = lmracl , 80 = 4mra.cl . This difference between the azimuthal a.ncl polar angle resolution is expected because there a.re only 15 measurements in the polar direction: 11 from stereo wire layers in the drift chamber and 4 from the cathode readout layers in the drift chamber and the vertex detector. Charged particles con1ing from the interaction point with a momentum lower t han 65 Me V / c are not detected clue to the material in the particle pa.th. With a. 1.5 Tesla. magnetic field , onl y particles with Pt >220 Me\! /c exit the ma.in drift chamber ; a 54 lower transverse momentum and Pc < 45 Me\! /c results in a track vvhich executes a full t urn within the active volume (curlers). The particles with lower Pc result in tracks with several turns. Charged Particle Identification Pulse height measurements in the main 51 layer drift chamber provide energy loss measurements ( dE/ dx) on charged tracks with a resolution of 6. 5% determined for Bhabhas and 7.1 % for minimum ionizing pions. The energy loss per unit distance is a function of the particle mass, as is illustrated in Figure 3.7. 10 6 --> (.) 11.) ~ >< "d iil "d 5 o~~~--~~~-~~~-~~~--~~ 0.0 0.5 1.0 1.5 Momentum (GeV/c) Figure :3.7: dE/dx in the drift chamber versus the track momentum . The resolution on the measured dE/dx depends on the energy loss distribu tion in a cell and the number of cells that a particle passes through in the drift chamber. Because of t he large Landau tail of the ioni zation distribution, we take the 50% truncated mean [51] of all the measurements a.long a track traj ectory as th e best 55 estimator of dE/dx. We note that dE/ dx measurements yield good separation of pions and kaons up to roughly 700 l\!Ie \I/ c, and good separation of pious and protons up to 1.1 Ge V/ c. \Ne define SGxxDI as the difference between the measured dE/ dx and the dE/ dx one would expect for a particle species xx, divided by the resolution where xx is either EL (e), MU (rt), PI (1r) KA (I{) or PR (p). 1 No 1r / X particle identification is employed in this thesis; particle identification is used onl y to help identify electrons. 3.2.3 Time of Flight This detector component, comprising of particle scintillation counters , is located just outside the central tracking chambers at a radius of 95 cm from the interaction point. These counters measure the time interval between a beam crossing and when the particle strikes the counters. The time of flight counters are used as a fast element in the trigger system and can be used for particle identification as well t. This system is comprised of 64 Bi cron BC- 408 plastic scintilla.tor slabs ( 10 cm wide , 279 cm long and 5 cm thick) arranged parallel to the beam pipe. Both ends of the scintilla.tor a.re connected to lucite pipes which transfer the scintillation photons to photomultiplier tubes . The light guides a.re necessary to keep the photomultiplier tubes opera.ting safely a.way from the magnetic field of the detector. In addition to the 64 barrel time of flight counters, ea.ch encl of CLEO is covered with 28 wedge-shaped scintilla.tors. The en dcap counters a.re read out with a single photomultiplier tube at the small end. These Hamama.tsu proximity mesh type tubes are designed to operate inside high magnetic fields. The solid angle subtended by the barrel counters is 81 % of 471 and that by the endca.p counters is 16%. The barrel counters have a resolution of 154 ps as measured using hadrons. In Figure 3.8, we show a scatter plot of the time of flight measurements (barrel) versus the track momentum for tracks in badronic events. !They a.re now used as a. bunch-finder for the multi-bunch operation. 56 0.0 0.5 1.0 1.5 2.0 2.5 Momentum (GeV/c) Figure 3.8: 1/ /3 versus track momentum in the barrel time of flight counters . For this plot, the time of flight information is expressed in terms of 1//3 with /3 = v/c. The velocity v is inferred from the measured time of flight information and the pa.th length of the charged tracks in t he central detector. The superimposed curves a.re l /3 E p 2 1+ ( -JVJ ) p (3.4) for tracks of momentum p and particle species of mass 1\1. The time of flight measurements extend the separation of the three particle species to higher momenta. than dE/dx , producing good pion/ka.on separation up to 1.2 GeV/c and ka.on/proton separation up to more than 2 GeV/c. 57 3.2.4 Electron1agnetic Calorhneter The calorimeter records the passage of charged particles, and m easures the energy of photons and electrons in the CLEO II detector. A photon incident on a. block of material interacts in one of three possible ways depending on its energy : • low energy photons (E~1 S 100 h: eV) result in the production of photoelectrons from the a.toms of the material; • in intermediate energy photons, Compton scattering of the photons with the atomic electrons is dominant ; • photons with energy above the threshold of 2m,0 ~ 1.02 MeV result in the creation of a e+ C pair from the interaction of the photon with t he material nuclei. At the CLEO energy sea.le, typica.l photon energi es are 111 the 10 Me\/ to 5 GeV range, and the photons primarily produce e+e- pairs. The electrons and positrons, in turn, undergo bremsstrahlung , lea.cling to a. ca.sea.cling shower of e+, e- particles and photons. This process continues until the energy is totally dissipated in the material. Some fraction of this energy is converted into scintillation light , enhanced by the eloping. The calorimeter is a 27 ,000 h.g array of 7800 thallium eloped cesium iodide crystals, ea.ch with a.n inner face of a.bout 5 cm (2.7 radiation lengths ) x 5 cm and a length of :3 0 cm (16 radiation lengths and 1 nuclear interact ion length) . The length of the crystal almost fully contains the electromagnet ic shower. A 6 mm thick UVT lu cite window separates the back encl of the crystals from 4 photocliodes, which detect the scintillation light from the crystals. The four-fold redundancy insures that isolated failures of photodiocles do not compromise the calorimeter performance, since all 7800 crystals in the CLEO II detector have a.t lea.st two working photodiocles . The four preamplifier signals from a single crystal a.re summed and shaped before being sent to an ADC. 58 Thallium eloped cesium iodide has a high light output with an emission spectrum that is well matched to the photocliocles. In addition, both t he radiation length ( 1.83 cm ) and the Moliere radius § (:3 .8 cm) are short. The dimensions of the crystals used in CLEO are a compromise. Longer crystals would give a superior resolution for the high energy showers by reducing the leakage at the back of t he crystal, but because of transmission losses, a longer crystal would have a lo-wer resolution for the low energy showers . Smaller lateral dimensions for each crystal, and hence a larger number of crystals , would improve the angular resolution. However , the increased number of crystals that would need to be summed to find shower energies would increase the electronic noi se. The cost of machining and instrumenting the device would also rncrea.se. The system is located just outside the time of flight detectors and is divided into the barrel and endcap region as illustrated in Figures 3.2 and 3.:3. The barrel portion of the calorimeter contains 61 44 trapezoidal crysta.ls arranged in 48 ::: rows of 128 azimuthal segments each. T hese crystals all point towards the interaction region and photons originating a.t the interaction point strike the barrel crystal surface at nearly normal incidence. The remaining 1656 crystals are rectangular and are arranged in concentri c rings at both ends of the detector. These cells are all arranged to have their axes parallel to the ;:; axis of the detector , and thus la.ck the proj ect ive geometry found in the barrel crystals. The barrel crystals cover the angular region between :32 and 90 degrees; the endcap pi eces cover 15 to 36 degrees . The total coverage is 95% of the solid angle res ulting in a nearly hermetic calorimeter. The resolution on the energy depend s on the amount of material between the interaction point and t he crystals. The presence of material degrades the resolution through photon conversions and the subsequent ioni zation loss of the resulting charged particles . Further, energy from conversions far from the crystals spread laterally and will not be associated with the proper shower. The energy resolu t io n in the CLEO II STh e ]Vloli ere radius characteri zes the lateral spread of showers. 59 calorimeter is excellent, and for the barrel region , it can be parametrized as f7E er _ 0.:3.5 . E( ¾ ) - E 314 + 0.19 - 0.1£ (:3.5) where E is the photon energy in Ge V. The angular resolution in the barrel region can be parametrized a.s r7q, (rnr) = 2.8 m + 1.9 , r7g(rnr) = 0.8r7q, sin 0 vE (3.6) where, once agam, E is the photon energy in GeV. The energy and angular resolution parameterizations come from the Monte Carlo simulation of showering in the CLEO II detector, including electronic noise. The barrel region has 16 radiation lengths material while the enclca.ps have a.bout 1 radiation length material at normal incidence. The energy resolution in the barrel is a.bout 1.5% at 5 GeV and 3.8% at 100 MeV. The endcap resolution is worse due to the drift chamber endplate in front of the crystals. The angular resolution at 5 Ge V is 3 mrad in the barrel and 9 mrad in the endcaps. The fine granularity of the calorimeter permits very good position resolution , critical in the reconstruction of 1r 0 decays to 11 (B(1r 0 --+ ''//) = 98.8 % ). The photons from 1r 0 's with E"o < 3 Ge V a.re well separated in the calorimeter and a.re identified as separate showers. The linesha.pe of E--1 is a.symmetric due to leakage and preconversions , and is calibrated such that E--, = Epea.k· Thus 1n--n pea.ks below n-1 rro, and has a lower mass tail (Figure 4.1). The rms width of the 1r 0 invariant mass peak varies from 10 Me V for the low energy 1r 0 's to 5 Me V for the high energy 1r 0 's. The electromagnetic calorimeter is used extensively in the analysis presented in this thesis. In addition to the 1r 0 reconstruction, it is used to help identify electrons, and to veto potential background events as explained in Chapter 5. Electron identification utilizes the ratio E /p of the energy measured in the calorimeter to the momentum measured in the tracking chamber. E/p close to 1 is consistent with an e hypothesis , since all the electron's energy should be deposited in the calorimeter. 60 Hadrons and muons both have smaller E / p. 3.2.5 Superconducting Solenoidal Magnet This solenoid was designed to provide a uniform 1.5 Tesla magnetic field parallel to the beam li ne. It had to be large enough to contain the electromagnetic calori meter inside the coil; the 3.5 m long solenoid has a 3.1 m diameter with a 2.9 m clear bore res ul ting in a 26 m 3 cyli ndrical volume. The magnetic field is uniform to ±0.2% in the drift chamber volume over 95 % of th e total solid angle. The!'e are two layers of 5 mm x 16 mm aluminium rectangu lar t ubi ng containing a flat ribbon of Cu-Nb-Ti superconducting cable, wound on th e inside surface of the alumi nium cylinder. The inner layer of tubing contains an 11 strand ribbon , whi le the outer layer contains a. ribbon of 9 strand s, all carrying 3300 A current. The entire system is cooled to a. temperature of 4E by a li quid helium circulation system . The flux ret urn is provided by four layers of iron outside the magnet , ea.ch 36 cm thi ck. These iron layers serve as absorbers for the muon detection system as well. 3.2.6 Muon Cha111bers The muon sys tem was designed to be highly effic ient with low fak e rates , and to cove!' the maximum possible solid angle. There are three superlayers of muon detectors between the iron layers for the magneti c flu x ret urn. The barrel chambers are arranged in an octagonal geometry as illu strated in Figure :3 .3 and cover 86 % of 41r steradian s. These chambers are imbedded at depth s of :36, 72 and 108 cm of iron. Additional chambers cover the two end s of the detector. Th e total equivalent thickness of iron absorber varies from 7.2 to 10 nuclear absorpt ion lengths , depending on the direction of the track. Each superlayer consists of three sublayers of plastic Iarocci streamer tubes, operated in the proport ional mode at 2500V with a 50-50 argon ethane mixture. The counters are about .5 rn long and 8.:3 cm wide. The cross sec tion of a counter is shown 61 in Figure :3.9. 9mm ......_ 1mm -L__ 10mm Figure :3.9: Cross section of the muon chamber proportional tubes. A 50 pm silver plated Cu - Be anode wire runs clown the center of each of the eight channels of the proportional tube shown in the figure. Three sides of the comblike plastic profile are coated with a layer of graphite which acts as a. conductive cathode. The a.node signals provide one hit coordinate; the orthogonal coordinate (a.long the counter) is measured with external copper pick up strips, of the same width a.s the co unters (see Figure 3.10). The anode wires from ea.ch counter a.re ganged together, and the readouts from a. number of neighboring counters and neighboring strips are ganged together a.t both ends through 100f2 resistors. Charge division on the a.node wires is used to determine the coordinate of the hit, eli m inating the need for a. large number of readout channels. The spatial resolution obtained is 2.4 cm for the counters. This resolution is adequate, since it is smaller than the uncertainty in tlw projected tra.ck position in the muon chamber due to multiple scattering in the iron absorber. Ea.ch reconstructed track in the central detector is ext ra.pola.ted into the muon detector taking into account the energy lost by c!E/dx. The pa.th length to each muon layer is calculated in nuclear absorption lengths. Then a. search is ma.d e for hits in the muon counters that are likely to be transversed by the track and a. 2-D \ 2 of the distance between the measured and the projected hit positions is cakulated. If the \ 2 < 16, we consider that layer to be hit. The tra.ck is consid ered a.s definitely 62 Copper Carhode Strip Anode Wire PVC Shell Gaphite Carhode ~===,;:;::===;;====;~=;;===;;===;;==;;===;;c===;;i~=;;===~ Copper Ground Figure :3.10: Cross section of one muon chamber superlayer. detected in a unit if at least two out of the three layers in t hat unit a.re hit. The track is assigned the depth of the outermost unit in which it is detected. If the track's depth is less than the depth predicted by track extrapolation, the track is considered as a. non-muon. 3.2. 7 Trigger and Data Acquisition The CLEO II trigger is designed to be very loose in accepting events, and at the same time to have a small dead time. The crossing rate for electron and positron bunches in CESR is 2.8 MHz, while the rate of interesting physics events is only a.bout 10 Hz. A hierarchy of hardware triggers, and a final software trigger, select events to be written to tape. At each level, either a set of criteria. a.re passed and the trigger proceeds to the next level, or the criteria a.re failed, the event is not read out , and the trigger directs the experiment to re-a.rm it se lf. The Level 0 (LO) trigger is fa.st , 405 ns, i.e., the decision is ma.de before the next beam crossing. It receives inputs from the time of flight counters, the vertex detector, and t he electromagnetic calorimeter. The LO trigger is passed every :300-400 crossings on average ( depending on the bean1 current, level of background, and so on) and the rate of events passed by LO is ~ lOkH z. After a LO trigger, all detector gating is disabled, and a. search is ma.de for the Level 1 (Ll) requirement. 11 takes inputs from the time of flight counters, the vertex detector, the drift chamber and the calorimeter. Approximately 1.-5 ps is required for all the informat ion to be ready for 63 the 11 decision, thus introducing a. 2% dead time. The 11 trigger reduces the rate to a.bout 50Hz. The surviving events a.re then subject to the Level 2 (12) trigger, which takes inputs from the vertex detector and the drift chamber and form s detailed pattern recognition to reject backgrounds from cosmic ray events, a.nd interactions of the beam with the beam pipe or the residual gas molecules . 12 decreases the event rate by a. factor of between 2 to 4. As with 11 , if the requirement of 12 a.re not met, gating resumes. Starting a.t the 11 level, the trigger is specified in terms of several parallel "lines" or "streams" tailored to specific physics processes of interest. There is a.n intentiona.l redundancy in these lines, so that many processes such a.s e+ c -+ e+ c - satisfy many of the 12 lines . This redundancy allows for inefficiencies in detector elements, and also allows one to determine these inefficienci es . Once a.n event passes the 12 trigger, the signals from all detector components a.re digiti zed , and read out into a data. acquisition (DAQ) computer. The final level of event filt ering is Level 3 (13) and occurs in software after the ent ire event has been read out by the detector, but before it is written to tape. H uses detailed information from reconstru cted events and furth er reduces the number of events by a. factor of 2. Every one out of eight events failing 13 is fia.gged as such and is saved for diagnostic purposes. 3.3 Simulation of Physics Processes and Detector Response An essentia.l tool for ma.king the measurements presented in this thesis is the simulated data. set produced by a. computeri zed Monte Carlo simulation of the physics processes invol ved and of the CLEO II detector. Computer simulations a.re very valuable in the analysis of the data. to extra.ct the parameters and to perform precision m ea.surernents with sma.ll sys tematic errors. Gi ven the complexity of the detector geometry and its response to particl e passage, as well as the complexity of the kinemati cs of final state 64 particles , the Monte Carlo simulation of the physics reaction and the detector response provides a. convenient and effective way of studying the data.. The simulation accounts for all the complicated correlations present in the data.. These simulations a.re carried out in two logically different steps. First, "events" corresponding to the initial physics process a.re genera.tee!. Then the detector response to the stable particles in the final state is simulated. 3.3.1 Event Generation Event genera.tors simulate the high energy collisions produced in the accelerator. They produce events which contain the type , energy-momentum and space-time fourvectors for a.ll the final state particles. The event genera.tor for T pairs is a. combined package of KORALB(v2.2) , TAUOLA(v2.4) and PHOTOS(v2.0) [52 , 53, 54, 55, 56]. KORALB simulates the process e+e- - , T+T- (,) . The simulation includes in its treatment 0( a 3 ) QED radiative corrections; up to one photon ca.n be ra.cliatecl from the initial a.ncl final state leptons. It also includes effects associated with a. finite T mass , interference of the photon exchange process with the lowest order annihilation through the zo resonance, spin polarization in a.ny direction for the initial electron and positron, and spin correlations of the produced ta.u pair. TAUOLA simulates the decays of polarized tau leptons into all major expected final states including µIJIJ , e I1I1 , 1rI1, l<IJ , pIJ , J{ * IJ and a 1 I1. Table :3 .1 li sts all T decay modes simulated in TAU OLA. Further , the decay of the vector resonances p and a 1 to two and three pions respectively, and the decay of the]\'* to A' 7r is modeled according to the full matrix element calculation. Order a radiative corrections, which permit one radiated , a.re includ ed for the leptonic decays. PHOTOS is used to generate up to one radiated photon in semi-ha.dronic decays . The 11011-Sta.ncla.rcl Model 1l + A (p = 0, 17 0) and 17 = l (p = 3/4,17 = 1) Monte Carlo event samples a.re generated ,vith a. modified version of the TAUOLA package [57]. 65 Tau Decay Modes Sim ulated in TAU OLA Decay Mode Branching Matri x element of T Fraction [%] incl uding Spin - -, e -Ve il , T 18.00 yes -tp - Vpl/ T yes T 17.5 1 T 11.10 yes /I r 7r - -tp yes T 25.1 5 /JT T 17.90 yes - , a1 11T T- - , J{ -1; , 0.71 yes , - -, ]{ * - /IT 1.34 yes T - - , ]\, _ Jr _]{ + JJ, yes * 0.1 5 T - J{ Or. - j;O /J T yes* 0.15 ,- -, A'- 1\·01ro 1;, yes* 0.15 , - - , 1ror.o ]\'- 11 T yes* 0.05 T - - t ] \ ' - 7r - 7r + /1 T yes* 0.50 T- r. - f : Or.0 // T yes* 0. 55 T - - , ry 1r - 1ro ,1T yes* 0. 17 0 yes* T- r. - r. 1 1;T 0.B 0 T - - t r.-r,-7r+r. 11, 4.50 no T - - , 7r - 7r"07r U7r"O /I , 1.00 11 0 , - - , 7["_7["_7["_7["+ 7["+// T no 0.08 T - - , r.-r.-r. + r.01ro11T 0.09 no T - - , r. - 1ror.or.or.o ,1 , 0.10 no T- - t r._ r._ 7r _ r,+ 7r +r. 0 11T 0.03 no T - - , r. -1r- r. +1ror.o r. 0 11 T 0.05 no 0 T - - , r. - wr. 11T 0. 39 no T- ]\' - A 'O /JT 0.10 no T - - , J \ ' -w/J T 0.10 no All Modes 100.00 Decay Radiation O (a) m. e. O (a) m .e. PHOTOS PHOTOS PHOTOS PHOT OS PHOT OS PHOT OS PHO T OS PHO T OS PHOTOS PHO T OS PHOTOS PHO T OS PHOTOS P HOT OS PHOT OS PHOT OS P HOT OS PHOTOS PHO T OS P HOTOS P HO T OS PHO T OS P HO T OS Table 3. 1: Tau decay modes sim ulated in TAU OL A. T he first seven decay modes t ake into account t he full matri x element including heli city. T he modes marked with t he "yes*'' in column :3 indi cate that on ly approximate form factors are used in t heir calculation . 66 3.3.2 Detector Shnulation The modeling of the response of the measurement device CLEO II is carried out by the CLEOG [58] simulation program which contains a nearly complete description of the detector 's material and geomet ry. CLEOG uses GEANT [59] routines to track particles through the detector as they travel through the magnetic field, recording their trajectories and those of their decay daughters. The package also contains a parametrizat ion of hadronic interactions between the particle and nuclear matter of the detector components (NUCRIN/FLUEA) , an electromagnetic shower algorithm based on the EGS package and facilities for managing decay in flight, multiple scattering , Compton scattering , pair production, ionization, 6 ray production and bremsstrahlung. For precision measurements, the time dependence of the detector status and performance also must be taken into account. Each Monte Carlo event is assigned a time and elate such that all events are distributed over a certain dat a-taking period with the correct luminosity weighting. The actual detector stat us at that very moment is taken into account; the stat us of the trigger and each component of the detector is recorded for each data- taking period. The CLEOG output files are in identical format to t hat of the ravv data from the CLE O II data acq ui sition system . Further, characteristic electronics noi se in all devices is added to the simulated signals to ens ure that the simulated output resembles real physics data as closely as possible. The characterist ic noise is obtained from random triggers of t he detector in the presence of colliding beams. VVe run the same event reconstruction on both the data and the Monte Carlo output for further analysis. 67 3.4 Future Upgrades to CESR and CLEO The first phase of both the CESR and CLEO upgrades are complete. CESR has converted to a 9 bunch operation with a small crossing angle. A new digital feedback system and improved vacuum pumping have made possible the handling of multibunch trains (9 trains of t hree bunches each). CES R deli vers a peak luminosity which increases every other month , and is expected to reach a peak luminosity of £ = 6 x 1032 cm- 2 s- 1 in 1997. The next phase of the upgrade is aimed to achieve a peak luminosity of £ = 10 x 10 32 cm- 2 s- 1 . It requires the use of superconducting RF caviti es to handle the 9 x 5 bunch trains, new vacuum pipe and pumps to handle the synchrotron radiation load and a more complex interaction region focusing element and mas king configuration. The first phase of the detector upgrade is now also complete. CLEO Il. 5 has a new :3 layer sili con microstrip vertex det ector (SYD) which replaced the precision tracking layers (PTL) in CLE O II. It surrounds a new 2.0 cm radius Beryllium beam pipe and masking system . The author has worked on the development of this detector device and its mechanical support. Most of the work involved the SYD data acquisition system and is desc ribed in detail in Appendix D . Th e next phase of the detector upgrade involves a nevv silicon vertex detector with four layers, a new drift chamber, a fast Ring Imaging Cerenkov Counter (Fast RICH) for particl e identification , and a new data acquisition sys tem and trigger. Tb e combination of the upgraded collider and detector to be commissioned in 1998-99 is expected to yield data samples comparabl e to the ones expected at the B-factori es, and will be able to probe t he phys ics of B and T decays with an order of magnitud e greater sens iti vity. 68 Chapter 4 Data Analysis In this chapter, we describe all the cuts applied to select the e - vs . - hrr 0 and p - vs . - h1r 0 samples studied. Three different types of criteria. a.re applied: criteria. based on the reconstruction of TT events, those based on the reconstruction of the tag tau decay T+ -----+ h+1r 0 Dr, and those based on the reconstruction of the leptoni c tau decay T- -----+ e- V('IIT. Tagging one tau deca.y helps ens ure t hat we select a. TT event. The T+ -----+ h+ rr 0 Dr decay mode, where h+ refers to the charged hadron (1r+ or s+ ), is utilized to tag the TT events in this analysis. It is dominated by p+vr , but also receives contributions from]{ *+ v,. r/+ v7 and other non-resonant modes. No attempt is ma.de to di stinguish pions from kaons in this analysis . Using this particular decay mode of the T lepton has several advantages. It has a large branching ratio('.::::'. 25%), and there is negligible uncertainty associated with particle identifi cation. This would not be true if lep tonic modes were used to tag TT events . The reconstruction of the ent ire event helps suppress backgrounds from ha.clroni c events , two-photon physics, qq, and cosmic ray events . The tag decay mode is also utilized to est imate the flight direction of its pa.rent tau, necessary to recons t ruct t he pseudo rest frame spectra. described in Chapter 7. In the following section , ·we present details about the event reconstru ct ion proced ure including tracking , track-cluster matching. lepton identification a.ncl the rr 0 reconstruct ion. The la.st section in this chapter includes the cuts applied to select the events in this analysis. 4.1 Event Reconstruction After the data a.re copied to tape, there begins a. process of "offline'' soft ware analysis, and the event reconstruction is clone with several software routines. Standard routines apply caJi bra.ti on constants to convert ra.w signals to measure energy, time, etc.; 69 tracking algorithms convert wire hit patterns to particle tracks; clustering algorithms associate crystal hits with one electromagnetic shower; and so forth. 4.1.1 Tracking The Michel para.meters a.re extracted from a. fit to the momentum spectrum of the charged lepton in the event , and to measure the momentum we rely on the tracking chambers described in Section 3.2.2. These chambers provide the input for a. tracking program DUET [60], based on a. tree algorithm. DUET creates 'links' of hits in close proximity, forms these into elementary 'trees' based on the fiducial volume from which they appear to originate, and then combines the trees into 'cha.ins' and fina.lly 'tracks '. These tracks a.re fit to a helix. DUET operates with an efficiency of roughly· 99% for particles from haclronic tracks within the region of primary acceptance of the tracking chambers (approximately cos 0 < 0. 9). DUET was designed to find as many tracks as possible, an d thus it provides a list of tracks which often contains spurious entries. The situation is furth er complicated by the 1.5 Tesla magnetic field. Only particles with more than 220 Me V / c of Pt actually exit the outer surface of the drift chamber; others execute a. full turn within the active volume and are called 'curlers' . Tracks with very small Pz execute severa.l turns . To pare clown the list of tracks, we use a program called TRKMAN [61] which addresses three problems revealed in visual scanning of events: "ghost" tracks arise when DUET fits two tracks to a set of hits created by the passage of a single particle; undesirable curlers result in tracks form ed from the second half of a particle's arc, or the first half of an a.re from a. particle's second (or third) trip through the chamber; tracks formed when DUET fits a track through a set of unrelated hits, or simply does a bad job on hits that do come from a single particle. TRKMAN algorithms kill more than 90% of the ghost tracks, eliminate more than SO% of undesirable curler tracks , and eliminate 86% of the third type of undesirable tracks. 70 4.1.2 Crystal Calorin1eter Clustering For photon measurement ( 7fo reconstruction) and electron identification , we rely on the Cesium Iodide calorimeter described in Section 3.2.4. An algorithm in the data acquisition hardware searches for all crystals (out of 7800 crystals) with more than '.: : '. 6 Me V deposited, defines them as seeds and writes them out. Then, any crystal that is one of the 24 nearest and next-to-nearest neighbors of a. seed crystal and has more than '.: : '. 0.-5 Me\! deposited is also written out. The crystal clustering program CCFC takes the crystals written out, and creates connected regions. In these regions, every crystal is the nearest neighbor of at lea.st one other crystal in the region. These regions are then divided if a secondary nucleus is found. The secondary nucleus is defined as a local maximum , separated from the absolute maximum by at least one crystal. Next the region is divided, with the maxima receiving their nearest neighbors and the next-nearest neighbors. CCFC then attempts to divide the energy of the shared nearest neighbors between the nuclei. This helps to resolve the two photons from a 1r 0 which have produ ced overlapping showers. Finally, all rema.ining hits a.re assigned to a cluster if they are the nearest neighbor of a crystal in that cluster . This allows some hits to remain unconnected with any clu ster a.tall [62]. The position vector of a. cluster is calculated in two steps. The first step is the deterrnination of a. centro id from the energy-weighted sum of the coordinates of the geometric centers of the crystals. Due to biases in the centroid met hod , the position of the cluster center must be laterally adjusted. The lateral adjustment depends on the energy and on the proximity of the uncorrected centroid to the geometrical center of the crystal in which it li es. Since there is no longitudinal segmentation of the calorimeter, the correct depth is determined ana.lytically as a fun ct ion of clu ster energy. For both t he lateral adjustment and t he correct depth, a. photon is ass urned to have created the clu ster [6:3]. The cluster energy Ec1,,s, the direction of the cluster from the beam position 0clus 71 and </>c1us, and the measure of the lateral shape of the cluster /f295 defined as : E9 E25 summed energy of the 9 central crystals summ ed energy of the 25 central crystals ' (4.1) where the most central crystal contains the cluster center, a.re all useful parameters. Photon clusters tend to have higher values of f 2~ than splinters from ha.dronic showers (split-offs). To enhance the utility of f 9 , 25 a. quantity PJ~ 5 is computed from Ec1u.s and 0c1us· It is designed such that for any given energy and angle , 99% of all photon clusters will have /f:}5 greater than PJ~ 5 . 4.1.3 Track-Cluster Matching With the tracking chambers for charged particles, and the calorimeter for photons, we a.re poised to reconstruct the entire event. This full reconstruction of the event is essential for the reconstruction of the pseudo rest frame lepton spectrum . This special frame of reference improves the sensitivity to the parameters and is described at length in Section 7.1. Accurate measurement of cluster energy is necessary, but not sufficient, for determining photon momenta.. Charged particles can also create substantial clusters , depositing energy through haclronic and electromagnetic interactions, and specific ionization losses. To discriminate between the clusters ca.used by photons, and those from charged particles, we associate the tracks with clusters. If a track left by a. charged particle projects directly into a. cluster, the chances that the cluster wa.s ca.used by a. photon are very slim indeed. Unfortunately, a simple projection of the track to the calorimeter with a cut on cluster proximity turns out to be completely inadequate. Very often, the centres of hadronic showers a.re quite far from the track projection, while at lea.st one crystal in a. cluster is usually near the proj ection. Further , the depth to whi ch a. track is projected is critical. Tracks with appropriate valu es of p1 will often graze th e calori meter, hitting crystals a.long their entire tangentia.l approach, never reaching an otherwise reasonable projection depth. Finally, some ha.droni c reactions give ri se to secondary photons (or even charged particles ) which travel back into the central detector and reenter the calorimeter, creating a disconnected region that would idea.lly be associated with a. track. To address these difficulties we use the CDCC [64] program which matches each track to multiple clusters and vice versa. It tries every track-cluster combination. If a. track passes within 8 cm of the clu ster center (TYPE = 1), or within 8 cm of a crystal within the cluster (TYPE = 2) , the cluster is matched to the track (and vice versa) . All TYPE = 1 or 2 matched clusters a.re cons idered to belong to the track. The subtlety of the method comes in the calculation of the distance of approach. The matched energy Ematch for a. track is defined as the cluster energies summed over all clusters with TYPE = 1 or 2 matches to that track. For identifying electrons Emal. ch/ Ptra ck 4.1.4 is a very useful quantity. M non Identification Muon identification is clone with a set of cleclicatecl detectors: the muon chambers described in Section 3.2.6. The muon id entification package MUTR [65, 66] extrapolates DUET tracks and its error matrix with a. muon hypothesis, ta.king into account specific ionization energy loss (clE / cLr), mul tiple scattering, and curvature from magnetic fields. Muons in this analysis a.re identified using the SMID [67] software package which improves on the MUTR performance in the Monte Carlo simulation. In the data., SM ID requires that DPTHMU 2 5 for tracks above 2. 0 GeV /c in momentum and DPTHMU 2 3 for tracks with a momentum in the 1.5 - 2.0 GeV /c range, where DPTI-IMU denotes the maximum number of absorption lengths that the particle penetrates in the muon counters. Tracks with a momentum clown to 1.0 Ge V / c can penetrate the first set of counters in the muon chambers located at approximately :3 absorption lengths. However, these tracks a.re not utili zed in this a.naJysis because the muon identification efficienc ies measured in the data a.re not well known * below a. momentum of 1.5 Ge V / c. SM ID further requires that the penetrated depth be con*T he 1.0 - 1. 5 GeV /c mom entum muons in crease t he samp le size consid erab ly. T he small er statistical errors obtai ned as a result of th e increased statistics , and the inclusion of a more sensit ive momentum region is offset by t he fact that th e errors on the Michel para.meters are now dominated by systemat ic errors res ulting from the poor knowl edge of t he muon identificat ion effi cienci es meas ured in t he data usin g µp and µp 1 events . sis tent with the expected dep th determined from t he track's momentum meas ured in t he tracking chambers (MUQUAL = 0) , t hat the total shower energy deposited in the calorimeter and matched to the track under consideration be less than 600 Me V , and that the track li e in the good barrel region of the detector defined by cos 0 S 0. 71 , where 0 is the polar angle of the track with respect to the beam axis. In the fonte Carlo simulation, the SM ID softw are package reads look-up tables with muon identification efficiencies and fake muon rates measured in the data. A real weight between 0 and l is set expressing the probability that the track is a muon . Finally, a logical flag is set if a random number is less than this weight. 4.1.5 Electron Identification To identify electrons, we utili ze the SEID [68] software package which reli es upon two independent and powerful pieces of information: dE / cl:r measurements from the tracking chambers and the ratio of the energy meas ured in the calorimeter to the momentum of the track E /p . In the data, SEID req uires that SGELDI > -2.0 , where SGELDI is t he difference between the measmecl clE / ch and the d E / cl.r expected for an electron di vided by the resolut ion , and E /p > 0.85. T he momentum of t he track under consideration is also required to be greater than 500 Me V / c, since electron id entification efficiencies (meas ured in the data using ee and ee, , events) are both high and well understood above this minimum momentum req uirement. The track is also required to li e in th e good barrel region of the detecto r. In the Monte Carlo simulation, SEID reads look-up tables with run dependent electron identificat ion efficiencies and fake electron rates measured in the data. A logical fl ag is set to identify the electrons in an manner identical to the one in t he SM ID software package described above. 74 4.1.6 Reconstruction of 7io -+ 1 1 Decays 1 Energy clusters a.re analyzed with the CCFC package. Unmatched barrel showers above 100 Me V in energy and lying in the good barrel region of the detector ( I cos 01 :s; 0.71 , where 0 is the polar angle of the shower with respect to the beam a.xis) a.re used in the reconstruc tion of the 7r 0 's . No requirement is ma.de on either the quality or shape of the shower. Thi s res ults in a high 7ro finding efficiency which is relati vely insensitive to un certainties in the modeling of photon showers in the Csl calorimeter and split-offs from ha.droni c showers by the GEANT-based Monte Carlo program. Reconstr1.1ction of 7ro decays is well simulated by the lVIonte Carlo program , as seen in Figure 4.1. T he di stribution of the difference between the invariant mass, rn,,,Y and the 7ro mass, normalized to the mass resolution , <TTn is shown here. The mass resolution varies from 5 to 10 Me V depending on the photon energi es and angles . The peak position, width , low mass tail, and background level a.re all well reprodu ced. 4 5 0 0 . ,........,---,-----,----,----,---,---,---,---,---,---,--,.......,---,-----,----,----,---,---,--, . - , MONTE CARLO e DATA 3000. U) 1- z w > w 1500. S.B. S.B. 0, -----!ll!!!!!L-L-.J.--1...-.L....1,_...L.._~l!l!lll,-----10 10 Figure 4.1: The difference between the 11 effective mass and the 7ro mass, normali zed by the rneasurement error. This distribution includes both electron and muon mode events , and has been shifted by 0.5 CT to allow for sym metri cal signal and sideband regions shown . 75 4.2 Event Selection We use the 4S2-4SA data sample which comprises -:::: 3.5 pb- 1 of data. The different data sets considered and their luminosities are listed in Table 4.1. Frorn t he luminosity-weigh ted cross section, the total sample corresponds to :3 .2 x 10 6 produced tau-pairs. Data Set 4S2 4S3 4S4 4S5 4S6 4S7 4S8 L1S9 4S A Collection Dates Nov 1990 - Jun 1991 Sep 1991 - Feb 1992 Apr 1992 - May 1992 Jul 1992 - Oct 1992 Nov 1992 - J an 199:3 Mar 1993 - Jul 1993 Aug 1993 - Sep 1993 Nov 1993 - Jan 1994 Jan 1994 - Feb 1994 Luminosity I 642 pb- 1 620 pb- 1 315 pb- 1 32 '> p I) -1 :318 pb- 1 463 pb- 1 ·)82 ~c p)I - 1 347 pb- 1 193 pb - 1 ~ Table 4.1: Luminosity break-down for the different data sets considered in this analysis. 4.2.1 TAUSKM The analysis begins with the tau skim cuts listed below. A skim is a set of loose preliminary event select ion criteria. performed to reduce the large initia.l data. sample to a more manageable size. This ski m is designed to provide an enriched sample of tau events without losing a significant number of t hese events. Since it is rarely possible that the skim requirements have no effect on t he signal, skim cuts whose effects a.re well modeled by the Monte Carlo simulation are selected . 1. vVe require between two and six "good" charged tracks. A good track is defined as one with hINCD = 0 and IDB CD I s; 0.01 , where hJNCD = O is the track classifi cation for a good primary t rack, and DBCD is the signed impact parameter with respect to the run-averaged beam spot. 76 2. T he total charge in the event I I: QI ~ 1, where Q is the charge of t he tracks seen. :3 . \Ne requi re no more than on e charged track ·with momentum greater t han 85% of the beam energy, to reject Bhahha. scattering e+e- ___, e+e- (,) and mu-pair events fl +p- ___, p+p-( , ' ). LL T he total visible energy in the electromagnetic ca.lorimeter m ust be less t han 85 % of the center-of-mass energy, to reject Bha.bha. events. 5. \ Ne require the visible energy in the charged tracks (assumed to be pions) and neutral showers to be greater than 20 % of t he center-of-mass energy, to reject two-photon physics, cosmic rays, beam-gas events, and spurious triggers . 6. If the number of good tracks is five or six, we require E.LASGL -/:- 10,11 to reject events identified as hadronic events, where KL ASGL is a global event classification variable. Events satisfying this selection cri teria. a.re writ ten into a separate data stream for offiine analysis. All other cuts appli ed a.re li sted below and are specifi c to this analys is. T he first set of cuts descri bed a.re designed to select t he event topology with a. high effi ciency. Addi tional cuts identify the lepton an d tag side of the event. Finally, we li st the cuts appli ed to minimi ze background contamination from a myriad of potentiaJ sources. Chapter .s di scusses these in detail. 4.2.2 Event Topology Events with exactly two "good " tracks are selected. A track is defined to be a. "good'' track when in addition to I~IN CD 2 0, and IDB CDI ~ 0.01 a.s defined earli er. IPQ CD I 2 0.1 , where PQCD is the signed t rack momentum. Events with three such defin ed good tracks a.re retained if TRKMAN t di scard s any one of t he t hree tracks. tTRh. MAN at.tempts to clean up eve nts by imp osing careful track q uali ty cuts a nd set.t ing a fl ag wh en it decides a track is sp ur ious . A track can be spurious for many reasons, as descr ibed ea rli er in t. his chapter. 77 The two good tracks are required to li e in opposite hemispheres, i.e. , separated by at least 90° in angle to ensure that they are produced from the two distinct tau leptons in the event. Further, ,ve require charge conservation : I: Q = 0. Events ·with one and only one iTo with an invariant mass, rnT, lying within 3 aof the 71" 0 peak ( Sl G N AL) a.re selected as shown in Figure 4.1. We note that the pea.k was shifted by 0 ..5 a- to make this a symmetric requirement. To estimate the combinatoric background , the sideband regions (S.B.): 5 < l(m-r1 - mrro)/o-,., 1 < 8 are used . The si deband subtraction also suppresses "feed-up" from T - t 1r11, events, where the random combination of showers result in a fake 7ro. Events with more than two photons may result in multiple combinations. The combination with the lowest energy unused photon-like cluster in the barrel is selected . Photon-like clusters are unmatched clusters with Ec1u.s > 50MeV, E9/E25 greater than PJA 5 , and li e more than 30 cm from the track. This choice does not force the combinatoric background to peak under the signal region . Hence, the sideband subtraction procedure is bias free. The track that lies closer in angle to the reconstructed 7ro is assigned to be the hadron from the decay of the tag tau lepton . Using a Nionte Carlo simulation of the decay topology, we find that the upper limit on the probability of this track assignment being wrong is 1.2 x 10- 4 at 90% C .L . for events where the other tau lepton decays into a muon, and :3.0 x 10- 5 at 90% C.L. for events where the other tau lepton decays into an electron. Since this wrong assignment probability is very small, it is neglected. No particle identification requirements are ma.de on this track , but we do require that its momentum be larger than :300 Me\! /c, and that it li es in the good barrel region of the detector (as defined earlier) to ens ure good tracking and trigger efficienci es. The track that lies further a.way in angle to the reconstructed 7ro is subject to lepton id ent ification criteria. and must be identified as either an electron or a muon. The SEID and SMID software packages a.re used to identify electrons and muons respectively. Both these packages treat the data and the Monte Carlo simulation events differently as described earli er in this chapter. 78 The event should trigger at least one of the seven 11011-prescalecl trigger lines. All events are also required to pass the Level 3 trigger selection criteria.. 4.2.3 Cuts to Minimize Backgrounds Stringent requirements are made to exclude any events with unused showers in the electromagnetic calorimeter. These requirements are designed to minimize the feedclown of multi-71' 0 tau decay modes into the tag mode. The tag mode is used to reconstruct the pseudo rest frame spectrum, and the presence of feed-clown modes would bias this spectrum. The highest energy unused shower in the good barrel region must satisfy Ec1us < 75 Me V , and the highest energy unused shower in the end caps (0.71< I cos 01 < 0.95) must satisfy Ec1us < 125 MeV. This veto on the event is applied only if the unused shower is isolated (more than 30 cm from closest track) and if its E9/E25 is greater than P~~ 5. Clusters which lie within 30 cm of each track are ignored as they are often clue to final state or decay radiation , bremsstrahlung and/or hadronic split-offs. Events with high energy unused showers which do not pass the photon-like selection criteria are discarded if the energy is greater than 125 Me V in the barrel or greater than 250 Me V in the end caps. In the "hot " region (I cos0I > 0.95) , an event is discarded if there are any showers with energies greater than 500 MeV. These veto requirements a.re further discussed in Section 5.1.2. Cosmic ray events in the muon analysis a.re reduced by requiring that the two tracks a.re not back-to-back: Iii +z.Sl/(lz.JII + lz5;1) > 0.05, where l-½ and l½ are the momentum vectors of the hadron and the lepton track respectively. Radiative Bhabha contamination in the electron analysis is minimized by requiring that the track assigned as the hadron in the event be inconsistent with being an electron, i.e., the SEID software package should not identify it as an electron. The average of the z-positions for the two tracks , ZVPTX at the point of intersection of the two tra.cks in the :T y plane , is required to be less than 0.05. The momentum spectrum for all events that survive all the above listed criteria is utilized to measure the Michel parameters as described in Chapter 7. 79 Chapter 5 Backgrounds Figure 5.1 shows the classification of backgrounds clue to all possible sources . Fake leptons a.re the single most dominant source of backgrounds and a.re described in detai l in Section 5.1.1. Fake muons a.re significant and a background subtraction is performed to remove their contribution. Feed-clown from other tau decays mimicking T- -----+ h-Jro 11r decays is minimized and discussed in Section 5.1.2. All other back- grounds a.re heavily suppressed by selection criteri a.. All non-T background sources (including the two-photon production of tau-pairs ) a.re estimated to total less than 1% for ea.ch mode . BACKGROUNDS TAU BACKGROUND NON-TAU BACKGROUNDS BHABHAS HADRONIC UDCS MU-PAIRS SIGNAL SIDE FAKE ELECTRONS 2-PHOTON PHYSICS BEAM WALL BEAM GAS COSMIC RAYS TAG SIDE FAKE MUONS FEED DOWN FEED UP Figure 5. 1: All potential background sources. BB 80 5.1 T Background Feed-a.cross from tau-pair decays is the dominant background source. Fake leptons fe ed into the signal side of the event and tau decays into modes with multi-1r 0 's fee d into th e tag side of the event. 5.1.1 Fake Leptons The data. events in this analysis (e-Jrn° ), and closely related data events, are utilized to estimate the fake lepton background spectrum . First , we calculate the probability that a hadron fakes a lepton signal , and then we estimate the number of hadrons in the sample that could potentially fake the lepton signal. The product of the momentum dependent fake rates and the potential hadronic spectrum res ul ts in a good est imate of the fake lepton spectrum. The moment um dependence and normali zation of thi s background spectrum a.re estimated entirely from the data. Knowledge of the background spectrum 's moment um dependence is crucial to this analysis , since the Michel para.meters are measured from the shape of the lepton momentum spectrum. The leptons in this analysis are identified as e or fl and the hadron is "tagged" by requiri ng a nearby reconstructed 1r 0 . The probabilities that hadron s fake leptons P(h ---+ e) and P(h---+ fl) a.re obtained by applying the lepton identifi cation cri teria. to the ha.dronic track ( tag decay mode) in the event. Events with two leptons and a fake 1r 0 in this sample could potentially bias the fake probabilities. Such events arise from radiative lepton-pairs and are heavily suppressed by the selection criteria. Further, the small remaining fake-1r 0 backgrounds ( ~ 2% of the sample) are explicitly removed with a 1r 0 -sideband subtraction of the probabilities . T he e-ta.g and fl-tag samples have consistent fake rates after thi s subtraction, yielding no indication of any residual lepton contamination in the hadron sample. The pa.rent hadron distribution is obtained by examining the track recoiling against the h1r 0 system in t he data. Here, by discarding all identified elect rons and muons, we obtain a hadron distribution normalized to the data sample. This pa.rent hadron sample contains hadrons from all possible sources, including the decays of intermediate 81 resonances such as the p± or t he at , where the photons from 1r 0 decay are not found , or do not satisfy our criteria. for vetoing the event. It also contains rea.l electrons and muons which do not satisfy the lepton identification cri teri a, but , si nce the lepton identificat ion efficiencies are close to 100% in the region of interest (above 0. 5 Ge V / c in the electron mode and above 1.5 Ge V / c in the muon mod e), this lepton contamination in the hadron sample is small. Hadrons which fake leptons are depleted in thi s ha.dronic sample, since t hey were identified a.s leptons and thus removed. Again , this is a. small effect since the fak e probabilities are small as shown below. Electron Fakes Electron s a.re identifi ed using E/p and dE / clx . Since the two identification criteria. a.re independent, the probabi li ty for a. hadron to pass ea.ch requirement separately is measured, and the two resulting probabilities are multiplied together for ea.ch momentum bin. The resulting fak e probabi li ties are shown in Figure 5.2 as a function of the hadron charge and the momentum. At low momentum, the probability that a. positive hadron showers in the cesium iodide is higher, thereby satisfying the E/p criteri on . T hu s, positive hadrons have higher fake rates below 2.5 GeV/c . 1.00 ,,,---.., ~ • h-h+ 0 .75 '--/ ,,,---.., Ht j Q) t .50 ..c '--/ Q_ ++ .25 + ¢ ¢ ¢ .00 0 + * t dH ? ¢ 2 3 4 5 Momentum (GeV/ c) Figure 5.2: Probabili ty for a hadron to be identified as an electron as a. fun ction of t he momentum and charge of the hadron. T he errors a.re both stat istical and systematic. 82 Backgrounds , variations of rate with angle , and the 1r / 1,· content relative to that of fake elect rons in the signal sample can lead to systemat ic effects and increase the errors on th e meas ured fake rates from± 5% to ± 1-5 % (integrated over momentum). The fak e electron rate ranges from 0.1-0. 5%, depending on the moment um and the charge of the hadron considered. Since this rate is small , fake electron s a.re neglected in the nominal calculations and a systematic error is evaluated to cover the resulting bias. Muon Fakes Muons are identified usmg DPTHMU ~3 for 1..5 Ge\! / c ~ P 1-1. < 2.0 Ge\! /c and DPTHMU ~5 for P1-1- ~ 2.0 Ge\! /c , MUQ UA L = 0, and L s Es ~ 600 lVIeV , where DPTHMU denotes the maximum number of absorption lengths that the particle penetrates in the muon counters, MUQU AL =0 denotes that this depth is comparable with the expected range determined from the track 's momentum in the drift chambers, and L s Es denotes the total shO\ver energy matched to t he track. Approx imately onethird of all hadrons deposit more than 600 Me V in the electromagnetic ca.lorimeter a.s shown in Figure 5.3. The few muons that deposi t more than 600 Me\! in this figure a.re probabl y hadrons that have been misidentified as muons . .----, HADRONS (DATA) ~ MUONS (DATA) 10-' =-====-'-""""'---"-"u.L...1.---"LC...Jo.___.___.___......,.___,_,_,u....u._._, 4 3 0 2 L EsHowER ( GeV) Figure 5.3: The total shower energy associated with the haclroni c (histogram) and muonic (hat ched region) tracks in the data sarnple. Both energy spectra have been normalized to unity. 83 The determination of the fak e muon probabilities and their moment um dependence a.re described in detail in Appendix B. The probability that a. hadron would fake a. DPTHMU = 3, 5, 7 signa.l in the muon counters, shown in Figure B.2, ,vere obtained after the add ition of the total shower energy cut described above. Above 2.0 Ge\/ /c moment um , the fak e muon rate ranges from 1.5 - 3.0% depending on the momentum, and below 2.0 Ge V / c the fake muon rate is a.s high as 8% . We furth er note that the Monte Carlo simulation of these fake probabi li ties does not identi cally reproduce t he data. [69 , 70] * . To obtain an es timate of the fake muon spectrum, vve now need a. good estimate of t he parent hadron distribution normali zed to thi s data. sample. Followi ng the procedure described earlier in the sect ion , we obtain using t he data, the di stributions shown in Figure 5.4(b) before and after t he appli cation of t he total shower energy cut. These di stributions a.re normali zed to the muon momentum di stributions shown in Figure 5.4(a ) and include hadrons from all possibl e sources . The maximum shower energy requirement clearly reduces the hadronic sample, but leaves the muon sample approximately un changed. 1200. e u '-.... >(].) (_') 1200. ,---, NO SHOWER CUT ,-,. (b) .--, NO SHOWER CUT ,-,. AFTER SHOWER CUT e u '-.... >(].) 800 . (_') AFTER SHOWER CUT 800. s'-.... 0 ....__, '-.... (/) (/) I- I- z 400. w > w z w > w 400. ••••• •••••• ••••• • • • • •••••••••• •• 0. 0. 1 2 3 4 5 1 2 3 4 5 Ph (GeV / c) Figure 5.4: Tlw figure on the left (r ight) show s the muon (hadron) momentum spectrum before a.ud after the a.pplica.tiou of the maximum shower energy requirement. All distribution s have been obtained in t he data. and are absolu tely normalized with respect to each other. Pµ (GeV/ c) *This exercisl:' to meas ure t he fak e rates usin g th e data was redone by ot her memb ers at. C LEO [71] with a larger data set, and th e Monte Carl o simul at ion has now been tun ed to read in th e fake rates as meas ured in th e data. . 84 The bin by bin product of the moment um dependent fake rates and the parent hadron distribution leads to a momentum dependent estimate of the fake muon spectrum normalized to the muon sample. This es timate is obtained entirely from the data and is approximately 1% integrated over the momentum range studied in this analysis. In Figure 5.5 we shmv the momentum dependence of this fake muon spectrum in the laboratory fram e ( a) and the pseudo rest frame (b ). The hatched histograms indicate the shape of the corresponding muon signal. 30.0 (a) ,.,....,, V ('.) 20.0 0 0 ,._,, '--. (/) 5.0 1- z (/) z w > w HADRON MUON s;j- 0 ,._,, '--. I- + ,.,. . , 7.5 ++ +++ '--. >Q.) (b) + HADRON , ••• MUON w > w 10.0 2 .5 .0 1.....L.---'--.L...1......L...L.....l.---'-_,___,,-'-"-"-"'-"-'--'-'-'-'--'-'-"""l.'.Ll .0 1 2 3 p (GeV/c) 4 5 .0 .5 1.0 E/ 1.5 2.0 EMAX Figure 5.5: The fake muon momentum spectrum used in the subtraction in the laboratory frame ( pseudo rest frame) analysis is shown in the figure on the left (right). The hatched spectra illustrate the shape of the muon spectra. The number of events in the muon spectrum has been normalized to the number of events in t he fake muon spectrum to compare the shapes . Although the background contamination from fake muons is small ( ~ 1%), it is important since this background clearly a.lters the shape of the spectrum. The fake muon spectrum is subtracted from the signa.l momentum spectrum before the fit is performed to obtain the lVIi chel parameters. Both the normalization and the shape of the subtracted background spectrum are varied to obtain a systematic error arising from the imperfect estimation of the fake spectrurn used in the subtraction procedure. 85 5.1.2 Feed Across Into Tag T -+ hn° u7 Mode In Table 5.1, we list all significant tau decay modes that can feed a.cross into the tag 7+ --+ h+1r 0 Dr mode. Both the branching ratio (Particle Data Group 1996 [72] ), and the detection efficiency, as determined using the generic tau Monte Carlo simulation of these events, a.re shown in this table. The ratio of the product of these two variables for ea.ch fee d-across mode to the sum of the products for all possible modes indi cates the amount of contamination from ea.ch mode. Tag B (%) B X EX 10- 4 E (%) e fl e fl < 0.001 < 0.01 < 0.01 12.03 ± 0.1 4 < 0.001 10.54 ± 0.03 7.46 ± 0.03 271.51 ± 1. 76 192.17 ± 1.36 25.76 ± 0.15 h+271° 1 r 3. 71 ± 0.11 3.14 ± 0.11 9.50 ± 0.14 0.39 ± 0.01 0.33 ± 0.01 0 h+31r 1 7 < 0.001 < 0.001 < 0.01 < 0.001 1.28 ± 0.10 0 3 h+41r !Ir 0.01 ± 0.01 ( 1.8 ± 0.6) X 10< 0.01 < 0.001 < 0.001 J{o;r+;ro Il r (4.1 ±0.6) X 10- 3 2.64 ± 0.10 1.72 ± 0.08 0.01 ± 0.01 < 0.01 0 3 A' s+71o /IT ( 1.38 ± 0.32) X 10- 2.36 ± 0.21 1.41 ± 0.16 < 0.01 < 0.01 3 A'+ J{ 0 DT ( 1.55 ± 0.28) X 10- 0.05 ± 0.03 0.08 ± 0.04 < 0.01 < 0.01 ;r+17710 Dr ( 1. 71 ± 0.28 ) X 10- 3 0.01 ± 0.01 0.01 ± 0.01 < 0.01 < 0.01 71+wDT 1.17 ± 0.20 0.67 ± 0.14 1.91 ± 0.09 0. 35 ± 0.07 0.61 ± 0.10 3 71+w1ro Dr (4.1 ±0.6) X 100.01 ± 0.01 0.01 ± 0.01 < 0.01 < 0.01 h+DT h+1ro Dr All modes 275.90 ± 1.77 196.49 ± 1.38 Table 5.1: Feed-clown and feed-up modes for both the muon and electron sample. B denotes the input P article Data Group ( 1996) branching ratios and E denotes detection efficiency as determined by the generic tau Monte Carlo simulation. All errors a.re statistical only. The w particle in the last two entries in the table decays via the decay mode w --+ 71° ,. The sum over the products of the branching ratio and the efficiency for ea.ch of these modes is used in the branching ra.tio calculation show11 in Chapter 6. 'vVe note that multi -71° modes feed-down into the tag mode when one or more of the 71° 's in the decay are not reconstructed . The largest background conta.rnination result s from the feed-clown of the 7+ --+ 1r+271° Dr decay mode. This feed-clown is 86 minimi zed by the appli cation of cut s on the highest energy, isolated unused t showers in both the barrel and endcap regions of the CLEO II detector. After these cuts, vve find t hat the backgro und from this mode is ( 1.34 ± 0.04 )% in the elect ron sample and (l.60 ± 0.05)% in t he muon sample. Removing the extra energy veto requirements, t hese background levels are a.s m uch as ten t imes these levels. In Figure 5.6 we show on a logari thmi c scale, the energy distribution of the highest energy unused shower in the barrel region defined by I cos 01 ::::; 0.71 , where 0 is the polar angle of the photon with respect to the beam a.xis. T he photons in t he distribution on the top of this figure survive "good" photon selection defined by t he l % E9 /E25 cut and lie more than 30 cm from the closest track. T he photons in the second distribution all fail these two criteria. The nominal cuts appli ed on t hese distributions are indi cated by the arrows. We require that the event not have any isolated unused shower passing the photon quali ty requirement above 75 Me V in energy. For showers which fail the photon quali ty and distance req uirements , t hi s maximum energy allowed is raised to 100 Me\/. \Ne no te that t he agreement between the data and t he generi c T Monte Carlo simulation whi ch includes the feed- clown modes is reasonably good, even out to large energies. The difference between the signal IVlonte Carlo dist ributi ou and the generi c , Monte Carlo distribution indi cates the size of t he feed-down . These veto requi rements remove signal events with radiative photons, hadroni c spli t-offs and/or beam related showers. These photons are all modeled in the Monte Carlo simulat ion . T he systematic error associated with their imperfect modeli ng are addressed in Section 9. In Figure 5.7 the di stributions for the highest energy unused isolated showers in t he end cap region of t he detector are shown . Once again t he figure on the top plots photons that survive the photon quali ty requirement, while t he figure shown on t he bottom plots showers t hat fai l this requirernent. T he veto cuts appli ed in the endcap region of the detector a.re loose r t han the corresponding cuts in th e barrel region on the detector , since photons in the endcaps are not as well simulated as the ones in the barrel. Further , the beam related noise is more in t he end cap region, and the t An unu sed shower is one t hat is not used to reconst rn ct t he 7ro . 87 > 10 e DATA .------, MONTE CARLO 4 ~SIGNAL Q) (_') lf) 0 ci 1o' ..___,, "z . (/) 1- w 10 2 > w 10 1 .0 > 10 .5 H 1.0 1.5 E sHowER ( GeV) e+µ B-no Q 2.0 e DATA .------, MONTE CARLO 4 ~SIGNAL Q) (_') lf) 0 .5 H 1.0 E SHOWER ( GeV) 1 .5 2.0 Figure 5.6 : Th e di st ributions for the single highest energy unused shower in the BAR.REL region of the detector. The di stribu tion on the top includ es all the hi ghest energy showers whi ch survi ve some photon quality requirements, while the di st ribution shown at the bottom plots the highest energy shower whi ch fails the photon requirem ents. 88 simulation of the drift chamber encl plate material lying in front of the enclcap crysta.ls is not perfect. 'vVe require that the maximum shower energy for showers that survive (fail) photon quality cut s is 125 MeV (150 MeV ). ~ 10 e DATA .---, MONTE CARLO 4 >Q) ~ SIGNAL 0 3 LO 1 0 0 0 -._., 2 "(/) 1 0 • 1- z w ~ 10 1 1 .0 10 .5 H 1.0 1.5 2.0 E sHowER ( GeV) e DATA .---, MONTE CARLO ~ 5 ~ >Q) ~SIGNAL 4 O 10 LO 0 0 -._., "z (I) I- 10 3 102 w > w 10' 1 .0 .5 H 1.0 E SHOWER ( GeV) 1.5 2.0 F igure 5.7: The distributions for the single highest energy unu sed shower in the ENDCAP region of the detector. The distribution on the top includes all the highest energy showers which survive some photon qua.lity requirements, while the clistri bution shown at the bottom plot s the highest energy shower wh ich fails the photon requirements . 89 All the effi ciencies li sted in Table 5.1 have been calculated after the appli cation of these veto requirements as well as all other selection cuts wit h t he exception of the cos O' requirement used to select events for the pseudo rest fr ame analysis . Events that surv ive either t he electron mod e or t he m uon mode selection cri teria are includ ed in each of these figures. The 1-3% feed-down is relatively unimportant for the laboratory fr ame analysis, sin ce the lepton side of the event is in principle independent of the tag side. Global cut s and the trigger do correlate the two sid es of t he event to a small degree, but this effec t is negligible. On the other hand , this feed-clown becomes increasingly important for the pseudo rest fram e analysis, where the tag mode is directly utili zed to reconstruct t he pseudo res t fram e of t he lepton. After t he appli cat ion of t he cos a, requirement , the background from feed-clown modes is reduced to t he 1. -5-2.0 % level; the cos O' distribution peaks at lower cos a for fee d-clown events as shown in Figure 5.8. T he remaining background is well moclelecl in the Monte Carlo sim ulation , and any uncertain ties associated with the imperfect modeling of the remaini ng background is evalu ated in Section 9.6.:3 . -DATA MUON MODE e SIGNAL MONTE CARLO X 11211° MONTE CARLO + m1°K MO NTE CARLO 0 10· 10' 10' 10' 1 .925 1.05 .80 .925 1.05 ELECTRON MODE 10' ,,,,1 10' 10' 1 I 10' I I/ ~ - .925 cos C, .1.05 Figure 5.8: coso plots for the data (soli d hi stogram) , t he signal Monte Carlo (clots), as well as t he two most signifi cant fee d-clown modes . T he bac kgro und has been normali zed to t he data. 90 5.2 Non-T Backgrounds In this section, we consider all t he non-tau background so urces li sted in Figure .5. 1. First , cosmic-rays, mu-pairs , beam wall and beam gas event s can enter t he sample. Second , two photon events e+e- -; e+e-T+T- , in which the two electrons escape detection by the CLEO II detector at low polar angles can survive t he selection criteri a.. Third , radiative Bha.bha. events ca.n fake t he 1r 0 in the event and enter the electron sample. Finally, we consi der the ha.droni c udsc + and BB backgrounds. Data. is used wherever possible to confirm that ea.ch of these background sources can be neglected . 5.2.1 Cos111ic Rays, Bea111 Gas and Bea111 Wall Events These background events typi cally have uniformly di stribu ted vertex Z-positions, as opposed to colli sion related events, which have a. roughly triangular distribution cen tered a.t zero and extending out to ± 4 cm. These sources tend to produce tracks in one hemi sphere and not from the beam spot . The two tracks in t he event a.re used to reconstruct t he event vertex. At t he point where t he two tracks intersect in the :ry plane, ,ve calc ulate the average of the z- posit ions for t he two tracks at thei r respect ive points of closest approach to the beam center in r - ¢, ZVPTX. In Figure 5.9, we show on a logarithmi c sea.le th e di stribu t ion of ZVPTX for the dat a and t he Monte Carlo simulation for all events that survi ve either the electron or the muon sample selection criteri a . We note t hat t he two di stribu tions agree well in the peak region with slightly larger tail s observed in t he data. In t he elect ron (muon) Monte Carlo sample, 0.0008% (0 .0011 %) of all events fall outsid e the IZVPTX I :S 0.05 ·requirement ind icated by t he arrows in the fig ure. These events a.re probably a result of poorl y reconstructed track z measurements. In the electron (muon) data. sample, 0.001:3 % (0.0016 %) of all events fall outside t he allowed ZVPTX region . Th is excess of events in t he data. samples is used to estimate the background contamination from these so urces. Ass umi ng a fl at ie+e - - qij (q = v,d , s , c ) 91 distribution for the background sources, we estimate that there is a. 0.05o/c (0.06 %) background contamination in the electron (muon) sample. e+ µ 10 4 10 3 ci 10 ..____., 2 ,,....... E s;1- 0 0 ........... U) ~ 101 w > w e DATA .----, MONTE CAR LO - ].. • ♦ t .I • ♦ t 10 - 1 '--.L-..l.-...J.LL..u._--'--IL.--L..U..U.---L---''--.L-..J... - .10 - .20 .00 ZVPTX (m) . 10 .20 Figure 5.9: Distribu tion of the ZVPTX vari able in the data. and the Monte Carlo samples . These di st ribu t ions include events that survive either t he electron or t he muon selectrion cri teria.. The background contam ination is negligible; several different requirements help contain the contamination . The TA US h:M req uirement that th e total visible energy of the event be at lea.st 20% of th e ce nter of mass energy rejects cosmic rays and two-photon physics events. Another TAUS KM requirement: there be at most one t r ack with moment um greater than 85% of the beam energy rejects mu-pair events. The full reconst ru ction of the 7ro in the event furth er reduces the contaminat ion from all these sources and the lzii + 1-Sl/( lziil + IP2I) > 0.0 5 requirement contains the contaminat ion from an y remnant cosmic ray events. Th is constraint also helps minimi ze any contamination frorn f.lfl events. 5.2.2 Two Photon Physics Two-photon events are usua.lly low in visible energy and in visible Pt with respect to the beam. Both these quantities a.re calculated using only the charged pion, the charged lepton , and the 1r 0 in the event. The tracks a.re corrected for dE/dx energy losses before they a.re used to reconstruct these variables . The figure on the left in Figure 5.10 shows the Pt distribution , and the figure on the right shows the distribution for the visible energy scaled to the beam energy. All events that survive either the electron or muon selection criteria. a.re included in these figures. We note that the data. and the Monte Carlo simulation agree extremely well, especially in the region close to the cuts indicated by the arrows . There is no excess above the nominal cut requirement and thus we conclude that there is no evidence for any contamination from thi s source. e+µ 3000. ,,--.. e+µ e DATA r-, MONTE CARLO u ,,--.. N 0 0 QJ ~ 2000. : :::::: 2000. 0 - :::::: 1500. (/) - 1z _w - > (/) I- 1000. w 1000. > w DATA MONTE CARLO 3000. ;:- 2500. ~ e r-, 500. 0. L.L.L..l....L...l-'--L.L.L..l....L...1-'--L.L.LL...L...I~--....,__, 2 3 4 0 5 p1 (GeV/c) 0 . ._____.___,___......._-'---'--'--'---L-.L......L-'--.J........1----'-...L--'-""'---'----' .00 .25 1.00 Figure 5.10: Distributions of the visible Pt and the visible energy sea.led to the beam energy. Both these plots have been made after the application of all selection criteria.. To confirm that no two-photon events survive the above requirements we use the variable 0min [7:3] , which is the minimum polar angle that at least one unseen particles must have for the event to conserve both energy and momentum. The angle 93 is defin ed by: 0 rnin = • -1 ( . Sill Pt 2Ebeam - . ) lh P1 - (5.1) , where Pt is the net transverse momentum, Ebea.rn is the beam energy. a,nd 1· 1 , T 2 are the momenta of the t wo charged tracks in t he event . For an y unseen part icles (other than neutrinos) to escape detection , 0min must be below the minimum angle covered by the electromagnetic calorimeter, about 11 °. Hence all t wo-photon events that pass the nominal requirements imposed to suppress them must populate onl y the region with 0min < 11° (the case where both beam electrons travel clown the beam pipe ), while tau decays can populate all angles, becau se the invi sible neutrinos can carry off momentum in any direction. In Fi gure 5.11 , data and tau-pair Monte Carlo events are overlaid in the variabl e 0miir \Ne do not observe any excess of data. over Mon te Carlo events in the region below 11 °, indi cated by the arrow in the figur e. We conclude that the background from t wo-photon physics is less t han 0.1 % and is neglec ted. 2500, e+µ • DATA .----, MONTE CARLO - 2000, (I) t- 1500, z w > w 1000, 500, 0, 0 10 20 30 0MIN Figure 5.11: Distribution of t he 0rnin variable in t he data. and the tau-pair Ivlonte Carlo sampl es . T hese di stribu tions include events that sur vive eit her t he electron or the muon selectrion criteria.. 94 5.2.3 Bhabha Events The cross section for e+e- --+ e+e- is quite large compared to the final states used in this analysis . Thus , the selection criteria. must suppress this process by a factor of roughly 106 to attain less t han 1% contamination. In t he m uon mode analysis , th e muon identification renders this background source negligible since electrons rarely fake muons. In t he electron mode analysis , the TAUSh:M cuts #3 and # 4 (see Section 4.2.1) reduce t he contamination from these events. The full reconstruction of the 1r 0 in the event helps reduce contaminations from Bhabha events among man y other sources . Radiative Bhabha events, however, can fake the e - h.1r 0 signa.l when random combinations of photon-like showers form a fak e 1r 0 . T he 1r 0 sideband subt raction should eliminate these events. In a.deli tion, ,ve require that t he ha.clronic track in the event not be identified as an electron by requiring that it s E /p ~ 0.9 , wh ere p = IPQ CDI is th e momentum of th e track closer in angle to the reconstru cted 1r 0 , and E is the sum over all CCFC shower energies matched to the track under consideration . In Figure 5.1 2, we plot t he E/p di stributions for the hadronic tracks in the electron and muon samples in the data.. Both hi stograms shown here a.re prior to the sicleba.ncl subtraction procedure. The excess of events in the electron sample over the muon sample above E/z1 = 0.9 , inclica.tecl by the arrow , shows the radiati ve Bha.bha event s that survive the se lect ion criteria.. After the sideband subtraction, this excess di sappears . The net effect of thi s requirement is to reduce t he size of the 1r 0 sicleba.ncl subtraction. Another test of the negligible radiati ve Bhabha background is the 0min variable shown in Fi gure 5.11. The presence of these events in the data. would res ult in an excess of events in the 0min < 11 ° region. Vie do not observe any such excess after all cuts, including the E/p cut on the ha.clronic track and the 1r 0 sicleba.ncl subtraction. One can utili ze the charge-weighted polar angle di stribu tion in Figure 5.1:3 to check that Bhabha.s do not contaminate t he sample. Both t racks from ea.ch event a.re entered with their respective cos O multipli ed by charge in this figure. Bha.bha. 95 . 12 ,--,----,---,--,---,----,--.,-----,-----.--,---,----, .----, e MODE .10 e µ MODE .08 .06 .04 .02 .00 L--'-----L..----JL---'----'------'--'---'----'--LC...&--,_J .0 .2 .4 .6 .8 1.0 1.2 E/p (HADRON TRACK) Figure 5.12: E/p distributions of the hadron track in the data. before the sicleba.ncl subtraction and E/p cut s are applied. The excess of events in the electron sample over the corresponding muon sample, above the E/p s; 0.9 cut-off indi cates the presence of the Bha.bha. background removed by the sideband subtraction procedure. events a.re heavily asy mmetric clue to the t channel diagrams and would res ult in large a.symmetries in the extrem e cos 0 bins. The mean of the data hi stogram is 0.0080, consistent ,vith zero and with the tau-pair Monte Carlo simulations. T here is no evidence for any Bhabha background in this distribution. This background is estimated to be less than 0.2 % and is neglected . ci 2000 .----, M NTE CARLO e DATA ...___., '-(/) ~ 1000 w > w 0 .....,...__.....___.___._.__...__.....___.___._.___.__.....___.___.__........, -.4 .0 .4 .8 -.8 CHARGE-WEIGHTED COS0 Figure 5.13: Distributions of the charge weighted polar angle, two en tri es per event, for the data (clots) and the Monte Carlo simulation (solid histogram). 96 5.2.4 Hadronic Backgrounds Hadronic events can be produ ced from e+e- annihilations a.n cl from two-photon collisions. The former have high charged particle multiplicities and little missing energy, whereas the latter typically result in events with low visible energy and visible Pt · Cuts on all these quantities help minimize this background source. The enti re event selection was run on 1.5 x 10 6 full y-simulated misc events; two events survi ved the selection criteria. Taking the ratio of the uclsc cross section to the radiatively-corrected tau-pair cross sect ion to be 3.6, one would expect eight such events in this sample. Since this corresponds to only 0.05 % of the total events , this background source can be neglected. One expects that running on fully simulated BB events, with the BB cross section of 1.07 nb , would lea.cl to approximately zero events surviving t he select ion criteria. Thus this background source is neglected. 97 Chapter 6 Yields and Branching Ratios vVhile it is not a.n intent of this a.na.lysis to measure the electronic a.nd muonic branching ratios of the ta.u lepton, this chapter presents the results obtained in a simple analysis to measure these branching ratios. No attempt has been ma.de to minimize t he systematic errors listed here. The la.test CLEO II measurements for these branching ratios ca.n be found in reference [8]. The leptonic branching ratio is computed using: (6.1) where Ns is the number of events surviving a.11 cuts * including t he 7fo sideband subtraction, .fo is the fraction of the leptons that a.re t ruly backgrounds ( e.g. , hadrons faking leptons) , Nrr is the total numb er of produced TT events, E, the tag dependent effici ency, and B is the ta.g mode branching ratio. The sum -i includes the ta.g decay mod e T+ -+ fi.+7r 0v , , a.long with all other tau decay modes that feed a.cross into the tag mode (see Table 5.1). The overall reconstruction efficiencies for a.11 contributing modes is obtained from the generic tau Monte Carlo simulat ion , and t he 1996 PDG [72] branching ratio valu es a.re used for all contributing modes . The Monte Carlo sample used in these ca.lcula.tions is approximately a. factor of five larger than the data sample t. The total number of produced TT events is given by: , JvT T = ;· L(J,T . (86.86 nb) . = L ( £ clt)run £2_ runs (1 + c5) , ( 6.:2) CM- run *The cos 0c requirement used to select. events suitable for th e reconstru ction of t he pseudo rest. fram e spectrum is ignored here. t Th e :Mich el parameter a nalysis uses a lVIonte Carlo samp le that is twice th e size of the generic tau Monte Carlo samp le used for the branching rat io calculations. T he adclit.ional 50% events com es from t he Monte Carlo generation of the signal modes on ly. 98 where ,C is the integrated luminosity, O",r = 86.856 nb-GeV 2 /s is the luminosityweightecl, radiatively-corrected cross section for e+e- --+ T+,-, and (1 + b) is the radiative correction factor. The h.ORALB Monte Carlo simulation package calculates the required continuum cross section, including mass and spin effects, Z 0 propagator effects, and the radiative corrections to order a 3 . The radiative correction to the point cross section is ( 1 + b) = 1.173, approximately constant in the 10.5 - 10.6 Ge V center of mass energy range utilized, with a 1% theoretical error clue to the uncertainty in the 0( a 4 ) corrections. The cla.ta.. used here were obtained with the CLEO II detector in running periods covering the energies below , and a.t the 1(48) resonance (10.52-10.58 Ge\!). Since tau events created via the e+e- --+ 1( 45') --+ T+ ,-x process are expected to ha.ve many tracks in the event , a.nd tau events resulting from the decay of the BB in e+c --+ 1(48) --+ BB can be neglected as a result of the small B--+ ,Dr branching fraction, it is assumed that all the TT events come from the continuum , and none from the decay of the 1 45. The cross section O"( e+c --+ 1( 45')--+ ,+T-) is expected to be approximately 0.01 pb. The integrated luminosity for each data set used here has been measured usmg \,\.ride angle Bhabha scattering events, f; + e- --+ ''it events, and p-pairs separately with errors of 1.3%, 1.1 % and 2.0% respectively. The three methods used all give consistent resul ts, although the QED cross section comp utations are different , and different trigger lines are important. The res ults for the three processes are averaged, and the overall systematic error on the luminosity determination is estimated to be 1.0% [74 , 75 , 76, 77]. Considering the muon sample, the nominal cuts give Nrr = (2705 ± 40) x 103 , = (196.49 ± 1.:38) x 10- 4 (the sum over all modes contributing to the tag mode as shown in Table 5.1), Ns = 18652, and (1 - fa)= 0.989 ± 0.001. TJsing L i( B 1 x e1 ) Equation 6.1, we get: 17.:35 ± 0.13(a) ± 0.08(b) ± 0.ll( c) ± 0.25(d) , (6.3) 99 where the errors come from ( a.) 0.7% from event statistics; (b) 0. 5% from l\/Ionte Carlo statistics; (c ) 0.6% from ta.g side branching rat ios; (cl) 1.4% from the error on the luminosity measurement. The background subtraction procedure used to remove the hadron-pun ch through conta.mina.tion does not significantly contribute to the error on the branching ratio. The error is dominated by the error on the lumi nosity measurement . For the electron sample, NTT is the sa.me a.s above, '£, ;( Bi x ci) = (275.90 ± 1. 77) x 10- 4 (Tabl e 5.1), Ns = 26815 a.ncl (1 - fa)= 0. 9982 ± 0.0001 lea.ding to: 17.93 ± 0.ll(a) ± 0.06(b) ± 0.ll( c) ± 0.25(cl) (6 .4) where the errors come from ( a.) 0.6 o/c from event statistics ; (b) 0.3% from Monte Carlo statistics; (c) 0.6% from tag mode branching fractions ; ( cl) 1.4% from Nrr · Once a.gain , the error is clomina.tecl by the luminos ity measurement . The efficiency is significantly higher than the muon mode as on e now includ es electrons clown to 500 MeV /c momentum (instead of the 1.5 Ge\! /c moment um cut-off in the muon mode). These ratio of these branching ratio measurements Be/ B 1, can be used to ob ta.in a meas urement of t he low energy spectral shape parameter 17 using Equat ion 2.6:3 t. Using the 7r - t ( IJf! decays to calculate 9 1,/ge = 1.0012 ± 0.001 6, f( 1· 11 ) = 0.9726, and the BES tau mass measurement rnr = (1777 .0 ± 0.26) MeV/c2 , we obtain '17 = 0.02 ± 0.06. The current world average results B 1,. = (17.:33 ± 0.09) %, and Be = ( 17.79 ± 0.09) o/c can be used to calculate 17 = 0.007 ± 0.029. These errors obtained on using the world average meas ureme nts are comparable to the errors obtained from meas ureme11ts in the muon sector. tTh e la rgest. system at ic error contributi on from th e lu min os ity cancels in the rat io of bran ching ratios. 100 Figure 6.1 shows both the electronic and muonic branching ratios obtained in this analysis, along with the corresponding world average values indicated by the hatched regions. The result obtained for B e and B ,, a.re consistent with the corresponding world average results. No attempt has been made to minimize the errors shown in this figure. LL_LJ ,ll PDG 96 El2Q e PDG 96 µ MODE e MODE X e 16 .0 16 .5 17 .0 17 5 18 .0 18 .5 Figure 6.1: The electronic and muonic branching ratios. 101 Chapter 7 Experimental Technique In this chapter, we describe the experimental technique employed to measure the Michel para.meters p a.nd 17 simultaneously, using the energy spectrum of t he charged daughter leptons in leptoni c ta.u decays . The energy spectrum of the charged daughter lepton in the ta.u rest fram e is idea.I to measure both these para.meters. Figure 7.1 plots this energy spectrum in the ta.u rest frame sea.led by the maximum kinema.tica.lly allowed energy in that fr a.me of reference, Ema~, = ( m; + 1n~) /2rn,r , for three different values of the para.meter p. The other Michel para.meters a.re fixed to their Standard Model expectations, a.nd we note that the three di stributions shown here a.re clearly distinct over the entire range plotted. - p = 0.75 • p = 0.00 ------ p = 1 .00 ......•····· .·• ..·• ..·• ..· ..•····· .... ...... ···•••••••••••·· .. ........ .00 .25 .50 .75 1.00 x=E/Emax Figure 7.1: The :r: = Ee/ Emax distributions in the ta.u rest fram e for different values of the p parameter. Each distribution has been normalized to have unit area.. vVhen both the tau lepton a.nd the daughter charged lepton (electron or muon) couple to the intermed iate Wf boson as V - A, one gets the Standard lVIodel prediction , p = :3 / 4, indicated by the solid line. If both leptons couple a.s V + A to the Ml_f boson, we expect the same p value. If only the tau lepton couples as V + A, 102 and the light lepton couples as V - A, we obtain p = 0, and the daughter lepton energy distribution in the tau rest fram e has to go to zero at ::r = 1, as indicated by the clotted line. Since the daughter lepton interaction is known to be V - fl to good precision (Table 2.6), in this analysis , we utilize this experimental fact to infer information on the tau coupling to the H/ boson. The energy spectrum of the daughter lepton in the tau res t fram e is also sensitive to the 17 parameter. As seen in Chapter 2, any deviations from the Standard Model expectation 17 = 0, would imply the existence of a scalar coupling which couples with the right-handed tau and the right-handed daughter lepton e. Interference between the amplitudes of this new scalar boson which mediates this coupling, and the Standard Model lVf boson would alter the energy spectrum of the daughter lepton. Figure 7.2 shows the expected change in the scaled muon energy distribution in the tau rest fram e when the 17 parameter is changed by ±1.0 (p=:3/4 fixed). We note that the three distributions shown are clearly distinct. Since this effect is helicity suppressed in the electron spectrum (it correspond s to a flipping of the lepton's spin) and it scales with the lepton mass (equation 2.58), it cannot be observed in the electron spectrum. -71 = +0.0 •71=+1.0 ------ 7/ = -1.0 ,,,::........ 1 d1 1dE .00 .25 .50 .75 1.00 x=E/Emo, Figure 7.2: The T = EP/ Erna.r distributions in the tau rest fram e for different values of the 17 parameter. Each di stribution has been normali zed to have unit area. 10:3 The di stributions in Figures 7.1 and 7.2 imply that the lepton rest frame energy spectrum is very sensitive to both the Michel parameters st udi ed in this thesis . Unfortunately, the two neutrinos in the decay T- -----+ e - ve 11, a.re not detected by the CLEO II detector , ma.king it impossible to reconstruct the tau lepton four-momentum, and thus precluding the explicit reconstruction of the rest frame spectrum of the daughter charged lepton .C. The observed lepton momentum distribution in the laboratory frame of reference is very different from its rest frame counterpart . This distortion is a. resul t of the Lorentz ~ boost at the i(4S) : , 5.29/ 1.777. Figure 7.:3 illustrates the m uon laboratory momentum spectrum for the Standard l\llodel V - A [p = :3/4, ry = 0], the V + A [p = 0, 17 = 0], the 17 = l [p = 3 / 4, ry = 1] Monte Carlo samples. -V-A •••••··....... ... . :·--- ......... e •----,' ...... ' I : "', V+A ----- 77 = 1 • .. . ............ ...;··-: ...... .... .... •; ...... .............. . ...... .. . .... ···········: ........ . .-. ........ . _ 0 2 3 4 5 PLABORATORY Figure 7.:3: The direct laboratory moment um spectrum for t he three different Monte Carlo samples, V ± A , and 17 = 1. Ea.ch distribution has been normali zed to have unit area.. The solid line indicates the 1.5 Ge\! /c minimum momentum cut-off imposed by the muon identification system. \;\le note that maximum sensitivity to the ry parameter li es in the low moment um encl of the spectrum; the high momentum region of the spectrum has much lower statistics since the spectrum falls off sharply at higher momentum. Good muon 104 identification requires a. 1.5 Ge V / c minimum momentum cut-off *, inclica.tecl by the solid line in the figure. Thus, most of the sensitivity to the 17 parameter is lost , and the direct laboratory frame spectrum is not very useful in measuring this parameter. 7.1 Reconstruction of the Pseudo Rest Frame As shown earlier in this chapter, the charged lepton energy spectrum in the tau rest frame is ideal to measure the Michel para.meters. CESR operates far above tau production threshold, where the observed laboratory momenta. of the daughter leptons depends on both the rest frame momenta. and the emiss ion angle clue to the Lorentz transformation. In order to perform a. Lorentz boost into the tau rest frame, the tau four-mom entum must be known. The energy of the tau can be cleterrnined by the beam energy up to initial and final state radiations. On the other hand , the direction of the tau cannot be exactly reconstructed because there a.re neutrinos amongst the daughter particles, and CLEO II , like most e+e- detectors, does not detect neut rinos. In this section , we describe a technique first exploited by ARGUS [9]: the directi on of th e tau lepton is inferred from the direction of t he system of charged hadrons ( h) originating from the decay of the other tau lepton in the event. This other tau lepton ( defined as the "tag" tau in Chapter 4) was required , by ARGUS , to decay into (3h )± or (3h )± 1r 0 . Due to its relatively high mass , these hadroni c systems both give a good approximation to the flight direction of its parent tau and, consequentl y, of the tau under study, since bot h tau leptons a.re fl ying back-to-back. The rest system determined with this approximation defines the pseudo rest frame. Using fits to Monte Carlo samples, ARGUS found that the accuracy of the p measurement was higher in the tau pseudo rest frame by a factor of 1. 5, and that the precision on the 17 measurement improved by a factor of 2. In the analysis presented in this thesis, the tau pair eve nts are tagged by the decay mode T+ __, h+1r 0 v, , Lo take advantage of its much larger branching ratio, *CLEO II muon identifi cation can be extend ed down to 1.0 G eV /c momentum , but the muon id entificat ion effici enci es in the low moment um region are not known well enough for t he precision required in this analysis. 10,5 thus leading to a higher statistics sample. Further, the background contamination is lower when one uses this tag mode instead of the 3h±(7r 0 ) mod es used by ARGUS. The h±-rr 0 system has a lower mass and thu s does not give as good an approximation to the flight direct ion of it s parent mode. \~le thus apply the cos a requirement , as explained below , to select events in whi ch the T flight direction is est imat ed well, and reconstru ct the pseudo rest fr ame for thi s subset of t he entire data sample. Events which fail the cos o- constraint a.re analyzed in the laboratory frame of reference. The electron-positron interactions res ult in tau pairs which are produced back-toba.ck as shown in Figure 7.4. The two tau leptons decay in opposite hemispheres of the detector and t he tag decay mode is used to identify t he tau events, as well as to est imate t he flight direction of its pa.rent tau. o- is the angle between the tau direction in the laboratory frame and the h+ Ko (A) system in the laboratory fram e. SIGNAL SIDE TAG SIDE µ "C Figure 7.4 : Event topology. To reconstruct the pseudo rest fram e we exploit the kinemat ics of the tag T+ --+ A_+;;;r decay, where A_+ is some ha.dronic system . This decay can now be treated like a two-body system , and the conservat ion of the four -momentum in the decay, p2 V l (7.1) 106 leads to the kinematic equation: (7.2) Here, EA , PA and rnA = JE~ - p~ are all measured quantities, and o is the angle of the T direction with respect to the measured hadronic A ( h+ 1r 0 , in this analysis) system in the laboratory frame of reference. Novv, ET = Ebea.m, p, = JEleam - rn~, and assuming that mv = 0, one can calculate cos a, an indicator of how well the true tau direction has been estimated in the event under consideration. Requiring cos a close to unity (cos a 2:: 0.970) selects events in which the tau flight direction is well approximated , thus providing a sufficiently accurate approximation to the true rest frame conditions. Since one now knows both the tau energy, and its flight direction for these selected events, the lepton from the decay of the other tau in the event can be boosted into its parent 's frame of reference resulting in the reconstructed pseudo rest frame spectrum. The cos a requirement has been optimized to achieve maximum sensitivity to the 17 parameter; this optimization is discussed in detail in Section 9.8. Figure 7.5 shows a logarithmic plot of this variable in the electron sample. The corresponding plot in the muon sample is nearly identical to this one. VVe note that the Monte Carlo simulation program simulates this variable very well. This figure also plots the distribution from background multi-1r 0 tag modes , T ----+ 1r-n1r 0 JJ, , n > l , where one or more of the 7fo 's in the event are not reconstructed. This background has a different distribution and could result in a bias in the reconstructed pseudo rest frame spectrum. Fortunately, it can be minimized using veto cuts on extra unused showers in the event, after which it is small as shown here. There are events in both the data and the Monte Carlo distributions with cos a > l , an unph ysicaJ region. These events are few and result from rneasurement errors. They are not used in the pseudo rest frame analysis. The pseudo rest frame spectra obtained for the three different Monte Carlo samples, V ± A, and 17 = l a.re shown in Figure 7.6. Here, one plots the energy of the 107 10 4 ,.......,--,---,---,--,..--,--,--,.--,--,-~-,..-~--,---,---,--,..--,--~--,---,-~ e DATA MONTE CARLO ~ FEED-DOWN r-i 10 3 102 10 1 1 IJ...J.l,.....,~-'----'-.I...-L......J.---1...ELI==""""-=""'-""""-""=al...J,;;eL.....J--L................ . 80 .85 .90 .95 1.00 1.05 cosc.x Figure 7.5: The distribution for the cos o variable for the data (clots ) as well as the generic tau Monte Carlo simulation (solid hi stogram). Backgrounds from multi-7!" 0 modes a.re included in the Monte Carlo distribution in the appropriate proportions (hatched region). The arrow indicates the nominal requirement: cos o 2: 0.970. muon m the pseudo rest fram e, ca.lcula.tecl usmg the ha.clroni c system to estimate th e T flight direction , sea.led by the maximum kinema.ti ca.lly possible energy in the Trest frame EM A X = (rn;, + m;) / 2rn.7 . V\ie note that th e three spectra. a.re distinct over the entire sea.led energy range, thus lea.ding to the improved sensitivity over the laboratory frame analysis. \l\fe furth er note that th e V - A spectrum does not completely resemble the corresponding Monte Carlo true tau rest fram e spectrum shown in Figure 7.1; in parti cular , all the events above :r = 1 a.re unphysi cal in the true rest frame. The difference is primarily a result of th e fact that the ha.droni c system is not a perfect estimator of th e tau flight direction, with contributions from radiative effects and mismea.surement. Tightening the cos o requirement to select "better" estimators of the tau fligh t direction (cos o 2: 0.995 , for ex ample ) would result in fewer entries in th e unphysical region , :r > 1, and the spectra would better resemble their t rue tau rest frame counterparts. This tighter requirement results iu an unaffordable loss in stat istics a.nd is thus not employed. The cos o 2: 0.970 requirem ent is approximately 60 % effi cient , as can be seen 108 .• ... . -V-A e - V+A -- - -- 7)= 1 .0 .5 1.0 1.5 2.0 2.5 x=E/ Emax Figure 7.6: The reconstructed lepton energy in the pseudo res t frame scaled to the maximum kinema.tically allowed energy in the T rest fram e for th e three 1\/Ionte Carlo distributions, V ± A, and 17 = l. Each spectrum has been normalized to have a uni t area, and has been reconstructed using events which sur vive the cos o 2': 0.970 requirement. 111 Figure 7.5. If one utili zed the T+ -+ 7r+7i' - 7r+ D, decay mode in stead , as clone by the ARGUS experiment , the cos o requirement would be approximately 100% efficient, since the 31r system is a better estimator of the tau flight direction . However, the probabi li ty for a tau lepton to decay into the 371'" mode is significantly lower; B( T+ -+ 7r + 7r -7r+ 1 T) '::::'. 13%. Further , there is negligible QED background associated wit h the h+ r. 0 mode, and the full reconstru ction of the entire event helps suppress backgrounds from haclronic , two-photon events and cosmic rays . The ;37r mode has larger qq background. 7.2 Low Momentum Muons The factor of 2 improvement seen by ARGUS in the 17 measurements using t he pseudo rest frame of t he , lepton was not entirely clue to the improved sensitivity resulting 109 from the clear distinctions in the shapes of the spectra observed in Figure 7.6. A significant. improvement resulted from the addition of low momentum muons (p 1, < 1.5 Ge V / c), identified without the use of conventional muon identification techniques. At CLEO II , the muon detectors can be used to identify muons clown to a laboratory momentum of 1.0 Ge\! /c, but the muon identification efficiency in the low momentum region is not flat and is not known to the precision required for the measurements presented in this dissertation. Charged particles with a laboratory momentum between 0.5 and 1.5 Ge\! /c can be kinematically identified as muons in the pseudo rest frame after elimination of all other possible decay hypotheses: evv, 1r11 , J{v , and hn7r 0 v. Figure 7.7 shows a plot of the pseudo rest frame energy for such tracks, scaled to the ma.ximurn possible energy in the tau rest frame, X = E 1,/EMAX where E iVIAX = (rnz,+m;)/2mr. The dominant background modes are also shmvn in this figure. e DATA .---, MONTE CARLO 'Y - e X p ---. 300 ~n/K s;t 0 0 ...__., "(11 1- z cj 150 w • 0 .0 .5 1.0 1.5 2.0 X = E,,/ EMAX Figure 7.7: The scaled pseudo rest frame muon energy spectrum in the data (clots), the V - A. Monte Carlo simulation (solid histogram), for p 's identified kinema.tically. The Monte Carlo spectra for the background modes a.re also illustrated; their contrib utions are small for £ 1,/ EMAX < 0.6 , indicated by the arrow. Ea.ch Monte Carlo histogram has been normalized to the dat a. For the two-body modes 1r11 and A'u, we have Xrr(f,·) = 0.89(0.95) in the true rest frame. This is broadened to the distribution shown as the hatched histogram in Figure 7.7. A cut at X ::; 0.6 reduces the 1r / I{ contamination to (2.6:3 ± 0.21 )%. The 110 electron identification efficiency (E/p::; 0.85 and SGELDl2: 0.3) for electrons with Pe 2: 0.5 Ge V / c laboratory momentum is well known , and is close to 100%. Electron identification is used to veto elect ron-like tracks and to redu ce the electron contamination clown to (0.64±0.11) %. No extra unmatched showers above 60 Me\! a.re allowed, either in the barrel or the endcap region, to minimize backgrounds from /rn° 11 a.nd other multi-pi zero modes; this contamination is estimated to be (0.78 ± 0.12) %. All the background esti mates presented here a.re calculated with the Monte Carlo simulation , a.nd subtracted from the data. Thu s, we recover a. significant fraction of muons lying below the momentum cut-off of the muon identification system. This sample is '::::' 96 % pure. Almost 35% of the background results from the electron and h:rr 0 cont amination. Both these backgrounds are di stributed uniformly a.cross the pseudo rest frame scaled energy spectrum, a.s can be seen in the figure, and do not have a signifi cant impact in this analysis. The result s obtained on analyzing the electron and muon spectrum usmg the pseudo rest fr a.me spectra, as well a.s the direct laboratory frame spectra, a.re described in detail in t he following chapter, and a. di scussion of the various sources of systematic errors is detailed in Chapter 9. 111 Chapter 8 8.1 Fitting and Results Fit Functions The decay spectrum of the charged daughter lepton (using Equation 2.58) , after integration over the two undetected neutrino momenta., a.nd averaged over the ta.u spin direction is: ~ df ( p fd :T . , 2 17) = x l+ 417(m e/m T) [12(1 - x ) + ~ p ( 8 3 x - G) + 2417 (l - x )] , m, :r m , e (8.1) where f. denotes the observed charged daughter lepton , x = E e/ E max a.nd Emax = (m; + m z)/2rnT. The radiati ve corrections do not depend on the Michel parameters a.ncl a.re neglected in this equation. Th e spectra.I shape Michel para.meters studi ed in this a.na.lysis a.re p and 17. These para.meters are not measured using the convention maximum likelihood estimator method . Instead of a. semi-analytic a.pproa.ch, we extract these para.m eter values from a simple x2 fit to a fun ction of three binned Monte Carlo spectra.: 1. the standard V - A spectrum with p = 3/4 and 77 = O; 2. the V + A spectrum with p = 0 and 17 = O; :3. the 17 = l spectrum with p = 3/4 and 17 = l. All effects associated with the boost, acceptance and resolution of the detector, efficiency of a.11 cut s, as well as radiative corrections, are included in the full lVIonte Carlo simulations of these t hree spectra.. Tau-pa.irs are gen erated and decayed with the h oralB( v2 .2) /Tauola( v2.4 ) / Photos( v 1.06) package, followed by the detector simulation package CLEOG using Geant 3. 15. 112 The t rue number of events generated by the accelerator Ny= L Ny;, where 1 clBt Ny , = £ (J" 8 1ur o B,-' <B cl·· f (S.2) './. l is the number of events generated in bin i, £ and O" denote the integrated luminosity and the cross section for c+ e- ---+ T+T- respectively, and Be and B1irro denote the tau branching fractions to the fov and /nr 0 11 decay modes. \'f\!e now use the Monte Carlo simulation to model: 1 cLBe e G:Y; °'"" . -B -i- = L Co..fo:i' (8.3) o: where f c,i is the fraction of events in bin -i for the three Monte Carlo models li sted a bove (V - A, V + A, and rJ = 1) , normalized so that L .f~; = 1 for o, = 1, 2, :3 , and t he three coeffici ents: 4p/3 - TJ C1 = Cv- A = - - - - - 1 + 4q( m,,/m,)' 17[1 + 4( rn"Jrn, )] 1 + 417(rn"/mr) • (8 .4 ) \'!\le note t hat L C0 = 1, independent of the para.meter values p a.nd 17. The pa.rent 0: di st ribution associated with the observed lepton spectrum may now be expressed as a function of the three Monte Carlo mod el di stributions: cfj\fobs - i-(p,'IJ) G:r vvhen one ass umes that the the efficiency .:: 0 JP( .1: lo)E 0 .(:1·)d:r is independ ent of the model ct. T he detection efficiency E0 .(;r) is in fact model independent , but the probability distribution fun ction P(x lo-) does depend on the choice of the model considered , largely a.s a. resul t of the m inimum momentum cut-offs di ctated by lepton identifi cation cri teria.. T hus Ev-A #- Ev+A =J E1J =l , and to account for this efficiency 113 dependence we require an additional correction factor. Now . the number of observed events in each l\!Ionte Carlo sam ple can be written as: J\ r90' '-'"O· , ~ c. L.__,; Ji\Tgo· .Ir 0 ·1. vca C (8.6) where N 90 is the number of events generated for th e model a , f o:i is the fraction of events in bin i of the model a distribution , and t: 0 . = No:/N_qo: is the efficiency for that model. The number of observed events in bin i can also be written a.s: Noi = NTi Ci = [, Be B,u,o L Co f o-i E; (J" (8.7) 0: using Equation 8.3, and thus the total number of observed events: N0 L N oi (8.8) 0: implying that Substituting the re.- ult obtained in Equation 8.9 into Equation 8.7 , the number of observed events in bin i can now be written as: No; i\i j\1 ·) ( 0,_ J\ 10 ~ O' l (8.10) 13 vvhere the term enclosed in the first set of parentheses depends only on the effi ciency E and the Michel parameters p and 17 , while the term enclosed in the second set of lH parentheses is the Monte Carlo spectra. normali zed to the number of observed events in the data N 0 . Thus , t he fun ction used to fit the lepton spectrum can now be written as : dNobs ( ) - l- P, T/ c:r ,, dN . / ' C v- A clx (3 4, 0) + clN C'' v+ A d:r (0,0) + dN / d:.r (:3 4, 1) , C'' 7) =l (8.11) with C~ (p , 17) and with each Monte Carlo di stribution individually normali zed to the integral over the observed data momentum spectrum. The coefficients Ca are the same as shown in Equation 8.4 , and since they appear in both the numerator and the denominator , we note that the ( l + 4 17 m e/ mT i- 1 term cancels. vVe now use t he simplified coefficient s: 4p 71 C v_4=-. 3 'I l . 4p and 3 ' Cv +A = l - - . c 7)=1 1Tl e = 17(1 + 4- ) . (8.12) 17?. T The background subtracted muon data spectrum is n0vv fit to t he function of the three binned Monte Carlo spectra, generated with the different values of t he para.meters, to measure simultaneously the Michel para.meters p and 17. This tvvo parameter fit is simple since the spectra considered are one-dimensional distributions. We nominally use 100 Me\/ bins ; effects associated with the choice of bin si ze a.re di scussed in Sect ion 9.13. As seen in Equation 8.1 , in t he electroni c decay mode, all sensiti vity to t he 17 parameter is lost as a result of the negligible mass of the electron relati ve to the tau mass . Thus Equation 8.11 simplifi es to: dNobs ) ----;;;;- ( p with Cv - A c \ l _A 4p clN dN -z-(3/4 ) + c ~'+A -d (OJ , :r G ;:r - , and 3 C\· +.4 4p = 1 - -3 l (8.13) and a simple one para.meter fit is n0vv used to extra.ct the Mi chel parameter p. Events whi ch survive the cos o 2: 0.970 requirement are analyzed using the pseudo rest fr am e spectrum; t he remainder a.re analyzed using the lahoratory frame spectrum. 115 The Monte Carlo spectra. genera.tee! with the different parameter values for the three different Monte Carlo models , utilized in this fit procedure, are shown in Figure 7.3 (laboratory frame) and Figure 7.6 (pseudo rest frame). The optimization of the Pe , p,,., and cos a cuts, along with a detailed evalu ation of systematic errors a.re described in Chapter 9. Since the results obtained in the two frames of reference a.re stat istically independent, the final results a.re obtained by combining them in a simple weighted average . Correlations between the para.meters, as well as data and Monte Carlo statistics, a.re ta.ken into account when the results a.re combined. 8.2 Electron Mode Results Approximately 60 % of the electron sample survives the cos a :2'. 0.970 requirement. These 18587 events are analyzed in the pseudo rest frame. Figure 8.1 shows the electron energy pseudo rest frame spectrum scaled by the maximum kinematica.l allowed energy, Enwr = (m; + rn;)/2mT. 1200 e 0 1000 00 0 PSEUDO REST FRAME e DATA r--iMC FIT 0 V+A 0 ,,-... s:;j- 0 0 ..__,,. --....,__ (f) 800 0 600 I- z w > w 400 200 0 .0 .5 1.0 1.5 2.0 Xe Figure 8.1: The electron scaled pseudo rest frame data energy spectrum fit to a linear combination of fully simulated Monte Carlo V - A and V + A spectra.. The pseudo res t frame energy is scaled by Emax = (m~ + m;)/2mT. 116 We perform a. x2 fit of the data spectrum to the function of binned JVIonte Carlo V - A and V + A spectra shown in Equation 8.1:3. The coefficients of the fit function a.re used to extract the Michel para.meter Pe· vVe measure: Pe = 0.7:33 ± 0.017 ± 0.007 , (8.14) with a x2 of 51.5 for 46 degrees of freedom. The first error accounts for the data statistics and the second accounts for the Monte Carlo statistics. We observe that the data and the fit to a combination of V - A and V + A Monte Carlo spectra. in Figure 8.1 agree extremely well. We further note that the V + A l\!Ionte Carlo spectra. is distinct from the data over the entire energy range shown. The 12981 electron events that fail the cos a constraint a.re analyzed in the labora.torv frame of reference. The direct momentum spectrum as measured in the la boratory frame is shown in Figure 8.2. 600 e ,..---... 000000 0 LABORATORY FRAM E 00 500 00 • DATA r - i MC FIT 0 V+ A 0 0 0 0 '--.. 0 >(l) 400 0 C) 0 ....__,, '--.. 300 I- 200 c.n z w > w 0 0 0 0 0 0 0 100 00 0 000 0 0 1 2 3 Pe (GeV/c) 4 5 Figure 8.2: The electron laboratory frame data momentum spectrum fit to a combination of full y simulated Monte Carlo V - A and V + A spectra.. Once again, the data and the Monte Carlo fit function agree well, and are well 117 differentiated from the V + A Monte Carlo spectrurn over t he entire momentum range studi ed. The cut-off at 0.5 Ge\/ /c is a result of the minimum moment um requirement for good electron identifi cation. As before, the coefficients of the fit function in Equation 8.13 are used to measure: Pe = 0. 730 ± 0.023 ± 0.008 , (8.15) with a x2 of 36.2 for 44 degrees of freedom. Again , the first error accounts for the data statistics and the second accounts for the Monte Carlo st ati stics . The results obtained in the two fram es of reference considered are statistically independent. They are also consistent ·with each other and with Standard Model expectations. The statistical error obtained in the laboratory fram e of reference is larger than the corresponding error obtained in the pseudo rest frame. Further, it is larger than that expected based on the relative sizes of the two samples . This is an indi cation of the reduced sensitivity to the Michel parameter in the laboratory frame relative to t he pseudo rest fram e. \Ne now form a simple weighted average of the two independent res ults in Equa- tions 8.1 4 and 8.15, to obtain: Pe = 0.732 ± 0.01 4 ± 0.005, (8.16) where the first error results from data statistics , and the second arises clue to the Monte Carlo stati stics. Both these errors are used in calculating the weighted average . They are also the largest so urces of error. Since the other sources of systemat ic errors are independent of t he choi ce of reference frarne , and a.re significantly smaller, t hey are not used in t he calculation of the weighted average res ult shown in Equation 8.1 6. 118 8.3 Muon Mode Results In this decay mode, the two parameters p1, and 17i,. a.re strongly correlated and are measured simultaneo usly. Since the muon mass is not negligible relat ive to the tau mass, we a.re now sensitive to the 17 parameter, although most of thi.· sensitivi ty li es in the low momentum region of the spectrum which is ha.rel to reconstruct using the CLEO II muon identification system . As explained in Section 7.2 , one can recover some fraction of the lost low momentum muons without using the muon identification counters. Including t hese additional 2931 muons results in the discontinuity observed a.t X = 0.6 in Figure 8.3 , where the scaled pseudo rest frame energy spectrum (12580 + 2931 muons) is plotted for cos a 2 0.970. The energy in the pseudo rest fr ame is scal ed by the maximum kinem a.tically allowed energy, Ema.x = ( mz, + rn.; )/2m,,.. This figure also plots the Monte Carlo 17 = 1 spectrum that has been normalized to the data.. \Ne observe t hat it resembles the data over mu ch of the energy range stu di ed. 1000 µ PSEUDO REST FRAME 750 s:;j- 0 0 "z (I) DATA 0 77= 1 - r---i MC FIT ,.---. '-/ • 500 f- w > w 250 0 iea'!.--L....L...J_j____L,_..l........l.----1...._.l_L....L__L.....L.....JL.J.._.....I:::!~- .O .5 1.5 2. 0 Figme 8.3: T he background subtracted pseudo rest fram e m uon data energy spectrurn fi t to a combination of fu lly simulated Monte Carlo V - A, V + A and 7/ = 1 spectra. The pseudo rest fr ame energy is sea.led by E ma.x = (rnz, + rn;)/2m, . The ·17 = 1 Monte Carlo spectrum shown by the open circles resem bles the data spectrum. The discontinuity observed at X = 0.6 , in the pseudo rest fram e spectrum , is a result of the addi tion of muons below t he laboratory momentum of 1.5 Ge\! /c. 119 The coefficients of the fit function in Equation 8.11 are used to extra.ct the Michel para.meters p,,. and 7h, simultaneously. Vl/e measure: P,, and 7h,. 0.780 ± 0.055 ± 0.025 0.140 ± 0.181 ± 0.088 , (8.17) with a x 2 of 26.9 for 34 degrees of freedom, and a correlation coefficient, C'pr, of 0.94:3. The l <Y error ellipse in 17 - p parameter space is shown a.s the clashed contour in Figure 8.5. These errors are much larger than the corresponding pseudo rest frame electron mode result. This is clue to the fact that we now perform a two parameter simultaneous fit, coupled with the lower statistics resulting from a higher momentum cut-off. Another important factor is the fact that the 'I] = l Monte Carlo spectrum closely resembles the Standard l\!Ioclel \/ - A spectrum. Since the two parameters are strongly correlated , fixing one of them to its Standard Model expectat ion improves the sensitivity on the other tremendously. vVe now measure: P,, and 7h, 0.740 ± 0.018 ± 0.007 wit h 7h, fixed at 0, 0.047 ± 0.062 ± 0.022 wit h PP fixed at :3/4. (8.18) The error on the pP· para.meter is still significantly larger than the corresponding error on Pe measured using the elect ron pseudo rest frame energy spectrum. This reduced sensiti vity is entirely a resu lt of the higher 1.5 GeV /c momentum cut-off required for good rnomentum identification. In the pseudo rest frame analysis, one does recover a small fraction of the low momentum muons lost as a res ult of the momentum cut-off. However, it is only a small fraction of all the muons below the laboratory moment um of L5 Ge V / c that are recovered . Muon events (9186) in which the pseudo rest fram e cannot be reconstructed, cos o· < 0.970, are analyzed using their direct laboratory frame momentum spectrum shown in Figure 8.4. Once again, the 17 = l Monte Carlo spectrum resembles the 120 data over much of the momentum range shown. 600 µ ,,.-.. LABORATORY FRAME 0 0 500 e 0 '-... r--i >Q) 400 0 (.'.) DATA MC FIT 77 =1 0 0 ....__,, '-... 300 f- 2 00 c.n z w > w 100 0 0 1 2 3 4 pµ (GeV/c) 5 Figure 8.4: The background subtracted muon laboratory fram e data momentum spectrum fit to a combination of full y simulated Monte Carlo V - A, V + A and 17 = l spectra.. vVe now simultaneously measure: p,,. a.nd 17,,. 0.607 ± 0.111 ± 0.088 -0 .431 ± 0.309 ± 0.259 , (8.19) with a \ 2 of 28.l for 33 degrees of freedom , and a correlation coeffi cient, Cp 11 of 0.972. The solid contour in F igure 8.5 represents the 1 <Y error ellipse in the 17 - p parameter space. These errors a.re twice as large as the corresponding muon mod e pseudo rest frame errors. One clearly observes the increase in sensiti vity obtained by analyzing the data in t he pseudo rest fram e. Once again, the two para.meters a.re strongl y correlated and one can better measure each parameter by fixing t he ot her to its Standard l\!Iodel expectation. We find that: p,.. and 17i, 0.75Ll ± 0.032 ± 0.01:3 with 17,,. fix ed at 0, - 0.0:34 ± 0.089 ± 0.041 with P,, fix ed at :3 /4. (8 .20) 121 All the res ults obtained in the la boratory frame analysis are consistent with the corresponding results obtained in the pseudo rest fram e analysis. They are also consistent with Standard Model expectations. Since the two analyses are statistically independent, we combine the results in Equations 8.1 7 and 8.19 to obtain: pµ 0.747 ± 0.048 ± 0.026 and 7h, 0.010 ± 0.1 49 ± 0.089 , (8.21) where the error contributions from both data and Monte Carlo statistics is used to combine the res ults measured in the two independent fram es . We also account for the correlation bet ween the two para.meters when cakula.ting this combined fram e result. The 1 <Y error ellipse in the TJ - p plane for this combined res ult a.long wit h th e results obtained in the two indi vidu al fram es is shown in Figure 8.5. 1.0 ..----,---,----,-------,-----.----,--,-----,---,----...---,,............--,-~---. - .5 0 LABORATORY FRAME PSEUDO REST FRAME COMBINED RESULT - ,-··, , , , ,,~o'fi, ' t,b o 0 e;/ -.5 -1.0 ~~---~~~---~~~-~~~ .45 .60 .75 .90 Figure S.5: Th e 1 <Y error ellipses in th e 17 - p plan e obtain ed by analyzing the data in th e pse udo rest frame, the laboratory frame and the two fram es together. The hatched region encloses the allowed region in 17 - p parameter space. All contours li e well with in the kinematically a.llowed region 111 17 - p space, as 122 defin ed by the hatched region . There are strong correlat ions between t he para.meters in all t hree results and we observe that each resul t is consistent vvith the Standard Model expectation indi cated by t he point of intersection of the two solid lines in the figure . These errors indi cate the contributions from data and !\!Jonte Carlo stat istics only; the systemat ics errors are addressed in the next chapter. One can also combine t he measurement resul ts for t he two parameters obtained with one parameter fixed to its Standard Model expectation. Combining the results obtained in Equations 8.18 and 8.20, we obtain: p,, and r;" 0. 743 ± 0.016 ± 0.006 with r;" fix ed at 0, 0.022 ± 0.051 ± 0.020 wit h P P fi xed at 3/4. (8.22) Once again , these resul ts a.re consistent wit h t he Standard Model expectations. A large number of experiments (MA C [78], ARGUS [79] and CLEO [80]) have measured p,, ignoring the r; para.meter correlations . This res ult compares well with th ese experiments and is much more precise. 8.4 Invoking Lepton Universality The res ults prese nted in t he previous two sections, which meas ure the Michel parameters using electron an d muon events, are consistent with each other. V-/e now invoke lepton uni versa.lity in the vector- like couplings whi ch requires t hat Pe = Pw The two parameters can now be extracted from simultaneou s fits to both t he lepton spectra. used in t he electron a.nd muon analyses . Such a procedure takes a.dva.nta.ge of t he fad that t he electro11 sample is in sensit ive to the 17 parameter a.· a. res ul t of t he m ,./rn , suppression (see Equat ion 8.1 ). The precise measurement of p,. helps constrain Pe,, thus reducing the correlation between the two parameters, and resul ts in a precise measurement of f/ ew It is clear that in t he leading model for scalar exchange cont ribu tions to 17 , that of a charged Higgs, lepton universality cannot be used , since the Higgs co upling strength is proport ional to the lepton mass (see Equation 2. 71 ). Thus, we cannot assume 17e = r;,,. However, in such models, the \i - A structure is not changed, and Pe = p,, to high precision. \/1/e denote our result for 1h, using the constraint Pe = pµ by 17eµ, although we stress that we are not assuming 1le = 1h11 or that scalar couplings are universal, only that V and A couplings are uni versal. Furthermore, vve do not measure 17 e and are insensitive to it. \ Ne first consider the events that are analyzed using the scaled pseudo rest fram e energy spectrum . A combined fit to both the electron and muon events results in a simultaneous measurement of the two para.meters: Pe,, 0. 7:39 ± 0.016 ± 0.006 0.025 ± 0.07 4 ± 0.030 , (8.23) with a. correlation coefficient, Cp,7 of 0.638, and a. x2 of 69.5 for 75 degrees of freedom. Again, the first error denotes the statistical error while the second denotes the contribu t ion from Monte Carlo statistics . Next , we consider the events in both modes that cannot be used to reconstru ct the pseudo rest frame spectrum, by virtue of the fact that they fail the cos o requirement. These events a.re simultaneously analyzed using their direct laboratory frame momentum spectrum to yield: Pe,, and 'T/ eµ. 0.727 ± 0.022 ± 0.009 -0.104 ± 0.106 ± 0.05:3 , (8.24) with a \ 2 of 62.7 for 78 degrees of freedom. On ce again the correlation coefficient is reduced and C\"1 = 0.558 . The resul ts obtained by simultaneously analyzing the two lepton modes in both frames of reference (Equations 8.2:3 and 8.24) are consistent with each other. Since they are statistically independent, they are now combined using a. simple weighted 124 average (accounting for the correlations between the two parameters) to obt ain: Pep and 17eJ.1. 0. 735 ± 0.013 ± 0.005 -0.015 ± 0.061 ± 0.026 , (S.25) with a correlation coeffici ent of 0.614. These results are the most precise to-elate m easurements for these parameters. The errors on both parameters are significantly lower that the corresponding errors obtained on analyzing the indi vidual modes. The l CJ error ellipse in the 77 - p parameter space obtained for this final result, along with the res ults obtain ed for the two different tau decay modes, is shown in Figure S.6. ---♦ . 125 ,~~/~~, ~ .00 .·• ...•···· ..... : ..~ .....: .. . · .. .· . .. ~ e MODE ----- µ MODE - - e+µ MODES -.125 - .2 5 .____.__.___,___.__....___,_...._..:..:=_~,.._...........__.____.___.__.,____,.__.___.______. .65 .70 .75 .80 .85 p Figure 8.6: The 1 CJ error ellipses in the 77 - p plane obtained by analyzing the electron and muon modes indi vidually along with the combin ed result. The error includ es both data and Monte Carlo stat istics . The Standard Model expectat ion is indi cated by the cross in the center of the figure. 125 Chapter 9 9 .1 Determining Systematic Errors Sources of Error The results presented in the previous chapter were obtained by comparing the observed charged daughter lepton 's momentum spectrum with combinations of distributions predicted from Monte Carlo simulations. It is thus important to know not only the absolu te efficien cy to good precision , but also the momentum dependence of this efficiency. Most of the cuts utili zed to select signa.l events as well as t hose aimed at rejecting the backgrou nds were designed to avoid any bias in the lepton momentum spectrum studied. The CLEO II Monte Carlo simul?,tion is used to determine the momentum dependence of the efficiencies for all cuts; the data a.re used to tune the simulation package wherever possible. Systematic biases in thi s ana.lysis could arise from the following li st of sources : • shifts ca.used because of an imperfect fitting procedure; • imperfect modeling of the physics pro cesses and detector response in the Monte Carlo simulation ; • imperfect simulation of the background sources and uncertainti es in the normali zation of the backgrounds relati ve to the signal; • imp erfect simu lation of the correlations between the decay of the two tau leptons in the event a.ri sing as a res ult of radiation , spin correlations and/or global cuts imposed to select events; • bin migration and resolution ; • other possible anomalous effects in the data. In thi s chapter we explore these potentia.l sources of systematic error in some detail to estimate conservative upper limits to their contribution to the errors. 126 9.2 How Well Does the Fit Technique Work? Genera.tor level ( perfect detector) tests were performed to test t he response of the fitting procedure. The first test was designed to study if this technique tracked the two para.m eters in t heir allowed physical space. Several :tvlonte Carlo samples were generated at variou s points in parameter space, and F igure 9.1 shows the measured parameters as a fun ct ion of t heir generated values. The V ± A, and the r; = 1 Monte Carlo samples used in the fi t procedure were generated with very high statistics and a.re the same for ea.ch of the fits performed. The simulated "data.'' samples, generated a.t different points in parameter space, all have approximately the same number of events as the true da.ta sample. Although t he errors obtained on t he different meas ured results depend on t he parameters , we note that there does not appear to be a.ny systematic bi as associated with the fitt ing technique. This test confirms that the fit technique will meas ure the para.meter of interest irrespective of its t rue value. This exercise was carri ed out for ea.ch para.meter individ ually, with the other para.mete r ass um ed to be fix ed at its Standard Model ex pectation. 1.0 1.00 7J = 0 FI XED Q 0 ~ .75 0 w 0::: ::, <( + .5 w 0::: (/) + p = 3/ 4 FIX ED ::, (I) .50 <( w .0 w 2 ♦ 2 -.5 .25 .00 .00 ♦ .25 .50 .75 GENERATED p 1.00 -1.0 - 1.0 - .5 .0 .5 1.0 GENERATED 7J Figure 9.1: Track ing the two para.meters over their all owed parameter space. The next test was to track the para.meters using two- dim ensional simul taneous fits. We find that 60 % of the tirne t he fit reproduces the generated para.meters al t he 127 1 CJ level, and 85% of the time, at the 2 CJ level. These numbers are consistent with what one expects from pure statistics . No systematic error is assigned associated with an imperfect fit procedure. Before the efficiency corrections 111 Equations 8.13 and 8.11 were appli ed. t he fit procedure did appear to have some systematic probl ems . As explained earlier in Section 8.1, the detector efficiency is independent of the Monte Carlo sample considered. However , the probability distribution function does depend on the model considered, and since the spectra. used in this st ud y were obtained after a.11 cuts applied in the data. (including the momentum requirement ), the efficiency corrections cannot be neglected in this study. 9.3 Trigger In the data. sets considered in this analysis , seven primary trigger lines a.long with some loose presca.led lines were active . Vve require a.t lea.st one of the seven trigger lines to be satisfied . The Monte Carlo simulation predicts a. trigger efficiency of (99. 58 ±0.01) % for t hee vs.h1r 0 sample, and (98.30±0.04 )% for the f.l vs .h1r 0 sample after all cuts. Almost all triggered events pass t he I~IL2/ LVL3 softw are filt er . We selected the tau decay mode T+ -+ h+1r 0 v, to tag TT events in this a.na.lysis partially because of the high trigger efficiency for this mode . Although the Monte Carlo t rigger simulation package (M CTR) is quite thorough, its inadequacies a.re addressed using real data.. Figure 9.2 compares the di stribution of the seven trigger lines in t he 4S2 data. set. The distributions are normalized to the nurnb er of events in the plot. There is qua.ntita.ti vely good agreement between the data and the Monte Carlo simulation for both the electron and muon samples . We observe sim ilar agreements for the other data. sets. Given the level at which the trigger is modeled, t he fact that t he t rigger efficiency predicted by the Monte Carlo simulation is close to 100% suggests that it cannot be too far off. Further, approximately 95%, of all events pass 2 or more trigger lines, and the trigger red undancy helps. Since the Michel parameters a.re extracted from the lepton momentum spectra, the 128 5000 e 6000 µ ,--, MONTE CARLO • ,--, MONTE CARLO • 3000 4000 2000 0 0 O::'. <( <( <( :r: :r: Q_ _J ::::, f- Q_ (I) m w w z u w 0 0 <( Q_ (I) 1000 3 f- f- _,____,___J....__.____J___J 5 TRI GG ER LINES 0 0 <( f- _J <( Y'. >- :r: u <( u m w w z u <( (_') O::'. O::'. f- ::::, m :::?: :::?: (.'.) <( Q_ DATA • :x::: O::'. :r: :r: (_') O::'. fN w _J 0 '----'-__,_ __._____.__ <( O::'. O::'. f- 2000 :::?: (.'.) <( m :::?: f- <( Y'. >- :r: u <( Y'. u • 4000 DATA w _J w O::'. f- 0 3 N f- 0 10 5 TRI GGER LINES 0 10 Figure 9.2: Distribution of the trigger lines in the 4S2 da.ta and Monte Carlo simulation. momenturn dependence of the trigger efficiency is vital. The solid dots in Figure 9.3 indicate this momentum dependence for both samples considered. 1.01 e • >z .97 (_) 1.01 • •• • ••••••••••••••••• w 0 0 (_) LL LL w OO 0 0 ¢ ◊ ◊ LL LL w .93 0 0 0 0 0 w 0:: 0 0 0 0 .93 0:: (.'.) (.'.) • 0 0 ¢ 0 f- 0 0 0 0:: 0 .89 •• ••••••• • • • • • • • • • • ••• >z .97 w u (_) ¢ w ALL TRIGGERS (.'.) (.'.) IGNORE ELTRACK 0:: oOooooOOc;,◊¢◊◊ ~ • ◊ ◊ .89 0 i~ f- ALL TRIGGERS IGNORE ELTRACK .8 5 L-L..-L-J.-L...JL-J.__.L..L...J.....L--'-'-L-L....L...J.....L--'-'-L-L....L...L...L-J .85 0 2 3 Pe 4 5 0 2 3 4 5 P~ Figure 9.3: The moment um dependence of the overall trigger efficiency (solid clots) for the elect ron (left) and muon (right) samples. The momentum dependence of all the trigger lines ignoring the ELTRA Ch. line (open clots ) is also shown. Vle observe that the overall trigger efficiency is independent of momentum over most of the range considered. Also shown in this figure is the trigger efficiency for all triggers excluding the ELTRA CI-;: trigger line (open clots) . When this one trigger line is ignored, the trigger efficiency falls significantly. It also develops a marked 129 momentum dependence. Since the overall trigger efficiency is dominated by the ELTRACE trigger line 's efficiency and over 90% of all events in this data sample pass this line, we estimate the trigger systematic error by estimating the systemat ic error resulting from the inaccurate modeling of the ELTRA CE line in the Monte Carlo trigger simulation. This line utilizes both the tracking and neutral components of the trigger. V\ie estimate the systematic error arising from both these components using the data. The trigger requirements for the ELTRACK line is shown in Table 9.1. 11: 12: Tracking 2TIGI-IT 2LOOSE lTRACE lPD PASS Time of Flight 2TFBAR 2TFBAR 2TFBAR Calorimeter lCBH lCBH lCBH Dat a. Set 4S2 4S3 4S4 + 4S2-4S8 4S9-4SA Table 9.1: ELTRACE (Line 4) trigger line definition. The tracking component of the trigger li ne can be studied using the subsample of events that survive the requirements of the ENERGY trigger line. This line contains no tracking requirements and a significant subsample of the electron mode events satisfy this line. Figure 9.4 shows the momentum dependence of the tracking component of the ELTRAC I~ line as measured in both the data and the Monte Carlo electron samples . We find that the efficiency is high and slightly overestimated in the Monte Carlo simulation. The neutral component of the ELTRACE line can be studied using the subsample of events that survive the requirements of the 2TRACI{ line. Figure 9 ..S shows the momentum dependence of the HIGH BIT neutral component of the ELTRACI{ line in the electron sample. Once a.gain, we find that the trigger efficiency is high over most of the momentum range studied. Further, the Monte Carlo simulation does an excellent job of modeling this efficiency over the entire momentum range. The difference in the measured data. and Monte Carlo simulation efficiencies in 130 >u 1.01 I e ' z w u LL LL .97 w ('.) z ::,.:: u .93 <( 0::: f- I ,----, MONTE CARLO DATA .89 • ('.) 0::: f- .85 2 0 4 3 5 Pe Figure 9.4: The momentum dependence of the tracking component of t he ELTRA Ch. t rigger line in the data and the Monte Carlo simulation ( E vs. p events ). >- e U 1.01 z w u LL LL .97 w _J <( 0::: f- .93 ::> w z I ('.) .89 ,----, MONTE CARLODATA f 0::: f- • .85 0 3 2 4 5 Pe Figure 9.-5: Th e momentum dependence of t he neutral (calorimeter) component of the ELTRAC I-.;: trigger line in t he data and the Monte Carlo sim ulation (e vs . p event s ). 131 Figure 9.4 a.nd Figure 9.5 a.re used to estimate the trigger systematic error a.rising from the imperfect simulation of this trigger line. \Ne use 3 a va.ria.tions in this difference to revveight tlw l\1Ionte Carlo electron spectrum. The Michel para.meters a.re rernea.sured using the reweighted distributions , and the largest change observed in the para.meters is used a.s a.n est imate of the systematic error. The errors resulting from the imp erfect simulation of the third component of the ELTRACh trigger line, the Time-of-Fli ght compon ent , is expected to be small relative to this estimate, and is ignored. Muons do not satisfy the ENERGY line and thus it is not possible to estimate the trigger systematic using the above technique. However , there is no reason to expect that the momentum dependence of the ELTRACh: lin e be any different in the muon sample. Thus we ca.lcula.te the trigger systematic errors using the same differences utili zed above to obtain the 3 a reweighted Monte Carlo muon distribution, and remeas ure the Michel para.meters . Once again, the largest shifts in the para.meters is used as an est imate of the systematic error. The h]L2/LVL3 efficiency is easy to calculate, since l in 7 events that fai l the L\/13 criteria. is saved. Events that fail are signifi ed by a "gar bage" bit in the event header word. Both Monte Carlo and data events identified by this bit a.re di scarded. _p The overall trigger contributions to the systema:tic error on all para.meters measured are li sted in Table 9.2. These errors a.re calculated for the results obtained after one combines the pseudo rest fra.rn e and laboratory frame analyses. P ep Trigger Statistics 0.002 0.01 4 0.006 0.048 0.019 0.149 0.002 0.01:3 0.00-5 0.061 Table 9.2: Trigger systematic error contr ibutions to each of the Michel param eters meas ured. This table also li sts the statistical errors on the parameters for comparison. We find that the contributions from imperfect trigger simulations in the Monte Carlo package are small relative to the stat istical errors. 132 9 .4 Electron Identification The electrons utili zed in this analysis were identified with the SEID package described in Section 4.1. 5. This package was designed for low multiplicity event topologi es , and for analyses in which precise knowledge of the efficiency is needed, but optimal background rejection is not . The systematic errors resul ting from fak e electrons a.re discussed in a later section; here we consider the electron identification effi ciencies . The nominal cuts imposed by the SEID subroutine a.re as follow s: IPQC DI > 0. 5 , E / P > 0. 85 and ICZC DI > 0.707 , SG' ELDI > -2 , (9.1) where PQ C D is t he signed track momentum, C Z C D is the angle the track makes with the beam a.xi s, E / P is t he ratio of the energy meas ured in the calorimeter and the momentum of the charged t rack as recorded by th e t racking chambers, and SG'ELDI is the difference between t he measured clE/ clx and th e dE / clx expected for an electron di vided by the resoluti on. Since the ori ginal CLEO II Monte Carlo simulation did not reproduce the effi ciency perfectly, SEID has ha.rel-wired effi ciencies extracted from a pure sample of radi ati ve Bha.bha event s in the data.. These effi ciencies , shown in Table 9.3, a.re measured as a function of both the electron momentum and the angle in the detector. The SEID effi ciency is approximately constant at 97. 5%, to within ±1 %. The errors in clud e both statisti cal and systematic uncertainti es associated with the data. sample used. There is a mild run dependence t hat is also handl ed automati cally by SEID . Th e effi ciency correction factors t ha t a.re appli ed as a fun ction of t he data. set are shown in Table 9. 4. 1:33 Moment um Range (GeV/c) 0. 50 - 0.75 0.75 - 1.00 1.00 - 1.25 1.25 - 1.50 1. 50 - 1. 75 1.75 - 2.00 2.00 - 2.25 2.25 - 2.50 2.50 - 2.75 2. 75 - 3.00 3. 00 - :3.25 3.25 - 3.50 3.50 - 3. 75 3. 75 - 4.00 4.00 - 4.25 4.25 - 4.50 4.50 - 4.75 4.75 - 6.50 SEID Effi ciency ( %) o. 7 > I cos 0 I > o. 6 o.6 > I cos 01 > o.3 0. 9549 ± 0.00 15 0.9758 ± 0.0008 0.9776 ± 0.0012 0.9816 ± 0.0009 0.9819 ± 0.001 4 0.9833 ± 0.0011 0.9851 ± 0.0016 0. 9812 ± 0.001 4 0.9787 ± 0.0017 0.9811 ± 0.0022 0.976,'1 ± 0.0018 0.9832 ± 0.0023 0.9774 ± 0.001 8 0. 9807 ± 0.0025 0.9814 ± 0.0024 0. 97 78 ± 0.0017 0.9808 ± 0.001 3 0.9805 ± 0.0022 0.980:3 ± 0.001 5 0.9775 ± 0.0009 0.9794 ± 0.0012 0.9773 ± 0.0008 0.9782 ± 0.0008 0.9829 ± 0.0010 0.9797 ± 0.0010 0.9793 ± 0.0008 0.9803 ± 0.0010 0.9805 ± 0.000 9 0.9770 ± 0.001 3 0.9768 ± 0.0012 0.9783 ± 0.0010 0.9828 ± 0.001 5 0.9797 ± 0.001 4 0.9775 ± 0.0009 0. 9774 ± 0.0008 0.9793 ± 0.0011 I cos 01 < o. 3 0.9 764 ± 0.00 13 0.9775 ± 0.001 4 0.9783 ± 0.0016 0.9803 ± 0.0017 0.9774 ± 0.0020 0.9784 ± 0.0019 0.9777 ± 0.0020 0.9735 ± 0.0020 0.9740 ± 0.0017 0. 9751 ± 0.0010 0.9735 ± 0.0010 0.9746 ± 0.001 4 0.976 5 ± 0.0016 0.9759 ± 0.001 5 0.9749 ± 0.001 4 0. 973:3 ± 0.0013 0.9716 ± 0.0011 0. 9745 ± 0.0012 Table 9.3: SEID efficiency as a function of th e rnoment um and cos 0. Dat a Set Correction Factor Data Set Correction factor 4S l 4S2A 4S2B 4S:3A 4S3B 4S4 - 4S5 4S6 ,t S 7 4S8 4S9 4SA 0.9702 0.9774 0.9788 0. 9788 0.9759 0.9729 0.9794 0.9769 0. 9885 0.98:39 0.9748 Table 9.4 : SEID efficiency run dependent correct ion factors as a function of the data set considered . 134 Figure 9.6 shows the momentum dependence of the electron identification efficiency with both the angular and run dependence integrated out. The angular distribution of electrons from the signal l\iionte Carlo simulation is used to integrate out the angu lar dependence (see Table 9.5) . Position Percentage of final electron sample o.o < I cos 01 < o.3 o.3 < I cos 01 < o.6 o. 6 < I cos 0I < o. 7 49.04 40.85 10.12 Table 9. ,5 : Angular distribution of the electrons in the signal Monte Carlo sample . >-- .980 z (_) w (_) I.J... I.J... w .970 . 9 6 0 '--'--'-.C.........--'-.1.......J..- ' --'---"- ' --'--'-'-_..__,--"-__._'--'---'-.C.........-'--' 5 2 3 4 0 MOMENTUM (GeV/ c) Figure 9.6: SEID electron efficiency (crosses) from radiative Bha.bha. events and ec: ( ee ) events a.fter the cos 0 dependence has been integrated out. Both statistical and systematic errors a.re shown. The hold line indicates t he best fit and the so lid lines indicate :3 G variations of the fit as described in th e text . The bold line in Figure 9.6 is a 4th order fit to the measured efficiency after the angular dependence has been integrated out . \ Ne now fix this polynomial fit funct ion to its best value and add a linear uncertainty of the form: (9.2) 135 to the fit fun ction. The data are re-fit, and we measure the free parameter o for different values of the inflexion point C. The errors obtained for o are the followin g: .6.o = ±0 .0001 5 for C = l.5G eV/ c .6.o = ± 0.00021 for C = 2.5GeV /c .6.o, = ±0 .00021 for C = 3.5GeV /c .6.o = ±0.0001 5 for C = 4.5GeV /c (9.3) The solid lin es in the figure show the modified fit function for 3 O' variations of a . This leads to the following weights: . . 0.0004 ,e I C 0.0004 W3 = l ± (Pe - 3.5GeV /c) Ge\! /c . , w 1 = l ± (Pe - l. 5Gev /c) G \'/ W2 0.0006 = l ± (Pe - 2.5Ge V /c) Ge\! /c _ . , r.: I 0.0006 l ± (Pe - 4.oGe\ /c) GeV /c 'W,1 - (9.4) Reweigh ting the measured electron momentum spectrum by the factor w 2 leads to the largest changes in the Michel parameters measured in the electron mode analysis, as well as the combined electron and muon mode analysis. The observed change in the parameters is used as an estimate of the electron identification systematic error on t he parameter measured . These errors are shown in Table 9.6 and are small relat ive to t he corresponding stat ist ical errors on the parameters. Source Electron Ident ification Statistics < 0.001 < 0.001 0.0H 0.01:3 Table 9.6: Electron identification systemat ic errors. ±0.001 0.061 1:36 9.5 Muon Identification Muons, ut ili zed in thi s ana.lysis, are identified with the S~HD package described in Section 4.1.5. This package identifies muons above 1.5 Ge V / c, and it uses efficiencies and fake rates measured using the data., to identify muons in the Monte Carlo simulation. The momentum dependence of the m uon identification effi ciencies has been measured using f-lf-l'"'f [81] events for fi ve different cos 0 bins, and is shown in Figure 9.7. 1.00 .95 .90 .85 ,,......_, .80 ~ ...__., .75 >... 0 C Q) 0 '+'+- w i I I i * .70 .65 .60 .55 .50 .45 .40 .35 * 0.0 < lcos01 < 0 .2 0.2 < lcos01 < 0.4 0.4 < lcos01 < 0.5 0 .5 < lcos01 < 0.6 0 .6 < lcos01 < 0.7 3 4 • □ 0 ♦ 0 2 5 Momentum (GeV/c ) Figure 9.7: Muon identification effici encies measured using radiative m uon pair events in the data as a. function of momentum and polar angle. \Ne note that the CLEO II detector can identify muons in the 1.0-1. 5 Ge V / c momentum range. The 17 para.meter is very sensitive to the low momentum muons, and including thi s low momentum region could significantly improve the results obtained. However , the fact that the muon identification effi ciency falls rapidly in thi s low momentum region and thus requires a. fin er binning, coupl ed wi t h th e limited data. stati stics in t he f-lf-l;' low momentum sample, rPsults in large errors on the efficiency meas urements in this region. These larger errors translate into larger systematic er- 137 rors on the T/ measurements. Thus, the large improvement in preci sion that could be obtained by inclu ding these low momentum muons is nullified by the equiva.lent increase in the systematic error. \Ne choose not to include these low moment um muons in thi s ana.lysis "' . T he procedure used to evaluate t he systematic error associated wit h the electron id entification efficiency is applied here to estimate the muon identification systematic error. 'vVe first integrate out the angular dependence of the muon identification effi ciency using the distribution of muons seen in t he Monte Carlo simulation of the signal T - ----+ µ-v,,ur decay mode (Table 9. 7). Position o. o < cos 0 < o. 2 o. 2 < cos 01 < o.4 I I I 0.4 < I cos 01 < o. 5 o. 5 < cos 01 < o. 6 o. 6 < cos 0 < o. 7 I I I Percentage of fin al muon sample 26.77 24.40 20.59 16.47 11.77 Table 9.7 : Angular di stribution of t he muons in the signal Ivlonte Carlo sample. The resul t ing meas ured efficiency is now fit to a fifth order polynomial , and the fit function is fix ed to its best value. 'vVe now acid a linear uncertainty of the fo rm: f(p,, ) = o(pµ - C) , (9. 5) and fitting this linear uncert ainty to the measured effic iency yield s the followin g measurements for the free para.meter o : ±0.000L! for C = 2. 0 GeV /c , and ~ a ±0.0008 for C = 4.0 GeV /c . 60 = ±0.0007 for C = :3.0 GeV /c (9.G) *Som e low mom e ntum muons a.re recove red in t he pseudo rest fr a m e a nalys is wit hout. usin g mu on id ent ifi catio n to se lect t hem as descr ibed in Sect io n 7 .2. 138 Using :3 CJ variations of this parameter leads to the weights: and w 3 ·; 0.0012 1 ± (P1-1 - 2.0Ge\i c) G \ / e ! C . 0.0024 1 ± (P1-1 - 4.0Ge \ 1/ c) Ge V / c . ( G \ '/ 0.0021 ·; e\i C w 2 = 1 ± p 1, - 3.0 e I c) G (9.7) These weights are used to reweight the Monte Carlo muon spectrum , and the Michel parameters are remeasured for each of the reweightecl spectra. Using the weight w 3 results in the largest changes in the Michel parameters, in both the stand-alone muon analysis, as well as the the combined electron and muon mode analysis. These changes are now used as estimates of the systematic error, and are listed in Table 9.8. This table a.lso lists the statistical error on each of the parameters measured. Source Muon Identification Statistics ±0.004 ±0.014 ±0.018 ±0.149 ±0.001 ±0.01:3 ±0.024 ±0.061 Table 9.8: Muon identification systematic errors. \Ne note that although the errors listed a.re not negligible, they are significantly smaller than the corresponding statisti cal errors . This would not be true if one relaxed the momentum requirement clown to 1.0 Ge V / c; the statistical errors would reduce by approximately 16% while the systematic error would increase by over 100% in the combined electron and muon mode analysis. 139 9.6 Backgrounds The background contaminations from all potentia.l sources and their estimation were described in detail in Chapter 5. The negligible background sources were ignored , while a background subtraction was performed for each of the substantia.l sources. In this section , we describe the systematic error estimates associated with the more significant background sources: misidentified leptons, and the feed-down from multi 1r 0 modes into the tag 0 T+ _, h+1r v, decay mode. The contributions from each of the non tau background modes is negligible, and thus there is no systematic error associated with these modes . Hadrons fake both electrons and muons. This background source is the largest source of contamination in the data sample, and is potentia.lly the most dangerous since the fake lepton spectrum is momentum dependent. The spectral shape Michel parameters p and T/ are directly measured using the lepton momentum spectrum, and to achieve the level of precision desired, one is required to understand absolutely both the normalization as well as the shape of this background source using the data. 9.6.1 Fake Muons Both the source of the fake muon contamination and the fake ra.tes are momentum dependent. Muons with p,,. 2'. 1.5 GeV /c are identified using SMID and the contamination in this momentum range is solely clue to pions and kaons faking the muon signal. SMID selects muon events in the data by looking at the signals in the CLEO II muon identifi cation chambers. The muons with ]Jµ < 1.5 Ge V / c are not identified using these signals in the muon chambers. Instead, one applies cuts to veto a.11 possible T decay modes resulting in a sample of muons as described in detail in Section 7.2. In addition to the hadron contamination , one now observes a non-negligible electron contamination. 140 Fake muons with pp. > 1.5 Ge V / c: The probability that a hadron will fake a muon, and the momentum dependence of this probahility are determined using the very clean hadron sample obtained from the decay of the tag tau in these data events T+ -) h+7r 0 v T , as described in Appendix B. These fake rates , coupled with the parent hadron distribution, also obtained using this data sample, as detailed in Section 5.1.1 , results in an excellent estimate of the fake muon momentum spectrum normalized to the data muon spectrum. The background estimation procedure does not in any way rely on the Monte Carlo simulation t. We perform a bin by bin background subtraction to remove statistically this background source before the data are utilized to measure the parameters of interest. The solid contours shown on the left (right) in Figure 9.8 depict the 1 <7 and 2 <7 error ellipses obtained in the 17 - p plane for the measurements performed using the laboratory (pseudo rest) frame momentum (energy) spectrum. The dotted contours depict the corresponding measurements when the fake muon background spectrum was not subtracted from the data. .8.--r-T-rr-r-r-c-rr-m-rr-m--,-,-.,...,.,-i-r.,...,-,-i-r,--,-~ .7 _ 3 µ µ LABORATORY FRAME PSEUDO REST -NOMINAL ••••• NO SUBTRACTION FRAME .4 -.1 !;' -.5 -.9 -1.3 ~~~~~~~~~~~~~~ .70 .90 .30 .50 p -.4L-L..L..L.L.....................................................~........~........~~ .60 .65 .70 .75 .80 .85 .90 .95 p Figure 9.8: The nominal error ellipses obtained in the 17 - p plane for the laboratory (pseudo rest) frame muon analysis are depicted by the solid contours on the left (right). The dotted contours are obtained when this background source is ignored. tThe old version of the CLEO II Monte Carlo simu lation program und erest imated the fake rates, and the newer version, which invokes NUCRIN to simu late the hadronic interactions , overestimates them. 141 Although the background subtraction is ::: 1%, we note that the change is fairly significant for both parameters in the pseudo rest frame analysis . In Figure 9.9, we illustrate the corresponding results obtained when the two leptonic modes are simultaneously analyzed. Once again, we observe a more significant change in the pseudo rest frame analysis. Vl/e also note that the central value of the para.meter p does not change significantly in both these plots. This results from the fact that p is nailed clown by the precise electron mode analysis measurement. e+µ LABORATORY FRAME .20 e+µ -NOMINA ----- NO SUB RACTION .2 0 PSEUDO REST FRAME .10 i;::- -.20 -.10 -.40 ~~~~~~~~~~~~~~ .60 .65 .70 .75 p .80 -.20 ~~~~~~~~~~~~~~ .65 .70 .75 .80 p Figure 9.9: The nominal error ellipses obtained in the ff - p plane for the laboratory (pseudo rest) frame analysis are depicted by the solid contours on the left (right). These contours are obtained by analyzing both the electron and muon modes simultaneously. The clotted contours are obtained when this background source is ignored. To evaluate the systematic error associated with the estimation of this background source we vary both the shape and the norma.lization of the background spectrum obtained from the data by 1 O', where O' is the error obtained in the data estimate of the quantity being varied. This error estimate includes a 15% systematic error on the fake rate determination. The para.meters are remeasured and the largest changes observed a.re used as estimates for the systematic error associated with this background subtraction procedure. These are listed in Table 9.9. V•./e note that these error estimates a.re not negligible. 142 Fake muons with JJ., < 1.5 GeV /c: As mentioned earlier , fake muons in this l0vv momentum region result from bot h hadrons a.s well a.s electrons. Hadrons resul t from the direct ,- --+ 1r- / x- 117 decay mode a.s well a.s from the decay of intermediate resonances such a.s the p, A' *, a 1 , etc. These low momentum muon fake background only affects the data. analyzed in the pseudo rest frame, since they can only be identified in that frame of reference. In Figure 9.10, we illustrate the nominal 1 <Y and 2 <Y results obtained in t he muon (left) analysis and the combined lepton (right) analysis. Also shown here are the corresponding 1 CY error ellipse obtained when one ignores the low momentum fake muons. In the muon mode, both measured parameters change significantly, while in the combined mode the p parameter is unchanged a.s a result of its precise determination using the electron mode events. µ pµ <1.5 GeV/c e+µ -NOMINAL ----- NO SUBTRACTION pµ <1 .5 GeV/c .20 .4 .10 ~ - . 10 - .2 0 '--L--1---L----1.---L---L.---'----'--L--'--'--'--'--....___, .60 .65 .70 .75 .80 p .85 .90 .95 .65 .70 .75 .80 p Figure 9.10: The 17 - p error ellipses for the nominal res ults obtained in t he muon (combined mode ) pseudo rest fram e analysis are shown on the left (right). Ignoring the low momentum fake muons vvould result in a big shift in the result , a.s depicted by the dotted contours. \Ne note that neglect ing these background s would res ult in very different result. Both t he shape a.nd the absolu te normalization('.::::'. 4% ) of a.11 these background s are estimated using the generi c , Monte Carlo simulation events. The different input 143 branching ratios in thi s simulation a.re listed in Table :3.1. The fake spectrum obtained in the Monte Carlo sample is normali zed to the cla.ta, and is sub tracted from it before the parameters a.re measured. Ea.ch mode is indi vidually normalized using the Particle Data. Group (PDG) 1996 branching ratios. To evaluate the systematic error associated 'W ith this background, we vary the normali zations of the indi vidu al T background decay modes by 3 CY , where CY is the error on the PDG world average res ul ts. T he systematic error estimates thu s obtained , along with the estimates obtained for the higher momentum region a.re shown in Table 9.9. Although neglecting the low momentum fake muons results in substantial shifts in the resul ts obtained , the background procedure is well defined and the systematic error estimates are smaller than the corresponding estimates for t he higher momentum muons. T he high momentum esti mate is dominated by t he errors 011 the fake rate measurements made using the data. An increased data set would result in smaller errors on those measurements, thus resulting in a snialler error estimate here. In this analysis, the systemati c errors obtained here are one of the more dominant ones . Source Pi, 2 l. 5GeV /c Pi, < 1.-SGeV/c Fake Muons Statistics ±0.024 ±0 .006 ±0.025 ±0 .01 4 ±0 .101 ±0.033 ±0.106 ±0 .149 ±0 .002 < 0.001 ±0 .002 ±0.01:3 ±0.022 ±0 .011 ±0.025 ±0 .061 Table 9.9: Fake muon systematic errors. The error est imates for the two different momentum regions are added in quadrature to obtain the fin al error estimate for thi s source. 9 .6 .2 Fake Electrons The hadron backgrouud to the electron sample is small an d comprises only 0.135 % of the electron sample in the data. In t he nominal ana.lysis, no background subt raction is performed. To evaluate t he systematic error associated wit h t hi s small background , we estimate both the fake electron rate and t he absolute normali zation using t he data, 144 following the procedure applied for the fake muons. The shift in t he nominal res ult obtained on applying this background subtraction procedure is used as an estimate of the systematic error. This is an overestimate of the error, but since it is small relative to ot her sources of error, more work need not be done to evaluate it . The error estimates for fake electrons in this analysis are shown in Table 9.10 . Source Fake Electrons Statistics 0.004 0.009 0.004 0.01 3 0.015 0.06 1 Table 9.10 : Fake electron systematic error estimates. As shown in Chapter 5 t he background contamination from Bhabha events is negligible. T hus , no systematic error is assigned associated with this background source. Figure 9. 11 shows on a. logarithm ic sea.le the tail end of the electron spectrum (before the cos a requirement), used to measure the Michel para.meter p . In this figure, the E / P requirement on the tag si de of the event has been removed to allow any existing Bha.bha background to sneak into the sample. Still, after the 1r 0 sideband subtraction, there is absolutely no indi cation of any background from this source. 3 ,-._ 10 ~ - - - - - - - ~ - - - - - - ~ - ~ ~ - - ~ 0 ,-----, No SB subtraction ~ ~ 10 0 0 10 .__,., 2 • - After SB subtraction 1 .......... (/) f- z w > w 10 - 1 .__....._____,____,J.____._____.____,J.____._____.___._....&.......l'-'---'---'----L---' 5.5 4 .5 5.0 4 .0 ELECTRON MOMENTUM (GeV/ c) Figure 9.11 : The tai l encl of the electron data. spectrum (solid hi stogram) on a logarithm ic scale. The dots indicate the spectrum after the nominal 1r 0 sideband sub traction procedure . 14.5 9.6.3 Feed-down into Tag Mode Tau feed-clown into the tag T+ -----+ h+ 1r 0 v T mode is minimized by the appli cation of veto cuts on any unused showers in the detector. In principle, feed-clown events on the tag side should not affect the results obtained in the laboratory frame analysis. The laboratory lepton momentum spectrum obtai ned for the decay of the other T in the event should essentially be independent of the tag decay mode, except for spin correlations and initial state radiation, which are both modeled by the Monte Carlo generator KORALB, and are addressed in a. following section. Feed-clown events become very important in the pseudo rest frame analysis , where the flight direction of the parent T is estimated by the h1r 0 system, and is directly used to calculate the boost, and to reconstruct the energy spectrum in the pseudo rest frame. An improper knowledge of the normalization , or a poor simulation of these feed-clown events would potentially result in a badly reconstructed energy spectrum. Changing the nominal veto requirements to let in more feed-clown events into the sample analyzed does not significantly change the results obtained. This stability in the results seen when the feed -clown background is increased by more than a. factor of ,5-10 indicates that the feed-clown modes a.re included in approximately accurate proportions, and that this feed-clown and the spin correlations a.re well modeled in the Monte Carlo simulation. The ratio of tau decays into the feed-clown modes to the tag mode decay is well known. To evaluate a. systematic error , we artificially change t his ratio in t he Monte Carlo distribu tions by 3 <J' , where <J' is the PDG 96 [72] error on this ratio, and remeasure the Michel parameters. The largest shifts observed a.re used as systematic error estimates, and a.re listed in Table 9.11 a.long with the statistical errors obtained for each of the measured parameters. VVe note tha.t this systematic error estimate is small rela.ti ve to the corresponding statistical errors. 146 Source Feed-clown Stati sti cs 0.001 0.014 0.002 0.0L18 0.007 0.149 0.002 0.01:3 0.008 0.061 Table 9.11 : Sys temati c error estimat es a.ri zing from the imperfect modeling of feeddown modes in the Monte Carlo simulation. 9.7 Beam Energy Corrections The da.ta used here were collected a.t two different beam energi es ; approximately 2/3 of the da.ta is collected a.t beam energies of 5.29 Ge V, a.ncl the rem ainder a.re collected at beam energies of 5.26 GeV. These running conditions a.re such tha.t the center of mass energy li es near the peak of Y( 45' ) resonance, and just below it, respectively. T he V - A Monte Carlo sample has been generated at the two different beam energies in approximately the same ratio as in the data sample. The non- standard Monte Carlo samples have all been generated at a beam energy of 5.29 Ge V . The contributions of the non- standard Model 1\/Ionte Carlo samples to the fit a.re small , a.ncl thus one does not expect any bias as a. result of the single beam energy sample. The solid contours in Figure 9.12 shows the 1 and 2 <J error ellipses in the T/ - p plane obtained in the nominal electron and muon mode combined analysis. Ignoring the fact that two different beam energies were utili zed during the data collection results in the clotted ellipses in thi s figur e. We note that the change is small relative to t he overall stati stical errors. Thi s change is entirely clue to t he muon data; the electron mode res ult is unchanged if t hese corrections a.re ignored. The pseudo rest frame analysis is not affected by the different beam energi es used , since the correct beam energy is use~! to calculate the pseudo rest frame energy spectrum. Thus the difference in the two 1 <J ellipses in Figure 9.12 is entirely clue to the event s ana.l .,vzecl in the la.boratorv ., fr ame of refer ence. Since we know the exact ratio of the two different beam energy samples in the dat a., the Monte Carl o sample is genera.tee! in approximately t he same rat io , and since the two different beam energi es used a.re close enough to ea.ch other to resul t in a non-significant change in 147 e +µMODE .10 ~ .00 - .10 - NOMINAL ---- · NO CORRECTION -.20 ~~~~~~~~~~~~~~~ .700 .725 .7 50 .775 .800 p Figure 9.12: The 1 CJ, 2 CJ 77 - p error ellipses for the nominal res ul ts obtained in the com bined electron and muon mode analysis are depicted by the solid contours. The clotted contour shows the resu lt obtained in the absence of any beam energy corrections. t he para.meters measured, no systematic errors a.re assigned here . 9.8 Tau Flight Direction Estimation in Pseudo Rest Frame Analysis Approximately 60% of the events in both the leptonic modes considered are analyzed using the scaled pseudo rest frame energy spectrum. One can reconstruct the pseudo rest fram e spect rum for these events since the tag h±7io system is a good estimator of its pa.rent , flight direction . We require tha.t cos a 2: 0.970 for t he events utili zed , ' where o· is the angle between the direction of the tag system and its pa.rent , flight direction in the laboratory fram e of reference. The Monte Carlo simulation does a.n excellent job in simulating this angle as shown in Figure 7.5. Feed-clown modes such a.s the , -, 7i21r 0 /Jr decay would di stort this distribution. The excellent agreement between t he cla.ta and the Monte Carlo distributions indi cates t hat the feed-clown modes a.re included in the Monte Carlo simulation in the appropriate amounts and with the correct. dynam ics.. 148 To understan d the systemat ics associated vvith the choice of the cos a cut, we divide the data. a.nd Monte Carlo distributions into ten different cos a bins and measure the para.meters in ea.ch bin. The figure on the left (right) in Figure 9.1:3 plots the results obtain ed for the p para.meter using the electron (muon) mode events . In the muon analysis, the ry para.meter is fixed to it s Standard Model expectation , since one does not have sufficient statistics to measure the parameters simultaneously in ea.ch cos a bin. Further , the bin sizes selected a.re not uniform , since the events with cos a close to unity a.re more sensitive to the parameters. µ e cosa<0.950 0.950<cosa<0.960 0.960<cosa<0.970 0.970<cosa<0.975 0.975<cosa<0.980 0.980<cosa<0.985 0.985<cosa<0.990 0.990<cosa<0.995 . .995<cosa<0.9975 0.9975<cosa< 1.000 .30 .40 .50 cosa<0.950 0.950<cosa<0.960 0.960<cosa<0.970 0.970<cosa<0.975 0.975<cosa<0.980 0.980<cosa<0.985 0.985<cosa<0.990 0.990<cosa<0 .995 0.995<cosa<0.9975 0.9975<cosa< 1 .000 ---+-- ---+-- .60 .70 .80 .9030 .40 .50 .80 .90 Pe Figure 9.13: The Michel para.meters Pe a.nd p,, for different slices in cos a. V-le find that the l\!Iichel para.meters measured a.re indepen dent of the choice of the cos a bin. Thus, there is no systematic error associated with the choice of the cos a req uirement, and vve select events with cos O' ~ 0.970 and analyze them using the pseudo rest frame spectrum ; the remainder a.re analyzed using the laboratory spectrum. This choice of cos u is optimal since it maximizes the sensitivity to the two parameters, and thus minimizes the final error obtained. In Figure. 9.14, we plot 6 ,n the error on the TJ para.meter , obtained in a. combined electron and muon mode Monte Carlo generator level analysis, as a. function of the cos a requirernent. The arrow indi cates the nominal choice for cos o:. 149 .100 .090 • j • • • • .080 <f .070 • • .060 .050 .950 .960 .970 .980 .990 1.000 cos ex Figure 9.14: The error on the ·ri parameter as a function of the cos a requirement in a Monte Carlo genera.tor level st udy using the combined electron and muon modes. 9.9 Radiative Processes Radiation shift s the lepton energy spectrum to lower energies . As a result , a ii - A momentum spectru m resembles the V + A or 77 = l momentum spectrum. This shift in the spectrum can bias the Michel parameter measurements. Since this ana.lysis is designed to search for small deviations from the Standard Model expectations, it is important that radiative effects a.re approp ri ately accounted for in t he Monte Carlo simulation. Radi ative photons a.rise as a res ult of three different processes: 1. initial and fin al state radiation; 2. external bremsstrahlung in the CLEO material; 3. internal bremsstrahlung or decay radiation . Electrons radiate ~ 10 times as much as m uons , and this effect is thus more pronounced in t he electron channel. The V - A Monte Carlo samples were generated using h:ORALB for the generation of t he T+T- pairs with initial and final sta.te radiation. TAUOLA is used for the decay radiat ion to order O( a) in wv and /lfl V events , whi le t he PHOTOS package is used to simulate th e decay rad iation in non-leptonic decays of the tau. The simulat ion of bremsstrahlung in the CLEO II detector is performed by the GEANT-based CLEOG 150 package. The non-Standard l\llodel Monte Carlo samples were also generated using the above mentioned packages with a small modification to enable the generation of ,±---+ e±1111r decays with arbitrary va.lues of the parameters p and 17. To lowest order, photons from all possible sources are simulated in the Monte Carlo samples. Table 9.12 li sts the percentages of the different types of radiative photons present in the Monte Carlo samples utilized. Mode e vs. p p vs. p No 1 1.4% 16.8% ISR/FSR 58 .2% 58 .4% Decay 16.1 % 4.0% Bremsstrahlung 96.0% 50.8% Table 9.12: Radiation photons in the :Monte Carlo samples. Initial and final state radiation has a large rate , and thus a great potential to distort the lepton's momentum spectrum. The h.ORALB package includes single photon radiation, correct to 0( a), and the 0( a 2 ) corrections are not expected to be any larger than 2-3% relative to the 0( o) calculations. To evaluate any systematic error that might arise due to the imperfect modeling of these radiative effects 111 KORALB , the relative normali zation of the events with these radiative photons 111 the Monte Carlo is changed by ±10%. This upper limit on the change in the relative normalization is obtained from data and l\!Ionte Carlo comparisons of the unused ( not used to form the 71° in the event) shower energy spectrum lying in the same hemisphere as the lepton in the event. Fina.I state radiation in e+e- ---+ ,+ ,- (,), as well as internal and external bremsstrahlung from the lepton are expected to li e close in angle to the lepton, and showers in the other hemisphere might be hadroni c split-offs . Figure 9.15 plots the energy spectrum of all unused showers above 60 Me\/ in the lepton hemisphere. 'vVe note tha.t the Monte Carlo simulation approximately reproduces the data over the entire energy range. Increasing the radiation by more than 10% in the Monte Carlo simulation would make the data and Monte Carlo shower energy spectra. inconsistent with ea.ch other. In fact , this 10% change is a.llowed on ly as a result of the low statistics in the data sample. 151 102 . - , MONTE CARLO e DATA 10' 10-' LL---'---'--'---'--'----'------'-+-.....,._....1....1...WL..1-----'--L.L.l.......L-1..IL-1.l.L..il_J_LJ 0 3 4 Figure 9.15: The energy spectrum for all unused showers lying in the lepton hemisphere in the event. Figure 9.16 shows the change in the Michel parameters Pe and '7,,. as the normalization of the radiation weighted events in the Monte Carlo V - A spectrum are changed. A change of -100 % corresponds to a Monte Carlo sample with no radiation , and vve note that such a negligence would result in a significant change in the measured value of the parameters. The arrows indicate the ±10% change used to estimate the systematic error resulting from the imperfect modeling of radiative effects in the Monte Carlo simulation. Decay radiation is a small effect and turning it off in the Monte Carlo simulation produces a negligible change in the parameters measured. The material in the CLEO II detector lVIonte Carlo simulation is known to 5-10%; one can thus vary the bremsstrahlung tagged spectrum by this amount to evaluate the systematic error resulting from the imperfect knowledge of the material. Once a.gain , we observe a negligible change in the Michel parameters. The overall systematic error resulting from imperfect radiative effects in the Monte Carlo simulation a.re listed in Table 9.13 for each of the parameters measured. These errors a.re obtained by adding the contributions from the three different sources in quadrature. \Ve note that the systematic error is not negligible, but is small relative 152 µ e ! ! 1.0 ! ! -1.0 -.10 ~~~~~~~~~~~~~~ 100 -100 -50 0 50 -1.5 ~~~~~~~~~~~~~~ -100 -50 0 50 100 % CHANGE IN RADIATION % CHANGE IN RADIATION Figure 9.16: The dependence of the Michel parameter p (left) and r; (right) on the normalization of the radiation weighted spectrum in the Monte Carlo simulation; 6P(mea.sured) = p(±x%) - p(nomina.l) , and 6n = 17(±:r%) - r;(nomina.l). to the sta.tistica.l error estimate for the corresponding parameter. P ep. Pe Radiation Statistics 0.005 0.014 0.003 0.048 0.050 0.149 0.001 0.01:3 0.004 0.061 Table 9.1 3: Ra.dia.tion systematic error contributions to ea.ch of the Michel para.meters measured. 153 9.10 Spin Correlations In this analysis, we consider e+ e- annihilations a.t fi :::: 10 Ge V. Since the beams are unpolarized and photon exchange dominates the interaction, the average , polarization is zero. However , spin-spin correlations exist between the two , leptons in e+e- -+ 7 +7- , lea.ding to correlations between the kinema.ti ca.l quantities of the decay products. These correlations a.re not directly utilized in this a.na.lysis , but a.n imperfect modeling of them in the Monte Carlo simulation would result in biases in the measurements of the Michel para.meters. In this section , we try a.nd evaluate how well these correlations are incorporated in the Monte Carlo simulation a.nd we estimate a systematic error to cover their imperfect modeling. The polarimeter variable or the spin analyzer w, a.s defined in Appendix C, can be utilized to separate statistica.lly the left-handed 7- from the right-handed 7- +. The Michel parameter measurements for t he samples with different spin contents should ideally yield identical results if the spin correlations are correctly modeled in the simulation . Figure 9.17 shows thew distributions obtained for the events used in the electron mode analyses. The corresponding figures for the muon events are identical. The figure on the left includes all the events that are used in the pseudo rest frame a.na.lysis, while the figure on the right includes the events analyzed in the laboratory frame of reference. We note that the two w distributions a.re remarkably distinct, indicating that the spin contents of the events analyzed in the two different frames of reference a.re very different. The fact tha.t the results obtained in the two different frames of reference are consistent with each other indicates that both the spin dependence and the spin population are well modeled in the Monte Carlo. 'vVe also note tha.t since the Monte Carlo samples were generated with the Standard Model values for the spin-depen dent para.meters~ and b, not only are spin correlations under control, but also the assumption that these two para.meters are given by the Standard 1\/Iodel is good enough tha.t the associated systematic error is small. trn th e Standard Model (to the extent of CP inva rian ce ) the left-hand ed T- is equivalent to th e right-hand ed T+ and th e right-handed T- is equivalent. to the left-hand ed T+ . 154 coscx > 0.970 1000 1600 coscx < 0.970 ,--, MONTE CAR LO DATA ,--, MONTE CAR LO DATA • 750 ,;- 'Sj' 0 0 0 s-......_ 800 :::;:: 500 (/) (/) I- I- z w > w • 1200 ,-,. z w > w 250 0 -1.0 - .5 .0 .5 1.0 400 0 -1.0 - .5 .0 .5 1.0 w w Figure 9.17 : The polarimetric variable w for the electron mode events used in both the pseudo rest frame and laboratory frame analyses is shown here. The above two figures indi cate that the Monte Carlo simulation of the spin analyzer distribut ion reproduces the corresponding di stribut ions in the data. Figure 9. 18 shows the ratio of the data and :M onte Carlo distributions normalized to the l\llonte Carlo di stribution. The solid lines indicate 3 CJ' variations in this difference and are used to reweight the Monte Carlow distribution. This ratio of the data spectrum to the Monte Carlo spectrum is fit to a linear uncertainty of the form : f(w) = a (w - C) (9.8) \Ne now fit for a as a free parameter for different values of C ranging from -1 to 1. The fit with the larges error is used to determine the weight used in the reweighting procedure , and using 3 CJ' variations of a we obtain the following weights : 0.05 l±(w)Ge\!/c e mode , pseudo rest frame 0.1 2 1 ± (w + 0.25GeV /c ) G:re \ I"/ C e mode, laboratory frame 0.25 l ± (Lv' + 0.25GeV /c) Ge\! /c fl mode , pseudo rest frame; p,, < 1.5 155 µ mode, pseudo rest frame; J]p. > 1.5 Jl mode , laboratory frame. (9.9) The Michel parameters are reca.lcula.ted with the reweighted spectrum , and the shifts fro m the nominal parameter values are used as an estimate of the systematic error resulting from imperfect simulation of the spin analyzer variable. coso: > 0.970 .50 ~~~~~~~~~~~~~~ .25 I .25 .00 I O'.'. .00 O'.'. -.25 -.25 - .50 u.....,.._,_.,__.____,__...._,..........._....,_......_.____,___.__.__,_...,__._..__.._., -1.0 -.5 .0 .5 1.0 - . 50 ._,__,_.,___._~...._,__,_...,__._..__.__.__.___,__~~~ -1.0 1.0 - .5 .0 .5 (.J (.J Figure 9.18: The distribution of the ratio (data divided by the Monte Carlo simulation) for the polarimetric vari able u..' normalized to the Monte Carlo simulation for electron mode events used in both the pseudo rest fr ame and laboratory frame analyses is shown here. The solid lines show the 3 a variations in this ratio, and a.re used to reweight the Nionte Carlo spectra.. The spin ana.lyzer is dependent on the following kinematic variables : the moment um/ energy of the charged and neutral pions, and the angle between the two pions. The error estimate obtained using :3 a variations in the u) variable in the Monte Carlo distribution directly addresses the angle between the two pions (and somewhat the p energy as well). We now consider t he momentum of the charged pion (see Figure 9.19) as well as the energy on the 71° ( see Figure 9.20) in the event. 156 COSCX 800 > 0.970 ' I 1200 .-----, MONTE CARLO e DATA 1000 u 600 ,...__ u >Q) >Q) '-..,, '-..,, (.'.) CJ --: 400 0 2 ::::::: (/) '-..,, (/) i: 200 w COSCX < 0.970 .-----, MONTE CARLO e DATA 800 600 400 I- z w > w > w 0 L....LI,.,__.___,__,.___.__,_._.L....L.__,__,.___.__,_._.____..._-'--'-....._.,_._.....,.__, 0 2 3 4 5 P,, (GeV/c) 200 0 0 2 3 4 5 P,, (GeV/c) Figure 9.19: The charged pion momentum spectrum for events utilized in the electron pseudo rest fram e (left) and laboratory frame (right) analyses . COSCX > 0.970 1200 .-----, MONTE CARLO e DATA 600 >Q) > 800 CJ CJ ~ I ,---., MONTE CAR LO e DATA 1000 ,...__ 6 coscx < 0.970 Q) 400 0 600 '-" ::::::: (/) '-..,, (/) I- I- 2i w > w z ~ 200 2 3 E,,° (GeV) 4 5 400 200 2 3 4 5 E,,° (GeV) Figure 9.20: The 1r 0 energy spectrum for events utili zed in the electron pseudo rest frame (left) and laboratory fram e (right) analyses. 157 In ea.ch of these electron mode figur es §, 'Ne note that the Monte Carlo reproduces the data. for most of the energy and momentum range; there a.re some significant discrepanci es in the low energy and low momentum regions. An interesting featur e observed in these figures is the marked differences between the spectrum used in the two different fram es of reference analyzed. These differences a.re direct ly related to the cos o: cut designed to select events in which the pseudo rest frame spectrum can be reconstructed. Requiring that the tag h±1r 0 system be a. good estimate of it s pa.rent T flight direction selects events in which either the ha.dronic track or the 1r 0 have a. large momentum. Thus the events in the laboratory fram e analysis show depletions in the high momentum/ energy regions . Vie also note a. minimum moment urn and energy cut-offs in the plots shown. T here is a JJ,1r± 2:: 300 Me V / c requirement to ensure efficient trigger and tracking conditions. No nominal requirement has been made on the energy of the 1r 0 ; the requirement that the minimum photon energy used to form a 1r 0 does, however , translate into an indirect minimum energy requirement . These nominal cuts, along with other cuts, correlate the two sides of the event and could potentially resul t in a misrneasurement of the parameters if t hey are not adequately treated in the Monte Carlo simulation. To estimate the systematic errors resulting as a result of these discrepancies, we once a.gain reweight the Monte Carlo distributions as described before, and refit for the Michel parameters. We fit t he ratio of t he data to the Monte Carlo spectra to a linear uncertainty of the form: (9.10) depending on the distribution being considered . vVe then fit for o: as a free parameter for different choices of C, and the fit with the largest error on o is used to determine t he weight used in the reweighting procedure. Using :3 er variations on o:, we obtain: 0.026 1 ± (P1r± - 2.0GeV /c) Ge \'/ / C §The corresponding muon mode figures a re similar. (9.11) 158 . 0.023 1 ± (pn-o - 2.0Ge\i ) GeV , 'W1ro (9.12) where C = 2.0 GeV /c in Equation 9.11 and in Equation 9.12 results in the largest shifts in the parameters from their nominal values in both the electron and muon samples . These shifts are used as an estimate of the systematic error resulting from the imperfect modeling of the charged and neutral pions in the Monte Carlo simulation. Table 9.14 lists the systematic error assignments calculated in this section . These errors are the quadratic sum of the largest changes observed in the measured parameters when the Monte Carlo sample is reweighted with weights calculated using the w distributions, the distributions of the momentum of the charged pion and the energy distributions for the neutral pions. This table also lists the statistical errors obtained on each of the parameters. We note that the systematic error resulting from the imperfect modeling of spin correlations in the Monte Carlo simulation package is not negligible, but it is significantly smaller than the corresponding statistical errors. Spin Correlations Statistics 0.003 0.014 er P;, 0.012 0.048 0.050 0.149 er Pe ;, 0.003 0.013 er'f/ e ;, 0.0:35 0.061 Table 9.14: Systematic errors resulting from the imperfect modeling of spin correlations, the momentum of the charged pion and the energy of the neutral pion in the Monte Carlo simulation. 9.11 Geometric Acceptance The two charged tracks in the event a.re required to lie in the good barrel region of the detector, defined by I cos 01 ~ 0.71 , where 0 is the angle that the track under consideration makes with respect to the beam direction. Figure 9.21 shows t he cos 0 dis tributions in the data and the Monte Carlo simulation for electron, muon and pion tracks. The two photons that are used to reconstruct the 1r 0 on the tag side of the event are also required to li e in the good barrel. These two requirements were selected 1.59 to ensure efficient tracking and trigger conditions. 1000 I e r--i • 750 ~ N MONTE CARLO DATA C! 0 500 :::::: (/) f- z w > w 250 0 -1.0 -.5 .0 .5 1.0 cos0 800 µ ~ N 0 0 r--i • 600 MONTE CARLO DATA 400 :::::: (/) f- z w > w 200 0 -1.0 -.5 .0 .5 1.0 cos0 1200 1000 n/K r--i +• ~ N 0 0 800 MONTE CARLO DATA 600 'z 400 (/) f- w > w 200 0 -1.0 -.5 .0 .5 1.0 cos0 Figure 9.21: Cosine of the angle the electron , muon, and pion tracks make w .r.t. the beam direction. The arrows enclose the good barrel region of the detector; all tracks must lie in this region. The Monte Carlo simulation reproduces the da.ta. in ea.ch of these distributions. The muon identification efficiency falls off rapidly as one extends beyond I cos 01 > 0. 71, and this requirement does not significantly reduce the muon sample. On the other hand , it does red uce the pion and electron samples significantly. To check if the above choice for the cos 0 requirement results in a systematic bias, we measure the para.meters for different definitions of the good barrel region. 160 Figure 9.22 shows the changes seen in the parameters as a function of the choice of the cos 0 requirement. VVe note that there is a strong correlation betvveen the points in each plot. Since no systematic effects are seen, we conclude that the geometric acceptance does not result in any significant systematic errors to this analysis . .80 e .75 ., Q .70 .65 .50 .55 .60 .65 .70 .75 .70 .75 .70 .75 cos0 .80 µ .75 ::t Q .70 .65 .50 .55 .60 .65 cos0 .20 .10 ::t ~ µ .00 -.10 -.20 .50 .55 .60 .65 cos0 Figure 9.22 : The Michel parameters Pe, p,, , and Th, as a function of the acceptance of the two charged tracks in the events. 9.12 Monte Carlo Statistics In principle, the Monte Carlo samples can be infinitely large and thus would result in no errors . In reality, however, the five different Monte Carlo samples used in this ana.lysis are all equivalent to approximately ten times the data in size. The systematic error arising as a result of the finite size of each of these samples, along with the total 161 data and Monte Carlo statistical errors are shown in Table 9.15. The V + A Monte Carlo samples do not contribute significantly to the fit, and a.s a result the error arising from their finite statistics is small. The 7/ = l l\!Ionte Carlo sample resembles the i/ - A Monte Carlo sample over most of the momentum range. As a result , its contribution to the systematic error is larger. \Ve also note that the total systemati c error on the 71 parameter due to limited lVIonte Carlo statistics is significant, but it is smaller than the corresponding error due to data statistics. (J' T/ e ,, (V-A) e (V + l l) e 0.00,5 0.001 - - 0.004 0.001 0.014 0.002 (V - A),, (V + A)µ - - (ry =l )µ - 0.015 0.009 0.019 0.054 0.028 0.065 0.002 0.001 0.001 0.019 0.002 0.010 0.005 0.014 0.026 0.048 0.089 0.149 0.005 0.01:3 0.026 0.061 Monte Carlo Data - I Table 9.15: Systematic errors resulting from finite statistics in the different Monte Carlo samples. 9.13 Bin Migration and Resolution Bin migration alters the observed lepton momentum and energy distribution s. The Monte Carlo package simulates this effect to the lowest order, but the poorly simulated tails could potentially be important . Figure 9.2:3 plots the momentum dependence of the difference between the generated and measured laboratory momenta for muon tracks in the Monte Carlo simulation. We note that although the bin migration is significant , this difference does not exceed 100 lVIe V / c. High momentum tracks migrate more, but they are less significant statistically, since the laboratory momentum distribution falls sharply at high momentum. All t he fits utilized to extract the Michel parameters were performed using distri- 162 ,---.. (I) 0 E __,., ::I. 0... . 1 0 .--,-,-,-..---,----,-.,.............--.....--,.......---,-..,......--_~.-.~-~-.~.~-~-=·~~ ... ....... ... .. ... .. .. .-·.. ·-. ... .... .. . . . . . .. .. ........ .. . . .. ... . ........ .. .... .. . . .. . . ... . . . .os ..... ·•··· ........ ··-····· ........ ........ . . ................... ....... . .. .. .. • • • • • • • • ......... •••••••• . •••••• • • • • • • • • • • • • ■ •••••••• ■ • •••••••• ■ •••• ■ ■ ■ •••••• •••••••• ■ • • • • • ■• ••••• ■ a ■ aaaaaaaaaa ■ a ■■ aaa aaaaa ■ aaaaa gggggggg::: :::::::: a .0 0 ~ - -____J_;•lgDQ!DD;iJ;CJgCg!;CCC~ggggg_gig,,,_ : :-• ■■■ aaaacaccaaaaaaaa ■ • •••• ■ aaaaaaaaaaa ■ aa ,---.. • C •••• • ■■■■■ aaaaaa ■■ • • • • ■ • • • ■• ■ ■••••• • Q) __s-.O5 • =:-=--' : :a-e:-e-:~:'-e-:-=-':-._-, :~:~:~:~::~:___, a••••••• •••••••• ■••••••• •••••••• • • • • • • • • •••••••• •••• • •••• • • • • • • • • ...... .. . ••••••••••••••• . .. . . ....... . . . . . . . ......... .. ..... . .. ......... ........ ... .... . . ... . .... . . .... ........ •••• ■ •• ■ ••••••• • • ■ ••••• ■ • • ••••• ■ • • •• •• • ■ • ::I. 0... . .. . . . .. - . 1 0 ..........__.__........._._..._._..,_..._.___.__..._._._....L.......J.__._-=--.....,.__._.&.:....L............ 0 4 5 Figure 9.23: The momentum dependence of the difference between the generated and the reconstructed muon momentum in the Monte Carlo simulation. butions with 100 MeV /c bins. Thus, one expects that the systematic error associated with the imperfect modeling in the Monte Carlo simulation is sma.11. To evaluate this systematic error , we change the bin size by a. large a.mount and remeasure t he parameters. The largest changes in the results vvere observed on using 50 Me V / c bins instead of the nominal 100 MeV /c bins. These changes (shown in Table 9.16) in the centra.l values of the para.meters a.re used a.s estimates for the systematic error. Also shown here a.re the corresponding statistical errors for each of the parameters measured. Although the systematic error estimates on many of the parameters measured are significant , they are much smaller than the corresponding sta.tistica.l errors . Bin Migration Statistics O' Pe /JP ;, /J r/p O' Pe i., O',) e ;, 0.001 0.01 ,:1 0.020 0.048 0.066 0.1 49 0.002 0.013 0.0 19 0.061 Table 9.16: Systematic errors resulting from bin migration . 163 9.14 Are There Any Anomalous Effects in the Data? There coul~l be a.ny number of anomalous effects in the data, and in this section we study the most obvious possible effects. The results obtained for the different Michel parameters are not expected to depend on the da.ta set studied. Hmvever , we know tha.t detector and trigger conditions vary as a. function of time and thus as a. funct ion of the data set considered. To ensure that these changes in the detector conditions do not bias the measurements, we consider the results obtained a.s a. function of the different data. sets used in the analysis . Figure 9.24 shows the resul ts obtained in the combined electron and muon mode analysis for the 4S2-4S8 data. sets. The 11011-(V - A) Monte Carlo samples have not been generated for the 4S9 and 4SA data. sets and · th us the res ults for these two individual data. sets a.re not shown here . We note that there is no obvious data. set dependence in both Peµ. (left) and T/ eµ. (right), measured with the other para.meter fixed at its Standard Model expectation. Further, the nominal result, indicated by the shaded band , is consistent with Standard Model expectations. 4S2 4S3 4S4 4S5 4S6 4S7 4S8 I- w (/) <( I- <( 0 .55 I- w (/) <( I- <( 0 ,65 ,75 Peµ, (77 = 0 FI XED) .85 - .6 4S2 4S3 4S4 4S 4S6 4S7 4S - ,4 - ,2 ,0 ,2 .4 .6 7/eµ, (p = 3/ 4 FIXED) Figure 9.24: The Michel pararneter Pe/I (1/ e 1,) with 1/eµ = 0 (Pei, = 3/4) fixed to its Standard lVIodel expectation is shown in the figure on the left (right) as a. function of the different data. sets used in this analysis. The results a.re obtained by combining the pseudo rest frame and laboratory frame results, and the errors represent the data. and Monte Carlo statistics contribution. The nominal results obtained using the 4S2-4SA data sets is indicated by the hatched region . 164 The Michel para.meters should be independent of the charge of the lepton a.na.lyzed. VVe now split the electron a.nd muon samples into their respective positi ve a.nd negative lepton samples a.ncl remeasure the para.meters in the combined electron a.ncl muon mode analysis. Figure 9.25 shows the 1 CY error ellipses obtained in the TJ - p plane for the positive lepton spectra. (closed dots) , and the negative lepton spectra. (open clots). Also shown here a.re the 1 a.ncl 2CY ellipses for the nominal result. We note that although the two charged samples a.re not identical, both a.re consistent vvith ea.ch other a.ncl with Sta.ncla.rd Model expectations . . 2 0 ,......,.----,-----,--,---,--.--,-----,----,---,--.,........,----.----,--,---,--,......,.----,---, .....• e +µMODE •• . 10 ~ • •• • .00 -.10 0 0 -NOMINAL 9J 0 e POSITIVE 0 NEGATIVE - .20 ,__._~_._~~,__._~_._......_....._.__.__._~~,__._~~ .700 .725 .750 .775 .800 p Figure 9.25: The 1 CY error ellipses obtained on analyzing the positive (closed clots) a.nd negative (open clots) lepton samp les incliviclua.lly a.long with the 1 CY and 2 CY nominal result (solid lines). The two halves of the detector (cos 0 > 0 and cos 0 < 0) a.re essentially identical a.ncl the para.meters should be independent of the location of the lepton in the detector. Figure 9.26 shows the results obtained in the two different hemispheres of the detector when the two leptonic decay modes a.re simultaneously analyzed. The open (closed) circles illustrate the 1 CY error ellipse obtained when a.11 leptons lying in the cos 0 < 0 (cos 0 > 0) hemisphere of the detector a.re utilized to measure the para.meters. The 165 figure also illustrates the nominal result. We note that although the two samples do not yield identical results, the results are consistent with each other and vvith Standard lVIodel expectations . . 2 0 r-,---,----,----,----,--,---r--,----,----,----,----,--,--..----,---,----,----,-...,......., e +µMODE .10 ~ .. •• .00 -, 10 -NOMINAL • 0 cos0>O cos0<O - .2 0 '---'-----'--'---'---'--'---'-----'--'----'----'---'L-..1.----'--'-.....__....__.__,__, ,725 ,7 50 .700 .775 .800 p Figure 9.26: The error ellipses obtained as a function of the position of the two leptons in the detector. The solid circles illustrate the 1 a- error ellipse in the 17 - p plane for leptons in the cos 0 > 0 half of the detector, while the open circles illustrate the corresponding ellipse for leptons in the cos 0 < 0 half of the detector. The solid lines indi cate the 1 a- and 2 a- nominal result. Since nothing unexpected was seen in this search for anomalous effects , there is no systemat ic error assigned here. 9.15 The Tau Neutrino All Monte Carlo samples were generated assuming a massless tau neutrino . A massive tau neutrino would alter the charged lepton momentum spectrum in the laboratory frame of reference, and would bias the pseudo rest frame spectrum which is cakula.ted ass uming a massless tau neutrino. A Monte Carlo generator level study was performed to study the effects of massive neutrinos . vVe note that the neutrino must have a 166 minimum lass of 70 Me V / c2 before it can have a.ny affect on the measured para.meters. Since the current limit on the mass of the tau neutrino 24 Me V / c2 is well below this mass, 'Ne do not assign any systematic error. 9.16 Total Systematic Errors The systematic errors studied in the preceding sections are compiled in Table 9.17 . We find that the total systematic error (all contributions added in qua.drat ure) on the p measurements are smaller than the corresponding statistical errors. On the other hand , in the 17 measurements the systematic error estimates are slightly larger than the corresponding statistical error estimates. Pe Electron ID Muon ID Fake Electron Fake Muon Feed-down Trigger Bin Migration Correlations Radiation MC Statistics Systematics Data Statistics Pµ. 17 µ. < 0.001 0.004 0.01S 0.025 0.002 0.006 0.020 0.012 0.003 0.026 0.044 0.048 0.106 0.007 0.019 0.066 0.050 0.050 0.0S9 0.171 0.149 0.004 0.001 0.002 0.001 0.003 0.00,5 0.005 0.009 0.01 4 Table 9.17: All significant sources of errors. P eµ 1Jeµ. < 0.001 0.001 0.024 0.015 0.025 0.00S 0.005 0.019 0.035 0.004 0.026 0.062 0.061 0.001 0.004 0.002 0.002 0.002 0.002 0.003 0.001 0.005 0.00S 0.01:3 167 Chapter 10 Summary and Conclusions In this chapter, we provide a brief recapitulation of the results presented and discuss the interpretation and significance of this work. \Ve also briefly discuss future improvements to these results. 10.1 Results In the preceding chapters, vve have presented in detail the measurement of the spectral shape Michel parameters p and ry , using data recorded by the CLEO II detector. These parameters are utilized to study the Lorentz structure of the charged weak interaction which manifests itself in the two tau decay modes: T- -----+ µ-v,,JJ, . Tau pairs are produced by the e+e------+ , +T - T- -----+ e- v ev, and process at CESR, run- ning at center of mass energies around the Y (45') resonance ( approximately 10.5 Ge V) . Both the leptonic tau decay modes are analyzed , and the results obtained are shown in Table 10.1; the first error is statistical and the second is systematic. The two parameters are strongly correlated, thus requiring their simultaneous measurement. Parameter Pe pµ 17 µ. P eµ 'r/ e,, This Thesis 0.732 ± 0.014 ± 0 .009 0.747 ± 0. 048 ± 0.044 0.010 ± 0.149 ± 0.171 0.73Ei ± 0.013 ± 0.008 -0 .015 ± 0. 061 ± 0.062 \i\forld Average [37] S.M. 0. 7:36 ± 0.028 0.74 ± 0.04 - 0.24 ± 0.29 o. 736 ± 0.028 -0.01 ± 0.14 3/4 3/4 0 :3/4 0 Table 10.1: The results obtained for the Michel parameters measured in this thesis . The first error is statistical and the second is systematic. The subscript on the parameter indicates the decay mode utilized to measure the parameter. This table also shows the 1996 world average results and the corresponding Standard Model (S.M.) expectat ion values. 168 Fi rst, we note that all the res ults presented in this table are consistent with both the results presented in the 1996 Particle Data Group [:37], and the Standard Model expectations. \ Ale further note that these results ( with the exception of p,,) are close to a factor of two better than the corresponding world average results. The PDG world average result for the p,,. parameter includes measurements that were performed with the ry,, parameter fixed at its Standard Model expectation, thus improving the precision of those measurements, and consequently the world average measurement. The results obtained in this analysis are more precise than all previous measurements as shown in Figure 10.1. Further, they are more precise than the PDG 96 world average results indicated by the hatched region. As mentioned above, the p,, world average band shown here is deceptive. I //i ! I ' DELCO ! I CLEO !/; MAC I/; Pe ARGUS CLEO II l// :I . .1// _CB pµ ALEPH .50 .30 ALEPH l// : I /i ARGUS ""t'ff:"" - ALEPH CLEO II !Pf i CLEO II .70 .90 I// 1 '//) : !~ 17 µ - //I .30 .50 .70 - .5 -1.0 .90 .0 .5 1.0 7Jeµ Peµ ARGUS ALEPH ALEPH ARGUS L3 L3 SLD CLEO II CLEO II .50 .65 .80 .95 -.50 - .25 .00 .25 .50 Figure 10.1: Comparing the results obtained for the five different parameters (labeled CLEO II) with other measurements. The hatched region indicates the PDG world average result. 169 10.2 Future Improvements The data avai lable at the CLEO experiment has significantly increased since this analysis. In fact , it is increasing every day, and in the future one might expect to further improve the precision on the results presented here. It is important to note that at present the systematic error on the 17 parameter measurements is approximately on the order of the statistical error. However , as the statistical error decreases with increased statisti cs , most of these systematic errors are also expected to decrease, since one gains an improved knowledge of the detector with improved statistics . As can be seen in Table 9.17, several of the sources of systematic errors studied are detector related. Both the muon identification efficiency (determined using e+e- -+ ll+ f.,i- data), and the fake muon or pion punch-through error (determined using the tag T -+ !rn- 0 1/T decay mode in the data) are expected to decrease with improved statistics. Re-tuning the Monte Carlo simulation to further reduce the differences between data and Monte Carlo efficiencies in the tag mode would reduce the error resulting from correlations between the two sides. The Monte Carlo statistical error can also be reduced either by the generation of larger Monte Carlo samples, or by using improved techniques such as the "reverse" Monte Carlo technique employed in reference [44]. Future experiments such as the B factories , CLEO III, and Tau-Charrn factories could have large tau samples which might result in improved measurements as well. We have learned, in this analysis , that the data are a factor of two more significant when ana.lyzed in the "pseudo" rest frame of the tau. One would achieve maximum sensitivity in the true tau rest frame , and measurements made at a T factory running close to threshold might be very interesting if one gathered sufficient statistics. 170 10.3 Interpretation of the Results The measurements presented in this thesis, together with the recent measurements of the asymmetry parameters from the CLEO II Collaboration [44] , have been used to determine new limits on the ten complex coupling constants gJw, where 1 = S, V, T indicates a scalar, vector, or tensor interaction; and t, w = R , L indicate a right-handed or left-handed chira.lity of the daughter charged lepton and the parent lepton respectively. s, +; (~~ - 1: • s, 9 RR : +1 \_ _/; +; V, RR - ~ I -1 ~ • , ~ ~/)' 1 -; • / +1 +; - 1 '---~ -; -; 9 \ ( -1 \ __ +; s, ,,,,-----~, 9 LR 9 RL +1 +; -1 +1 -; -; +; +i V, (8 +; 9LR \ +1 -1 '. (~\ -1 +1 9 LR +; (-~ \ • ~-__/ -; : +1 :+1 \ -1 I -; -; T, -1 · -1 \~/ -; +; V' g LL T' 9 RL +1 / -; Figure 10.2: 90% confidence level experimental limits for the normalized T-decay couplings g;~ g;~/Nn, where N 11 max( lg;J) = 2, 1, l/J3 for n = S, V, T . The res ult s presented in this ana.lysis are included in the calculations. = = These new limits are shown in Figure 10.2, and we note that these limits are significantly better that the corresponding limits ob tained using the 1996 world average tau Michel parameters (see Figure 2.4). However , these new limits are still much weaker than the corresponding muon sector limits shown in Figure 2.3. Although consistent with Standard Model expectations, the limits on the couplings obtained in the tau sector do not prove V - A in the same sense as has been clone in muon decay. 171 Even if we assume infinite precision for the measurements of the Michel parameters, we do not improve the limits on the left-handed tau couplings. Thus, to significantly improve these limits, we require additional experiments such as the measurements of the daughter charged lepton polari zation , or of the neutrino correlations, or of the cross section for the inverse decay Ur c- ----, T- iie . The limits on non-standard couplings presented here leave plenty of room for physics beyond the Standard Model. The measurement of the r; parameter is particularly interesting, since a non-zero 17 measurement can be used to determine the mass of the charged scalar Higgs in the Two Higgs Doublet Model. We find that r; is consistent with zero, and the measurement presented in this thesis can be used to set a limit on the mass 7rlH of the charged scalar Higgs as a function of tan fJ, the ratio of vacuum expectation values of the two Higgs doublets. lJsing Equation 2.71, we obtain a lower mass limit: m1-1 - -_ > 0.97 GeV (90% C.L.). tan p (10.l) This new limit on the mass of the charged Higgs becomes competitive with that from direct searches for a charged Higgs(> 43. :j GeV, 95% C.L. [82]) only in the region of large tan /3. The measurement of the low energy 17 para.meter is also important for the evaluation of the Fermi coupling constant given by: (10.2) where C is the daughter charged lepton and Tr is the lifetime of the tau meson. The measurement of the 7h,. parameter is important for the muonic decay mode since m"Jmr is not negligible. A non-zero r; measurement would alter the uni versality of this coupling constant. The p parameter measurement can be used to set a limit on anomalous dipole couplings described in Section 2. 7, and we find that the anomalous dipole comp lex 172 form factor ""~r = -0.0-! ± 0.04. Thi s res ul t is still not quite at t he desired level of precision. Ho,vever , it is clear that fu t ure experiments at CLEO or the B-factori es vvith more than an order of magnitud e increase in statistics should begin to probe values or order 0.01. The interesting range of 1""~ I may no t be much larger than 1 Ii." a.bout 0.01 - 0.001 , since the corresponding 1i; couplings were found to be quite small. Cons id ering the left-right symm et ri c model for the electroweak interact ion , where pari ty violat ion has its origin in the spontaneous symmetry breaking of the left-right symmet ry, one can set limits on the mass of the pure right-ha.nclecl n ·n boson as shown is Section 2.7. \,\!hen the mi xing angle(, between the l;I/ L a.n cl WR bosons, is zero , vVR is id ent ical to H'2 in Equation 2.72, and we find that: mwR > 30Ll Ge\! /c 2 at 90 % C.L. The mass limi t obtain ed for ( free is: . > ·)60 C', e-\ ! / c2 a t oocl7' •J 10 C' . L. , 111. 1-1, R ~ where the res ults obtained in reference [44] a.re used in conjunct ion with the res ul ts obtained in thi s anal ysis to calculate t hese mass limi ts . 10.4 Conclusion In conclu sion, we have ma.de t he most precise to-elate measurem ents of th e spectral sha pe IVIi chel para.meters p and 17 , using th e leptonic decays of t he tau . We find no deviations from Standard Mod el ex pectations. The precision ou t hese parameters is now beginning to get interesting, as we approach the precision levels required to set limit s on physics beyond the Sta.nclarcl Model. 173 Appendix A A. l Some Mathematics Solving the Covariant Integral Ia f3 The differential decay rate for the decay, r-(p,) --+ e-(pc) + 11c (p1) + 11T (p 2 ), vva.s found to be: (A.1) in Chapter 2. The covariant integral , (A.2) onl y momentum vector remaining. Now , g o: /3 J C> /3 (A. :3 ) a.ncI qO q (j 1 ·0 13 (AA) To evaluate the Lorent z invariant integral I , 'We choose a convenient fram e of 174 reference in which the two neut rinos have equal and opposite momenta. Now, IPil = I (A.5) T hu s, ·) 2 2 4A( q- ) + q B(q ) q2 A(q2) + (q2) 2 B(q2) 2 1rq ' q4 7i 2 ' (A.6) and solving simult aneo usly for A (7f1 ) a.ncl B(q 2 ) lea.els to (A.7) A.2 Calculating the Limits of Integration the Dalitz plot variables was found to be: (A.8) in Chapter 2. To calculate the limit s of integration , ,ve assume rn 1 = rn 2 = m e = 0. Thus O s; Ee s; mr/2 and O s; Et s; l. In the tau rest fram e, Pr - p1 = P c2, leading to E 1 Since 2 ( ma.:r ) 771·e2 min l ') ·) ·) l = -.2rnr - [m; + 'I Tli - m c2 . (A.9) 175 E 1 ( mm ma:e) -J -1 _717 T [mT2 + 1n12 - (E*e + E*)2 2 + ( Pc* ± P 2* )2] · . 1 2 Em rn = --[ - 4E~ E*] 1 ') mT l 2 • (A.10) (A.11) -111 T Using PT =Pc + P12 , ])12 - P2 = P1, and PT - Pe = ])12 , vve find rnT2 - rn e2 2m,12 , 2 m12 E*2 and 2 m .12 + .m22 - m12 2m12 rn;') + J7?,(') - 2 m 12 2mT E. (' (A .12) respectively. E';: an d E; are the energies of t he lepton C and the anti-neutrino 1c in t he rn. 12 rest fram e. Substituting in Equation A.11 , and neglecting the neutrino masses and m t, we get 2 1?112 2m, -(al·1cl '-cmin 1 l - C 0f: . ] _:_(m2 , - 2Et) . (A.1:3) Thus, using the li mits of integrat ion calculated above, the decay rate or transitional probabili ty in Equation A.8 can be written as : (A.1 4) 176 Appendix B Muon Fake Rates Th e fake rate is defin ed a.s the fract ion of hadrons that a.re m isidentifi ed as muons lea.cling to a fake signal. There a.re four physical processes which contrib ute to t he fake signals: • hadrons reach the muon cham bers without interacting with the hadron absorber; • hadrons interact with the a bsorb er a.ncl th e product of t he interaction res ult s in a. muon signal; • hadron s decay in flight into m uons and t he daughter muons a.re detected; • the random overlap of track projection with noise hits in the muon chamber. In t hi s appendix. vve est imate the overaJl probabili ty that a. hadron is misidentified a.s a. muon using t he data.; no attempt is ma.de to isolate the different processes li sted above . The charged hadron in the T -t h. 7r 0 v decay n1ocle is used to st ud y t he behavior of hadrons in the muon system. The other Tiu t he event is required to decay leptoni ca.lly. All eve nts must satisfy the selection cri teri a. li sted in Section 4 with the exception of t he extra. energy veto. Thi s cut is relaxed to include the T - t h27r 0 11 decay events where t he second 7ro is not expli citl y reconstructed , t hu s increasing the hadron sample wit hout any contamination from non-hadrons. The ex pli cit reconstruction of the 7ro in the event along with t he sicle ba.ncl sub traction described in Section °!.l.G helps minimi ze t he contamination from cosmic rays and m u-pair events. T hese event s are also suppressed by TAUSE l\11 cuts (#2 and #G) described in Section -1.2.1 and by requiring t hat ( 17½ + p-; I) / (lz5; I + IP-; I) > 0.05. Most of t he hadron s identifi ed in this data sample a.re pions; t he re is 2% admixture of kaons clue to the Cabbibo suppressed decay T - t X *u followed by t he 1,·"' - t 1,· 7ro . F igure B.l shows t he DP THM1J versus momentum di st ribution s for identified hadrons and muons in the data. sample. Only a few percent of all hadrons st udied 177 populate th e plot on the right; the remaining hadrons all have DPTHMU =0. On the other hand '.:::: 98 % of the muons st udi ed appear in the plot on the left ; m uon identification inefficiency results in the small loss. 10.0 10.0 µ · ''I llllllllllll lllflllll 111111' ' I 11 ,,1j~~~m~~~~ii~Hli!m111111 1• I •11!~~~~11111111111111111111,,,'' '' ' ' - ~ • , ,ililDJim11, 111111111111, 1,11,,, , • •• o__ ••miu.11 1111 " ' ""'" . ........ .. •· · ·· , ,00~11111111 II I I I II II I 11 II II II IOI I I''• : .o~~~~~~~~~~~~ 0 I 1 11 I 1 1 11111111111 111111111111 "11111ll11111111•11• I 11•1 :::, 0 1 II ,11,111111111111111111,1,,,, .. •, 1•l~~~~~~~H~miiimum111 1, 2: 5.0 11111111 Ti I ' I I :::, ~ • ••IIIIUlllll1" •111111 Ill •I• '" o__ •lli!!imllllll1111ll111111ol Ill I• "' 2: 5.0 0 ,a~imm,11111111111111111, ' .0 ~~~~~~~~~~~~ 0 2 3 4 5 P,.(GeV/c) F igu re B.l: DPTHMU versus the mom entum of the charged track . The figur e on the left (right) is for identified muons (pions) in th e data sample. The number of ent ri es in both plots have been normalized to uni ty. l\!lost of thP hadron signal li es in the first set of muon coun ters and a DP T H1VIU > 5 requirem ent would reduce the fake m uon contamination consid erably. T hi s requirement would also reduce t he stat ist ics, but more irnportantly it wo uld eliminat e a. large fr act ion of the muons in the l.0-2.5G eV /c momentum region. These low momentum muons a.re es,.ential in t he m easurem ent of th e low energy 17 parameter. On e is th us forced to all ow DPTH1VIU>3 m uons into the e vent sample and perform a statisti cal background subtraction in stead to remove the hadron contamination. In add ition to the DPTHM l.T constraint, the muou id ent ifi cat ion cod e also requires t hat MUQ U AL = 0 for identified m uons. Thi s variable is set to zero for a.11 tracks where the pe net rated absorption lengths (DPT HMU) is consistent with the expected depth calc ul ated from t he track 's mom entum in t he drift chamber. l\!luon identification , in th is analysis, also requires that the total shower energy deposited in the 178 electromagnetic ca.lorimeter , and matched to the muon track, does not exceed 600 Me\! (see Figure 5.3). The above three criteria., for a track to be identified as a. muon , are novv applied to the hadronic track in the sarnple to obtain the momentum dependent fake rates for the three different DPTHMU requirements shown in figure B .2. The Monte Carlo estimates are not identical to the data estimates and are not utili zed in this analysis. ,,......_ DPTHM U . 12 .--, MONTE CAR LO e DATA ~ .1 0 ..._, w .08 f<( .06 0::: w >3 • ♦ .04 + ♦ :::.:: .0 2 <( LL .00 2.5 0 5 P,,(GeV/c) ,,......_ >5 DPTHMU .050 .--, MO NTE CARLO• DATA ~ .040 ..._, ~ ,0 30 <( 0::: .020 • w ~ .010 LL .000 0 2.5 5 P,, (G eV/c ) DPTHMU >7 .030 ,---,----,,---,-----.---r----r--.---,----,,----, .--, MONTE CAR LO• DATA t 2 .5 5 P,, (GeV/c) Figure B.2: Hadron fake rates and their mom entum dependence meas ured for the three different DPTH lVIU variabl es . These fak e rates are measured after the appli cation of the maximum allowed shower energy sum associated with the pion track . 179 The Spin Sensitive Variable w Appendix C For the decay of a polarized tau, the differential partial width is given by: (C.1) is the matrix element assuming the standard V - A interaction for a semi-hadronic T decay. B denotes the spin independent part of the decay and the polarimetric vector; H" denotes th e spin dependent part of the decay and contains all the spin analyzing information in the decay. The spin vector of the tau is denoted by s,,, and s =0 0 s = ±z3r in the tau rest fram e. The unit vector, z3r , is the spin quantization and direction and is positive (negative) for right- (left-) handed tau spin polarizations. It is equivalent to the direction of the T in the laboratory fram e of reference. Considering the T± --+ Hf ± --+ 71"±7ro /Jr decay mode, (C.2) where the hadronic current, J , can be written as: (C.:3) P 1 ' = (Prr + Prro )1' P 2 1 = 2 1 n " " o = 2 q . Q 1 ' = (p,, - p,,o )1' and F( 2 q ) is the Briel Wigner for the p/ p'. Now .. the differential partial width can be rewritten as: -, !J) . _ f o ( 1+ · s± • Fl) _ f ( JJr •~ B - o 1± cII ± - (C.4) 180 Defining w (13. • H)/ B rl7 T ( 2 ( // . Q )( ]) T • Q ) - Q 2 ( JJ T • J/ ) ) 2(,.Q)(11. Q) - Q 2(,. 11) (C.5) we get : fo(l ± w) . (C.6) Thus, w > 0 preferentially selects right-handed ,- (left-handed,+) and w < 0 preferentially selects left-handed,- (right-handed,+). As seen in Equation C.5, one needs to know the T momentum to evaluate w. Neglecting initial state radiation , the , momentum lies on a cone around the flight direction of the daughter hadronic (r.7r 0 ) system . Using thi s approximation, the exp erimental observable w is obtained by numericall y integrating over the unknown azimuthal angle ¢ of the tau. Thi s integration reduces t he polarim et ri c power of w, but is of no importance to the analysis. Figure 9.17 shows plots of thew variable for events analyzed in both the pseudo rest fram e of the tau (cos a ~ 0. 970) and the laboratory fram e of reference (cos a, < 0. 970). The events ana.l yzed in the pseudo rest fram e have approximately the same mix of left-hand ed and right-handed taus , while the events analyzed in the laboratory fram e have a much larger concentration of left-handed ,- and right-handed ,+. 181 Appendix D SVD Development The CLEO II. 5 detector has a new silicon microstrip vertex detector (SVD) insta.llecl as a major upgrade to the tracking system . Thi s new detector component was physically installed between May and September of 1995. The detector surrounds a new 2.0 cm radius beam pipe, and replaced the precision st raw-tube tracker described in Chapter 3: Schematic encl view (top) and side view (lower ) pictures of this new detector are shown in Figure D.1. Beryllium Beampipe Fiber Composite Supports - - Beryllium Oxide - -- Hybrids -E-----20cm ---------a.< Figure D.l: Schemati c encl (top) and side (bottom) views of the CLEO II.5 Sili con Vertex Detector. 182 The thick black lines in the encl vievv schematic indicate the locations of the Hamarnatsu clouble-sicl ecl silicon strip detectors . There are a total of 64 silicon detectors in the assembly, and 96 silicon wafers. Pairs of silicon wafers are ganged together lengthwi se in the third layer. The sensitive strips on the detector sides that face away from the center run in and out of the pap er , and are used to measure particle trajectories in the plane of the paper (r - ¢ ). The strips that face inward run in the plane of the paper, and measure traj ectori es in and out of the plane of the paper (r - :: ). For thi s side, an extra layer of metallization on the silicon is used to route the signals to the electronics at the ends of the detector. Both sides ( r-¢ and :: coordinates) are read out at the ends of the wafers in order to reduce the amount of mass in the ficlucia.l region of the detector where multiple scattering would otherwi se dominate th e resolution for soft tracks. These strips form the active elements of the de vice and are arranged in eight octants of twelve wafers ea.ch. The detectors a.re supported by U-channels of carbon fiber composite. Hybrid circuits built on a substrate of beryllium oxide, that in corporate CAMEX and JAMEX integrated circuits, are used to read out the detectors. Th e entire st ructure is supported by a carbon fib er composite tube. I have contri bu tecl to two different aspects of the design for this new vertex detec tor. First , in the summ er of 1992, I worked on the new mechani cal support structure for this detector. Over the follO\-ving two years , I spent a significant fraction of my time , a.long with two post-doctoral fellows, designing, constructing, testing , and installing a data acquisition system to read out the ne,,1 detector. Both these invol vement s are described in more detail in the following sections. 183 D.1 Silicon Vertex Detector Mechanical Assembly The demands of the mechanical design are fairly rigorous: the st ructural integrity must be very good in order to position accurately the devices; the mass of the structure in the fidu cial region must be low to minimize rnultipl e scattering; the thermal properti es must be such that adequate cooling is provided for the CAMEX chip and its line driver; and the thermal expansion coefficient of the materials used must sufficiently conform to that of the sili con. For thi s det ector , we opted to use a l l-sha.ped channel of boron carbide foam sandwiched between the layers , and held in place by a beryllium oxide (BeO) support st ru ct ure. T he radiation length for tracks at normal incidence introduced by the foam represents only a :30% increase beyond that of the three sili con layer, for a total of 1.26%. Furthermore, both materials have t hermal expansion coefficients similar to that of sili con , while the BeO also has a thermal conductivity similar to t hat of a good metal. We const ructed (with the help of ma.chine shop personnel a.t Newma.n Laboratory, Co rnell University) a. full- sea.le model of t he new interaction region (defined by the inn er walls of the drift chamber) in order to carry out mechanical tests of the support system for the new sili con vertex detector. The new interaction region design called for a red uced beam-pip e radius (of 2 cm ). Reduction in the radiu s results in an increased rate of backgrounds which are controlled by masking the beam-pipe. This masking in creases the weight of the beam- pip e by abo ut an order of magnitude. Water cooling, needed to handle the larger thermal loads expected at high er beam currents, further increases the weight of the beam-pipe. Since the sili con vertex de tector is expected to achieve a.n ord er of magnitude improvement in posit ion resolu tion , it requires a very stable support system. The full size mock-up of the interact ion region and the present support sys tem was const ructed using alumini um instead of steel, as in the original design , to ensure that stresses and strains vvould be enhanced and weak spots in the design would be easily identified. Once identified, the weak spots vvere redesigned and improved versions 184 were constructed and tested. The entire support system in the interaction region hangs off of the drift chamber endplates. These plates are very thick , heavy and stable, and it was assumed here that the addition of the SVD along with the new and heavier beam-pipe will not affect their stahilit_y. Various mechanical tests were performed to verify this assumption as well. D.2 The CLEO 11.5 SVD Data Acquisition In this section, the work completed to devise and implement a readout scheme for the silico11 vertex detector is described briefly. The read-out consists of 416 CAMEX/ JAM EX chips , each with a single analog output that multiplexes 64 chargeintegrated signals, for a total of 26 ,624 channels. Because of the large number of channels, it is necessary to sparsity the data; since the occupancy is low (a typical hadronic event hits less than a thousand microstrips), it is feasible to do so. The design criteria, which are partly dictated by the present system and timing constraints, are as follows: • The front-end electronics must digitize and store all channels in 1 ms. ( CLEOII 's present front-end electronics digiti zes the data in 2 ms, but there is a provision to reduce this by half). • Within 10 ms the data must be sparsi fi ed , with the event fragment read y for the event builder process. • The hardware and software must be compatible with the current data acquisition system. • The ground for the readout elect ronics must float at the bias voltage of the detector. The system consists of several components; a schema.tic of how all the pieces fit together to make the data acquisition system is shown in Figure D.2. ,:--t-_:1) ,:,, ..-; v I ~ 0 -. 0 ;,;: Cf) (D u D ~ (I) (") M- :::. c-,~ ..._. 0.... (") (1) ~ M-- ~ (/J (I) ..-; ~ • • H /'l) (") ,,.... 0.... c-,-- ~ (l) ~ lfJ ...... . 7 ~ trj >< ,~ ·-.::;; ~ (") H ~ ' • (I) ....... w 0 $ : (D c-+- ~ n I-+,~ ~- - (l) ~ - ~ ~ ~ F H ...; 0 ~ ► §' c-+- .::: ,,....· Q § ( §: (") ,.0 ~ /'l) ~ (") c-,-- ~ ~ ,.0 .::: /'l) (") ..-; H ~~ ~(1) c-,-r, 8 en;--...; /'l) M- .::: ,.0 (") ~ X r, ~ ii) ~ 0 ~ to 5'tl ~ . -; ~ - ..-; ..-; 0.... :f: < (1) < (I) I-' (1) ~ ...... . ~ 0 (I) (") -, (!) (") ::;--: H• :;cl . (l) i-1 (1) ~ c ~ - () 0 ~ (""°'\ ~- ~ (Tq I---! ~ ....... u ~ n c,....... . o . cn. .......... ,:-+ """"" ~ ....,~ ~ (D 0 ~ :::; >-en tv 0.... 0 ~ ro Q 0e-; .,,,,,, ~ (1) ~ :::; ::n ~ M- 0 (l) ~ ~ ~ 0.... ~ ~ iJ} x3-4 DISK Host Computer SLOW CONTROL/ MONITORING SC Crate in Pit data TRASH RCVRs; 12 BIT ADC & LATCH; FIFO x32 fail LEVEL 3 data ower I control data EVENT BUILDER MAIN SPARSIFIER CPU (68040) VIC DAQ90 INTERFACE VIC DAQ90 INTERFACE MVME162 Pre-Sparsifier 68040 DATA BOARDS x13 control SVD Crate in Pit RECEIVER BOARD RBs in CLEO x16 control ower . I PATCH PANEL data ---··-- SEQUENCERCAMEX INTERFACE CRATE SCis on CLEO x2 JAMEX x3-4 ower Hybrids in CLEO xl28 o en~ '"I:J 2; Q (Tq oq· CAMEX O....~ c-t- C w I-! V OR SH • (") (1) (1) u - ........ In Clamshell (svn DAQ) IE VME DAQ90 Crate in Pit :,.1 HOST in Pit SVD Crate HOST CLEO PULSER I CALIBRATION POWER SUPPLIES >--' <:.n C/) 186 Databoards: There a.re 13 data.boards in the SVD crate, ea.ch with a.n analog and a digital section. The analog sect ion services :32 CAMEX analog outputs with a. sample/hold circuit and a.n ADC (analog to digital converter) for ea.ch . The sample/hold allows one set of CAMEX channels to be digitized, while the next set are addressed. The digital sect ion begins with a. first-in-first-out memory (FIFO) into which ADC data is vvritten. The FIFO can hold several events if necessary. Following the FIFO is a ''pre-sparsifier ," a standard Motorola MVME162 boa.rd (based on the 68040 CPU) that will spa.rsify the data by suppressing common-mode noise, tagging data above threshold , and genera.ting a.n address for ea.ch. One MVME162 boa.rel resides on each data.board. From here, data. a.re placed into the }/IVME162 memory which serves to buffer events a.t the front-end so that CLEO can be re-enabled a.s quickly as possible. Sequencer board: A customized boa.rd that generates the appropriate sequence of clocks and channel addresses to the CAMEX chips and the cla.ta.boa.rcls. A signal from the CLEO-II event trigger sets it into action. Sequencer-CAMEX Interface (SCI) crates: These crates route the control sig- na.ls and output signa.ls to the appropriate places , maintain the floating grounds , handle test pulsing of the CAMEXes/ J AMEXes, control grounding of the test pulse lines , and interface the detectors vvith the slow-control system for monitoring. Since I worked primarily on the design of these crates, they a.re discussed in more detail in the following section. Main sparsifier: This is a. 68040 CPU boa.rel identical to those in the existing DAQ90 system. In addition to supervising activity within the crate, it fetches the pre-sparsifiecl data from the data board CP1Js and notifies the ma.in event builder in the DAQ90 system that the event fragment is ready to be incorporated into a formatted event. VICbus VME crate link: Connects the SVD VME crate to the ma.in DAQ90 VME system for data transfer and control messages. 187 D.2.1 SCI Crates The Sequencer-CA MEX Interface (SCI) crates a.re the links between the silicon vertex detector and the outside world . They provid e all the si li con vertex detectors with their required power, bias voltages and control signals. There a.re two identical SCI crates, one servicing ea.ch half of the detector. The final printed circui t boards for both the Controller and I/ O boards , whi ch populate these crates as shown in Figure D. 3, were la.id out using the design tool CADE 1CE. SCI CRATE -I -I -I -I -I -I -I -I -C I I I - -- - - - -- - - I L-- - - -- - - -- --- N rr :B B B B B B B B R 9u I I I I I I I ______ I : 1 : 1 : 1 :1 :1 : 1 '.L ____ __ : ------ I •I- - - - --I '.1 I :o 0 0 0 0 0 0 0 -I -I -I -I -I -I -I -C - ---- -- · - ---- -- - - - I I I I I I I I 0 :o 0 0 0 0 0 0 0 - I I ·I I ; t I - 0 0 0 0 0 0 0 0 N - -- - - -- - - -- T ---- ____ __ I :L _ _ _ _ _ _ 0 0 0 0 0 0 0 0 0 x A- A :A A- A :A A- L LA- A :A A- A :A A- A :r:-, ,R R R R R R R R liJ ---- --, :,- - - - --- R R R R R R R R L I '.I t :1 I :n D D D D D D D E I I L - ~ - - - -- ~ - - - -- ~ lf - ~ GND=-Vdet I '. I lR ---- -- I :1 I :1 I L------ D D D D D D D D E - -- - - - Pl - SPLIT VME BACKPLANES GND=+Vdet ~ ~ ~ I I I I I I I I I I P2 P3 - - - IR : - -- - 'f ~ I I I I I I I I B B B B B B B B R I '. t I :I 0 - -- - - -- - I I I I I I I I 0 - ~ ~ (front view) Figure D.:3: The SC I crate. Their ma.in fun ct ion of the SCI crates is to fan out a.II the relevant signals from se,·era.l discrete som ces to ea.ch of the 416 CAMEXes. These crates shape seve ral of the higher-frequency sequencer signals in an effort to rninimize the noise they broadcast. to t he signals of the nearby vertex detector (VD) and drift chamber (DR) subdetectors. They also provide many of the signals mon itored by the slow control system . The analog data. output signals are routed out through the SC I crates to a large patch panel wh ich translates between the outpu t signal multipli city, di ctated 188 by the 26 CAMEXes per detector octant, and the input signal multipli city of the 32 ADCs of each data board. All power lines coming from the power supply system pass through the SCI crates. Their voltage levels are monitored, and in certain cases, derived and adjusted . Finally, the SCI crates oversee the grounding and ungrouncling of ea.ch CAMEX/ JAMEX test pulse line during running and calibration respectively. Studies have shown that th is grounding/ungrouncling of t he test pu lse lines is criti cal to their proper operation. Voltages and control signals enter the SCI crate through the controller boa.rel ; a. schema.tic for whi ch is shown in Figure D.4. Some of these signaJs are changed from square to ''trapezoidal" in shape and decreased in amplitude to redu ce broadcast noise. SCI CONTROLLER BOARD ➔~~Optical -c_o_n_tr_o~l > Isolation SC Ad r. > SC Data Jl Pulse 1 - - - - - - - - - - - - - - -.- Control Signal Shaper Bus Address Bus Optical Isolation Data Bus SC A/D l at1on • ~---t---;Iso ._,__ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _1-1Monitor Buffer Bus 9u (side view) F igure D.4: The SCI Controller Boa.rel. The voltages and control sign als a.re placed on the backplane for di stribution to t he I/ O boards; a. schema.tic picture is shown in Figure D. 5. Ea.ch I / 0 boa.rel provides 189 voltages and control signals for half an octant ( there a.re eight octa.nts in each half of the SVD). In response to the appropriate a.cl dress placed on the backplane through the controller boa.rd by slow control, the 1/0 boa.rel put s various monitored analog quantities on the backplane. These quantities are then sent out via. the controller boa.rel to be digiti zed and placed in the data stream or used to generate alarms as appropriate. Ea.ch 1/ 0 boa.rel has incl ivicl ua.lly fu sed voltage lines supplying the CA MEX/ JAMEXes , in order to facilitate shutting clown individual chips in the event one fai ls, or, for example, begins to clravv an excessive a.mount of current. The analog output signals from the chips also pass through the 1/0 boards where they a.re bundled together and sent to the patch panel and the data.boards to be digitized. SCI I/0 BOARD c trl 1/2 Octant V's data Analog Output Data Derive & Fuses & 1-E:::::-V_'s--;Remotely f,,,,E'~V_'_s--+~ Monitors Adjust Voltages Monitored V's Power SC Data Isolation 9u (side view} Databoard A/D Figure D.5 : The SC I 1/0 Boa.rel . These SCI crates a.re also used to provide the "floating gro und" for the detectors. There a.re two sets of strips that a.re used to readout the detector. The sense strips a.re the actual p or n material impl anted into the bulk of the detector. The readout 190 strips a.re separated from the sense strips by a. thin layer of SiO 2 , which acts a.s a. capacitor. The electron-hole pairs generated by a. passing track a.re collected on the sense strips, and the resulting signal is capacitively coupled onto the readout strips. In th e original readout scheme, the p and n sense strips were to be kept at - 50 V a.ncl + 50 V respectively, so tha.t the detector would be biased whi le the readout strips (whi ch a.re a.tta.ched to t he input of the CAMEX pre-amplifier) would be kept a.t ground. Unfortunately, the thin layer of SiO 2 seemed to develop "pinholes" occa.siona.lly (on '.: : :'. 5% of the strips) , thus joining the 50 V bi as voltage to ground through the preamplifier chips . A large ( '.: : :'. Mn) resistor limited the current draw, but this still ca.used the channel and many of its neighbors to function improperly. To combat thi s problem , it was decided that all of the readout electronics would have "floating ground s" that were at ±50 V relative to earth ground . That way if a. pinhole occurred , small er currents would be drawn. vVhen it became clear that the pinhole rate was too high , Hama.matsu added an aclclitiona.l layer of silicon nitride. Thi s reduced the pinhole rate to less than 1% on the later detector deliveri es. Th e flo ating ground readout scheme ha.s been implemented. Opto- coupler chips a.re used to flo at th e incoming TTL logic signa.ls from earth ground to floating ground. Capacitors a.re used to bring the flo ating analog CAMEX output signals back clown to earth ground. All of thi s translation is clone at the SCI crate. D.3 Schematics Figure D.6 shows the cleta.ilecl schema.ti c layout of the SCI Controller boa.rel. Ea.ch rectangle on this sheet represents a. specifi c part of thi s boa.rel ; their specific function s a.re mention ed below. The differential control signals from the receiver boa.rel enter through the sequencer connector shown on t he top left-ha.ncl corner of this schema.ti c. These differential signals a.re received by the electroni cs in the schema.ti c box labeled RECEIVER.SCH , before they a.re level shifted from ear t h ground to the floating voltage by the op- 191 tocouplers in OPTOP.SCH. The highest frequency pulse signals are converted to trapezoidal signals to reduce their risetimes, and thereby reduce the broadcast noise to neighboring detectors (for example, through the drift chamber prea.mplifiers). The risetime, and lower and upper limits of these pulses , are adjusted using three potentiometers on each Controller boa.rel. All this shaping electronics lies in the schema.tic box labeled TRAPEZP.SCH. Next, the control signals and address lines a.re buffered in BUFFER.SCH before they a.re placed onto the Jl backplane for distribution to the I/0 boards. BACKPLANES.SCH includes the schema.tics for the three backplane connectors on this boa.rel. The .Jl connector collects the control signals from the buffers for distribution to the I/O boards. There a.re a total of 44 and 53 monitored quantities for P and JV-side sections, and these a.re collected from the I/O boards through the .J3 backplane. The .J2 connector supplies the Controller boa.rel with all the required power, and is connected to the Pclist boa.rel of the power supply system. Voltage dividers in VOLTAGE.SCH a.re used to prepare appropriate voltage levels needed by other parts of the Controller boa.rd. A Comparator in SCENAB.SCH 1s used to provide the slow control enable signal. The Slow Control sys tem determines which of the 36 boards in the two SCI crates is to be monitored at any given time by sending a. 6-bit address to the Controller boards. This address is placed on the .J2 backplane and ea.ch boa.rd compares it to the unique hardwired geographical slot address. The 74ALS520 chip which performs this comparison can be strobed (output enabled) either by using the 7th bit , or can be enabled at all times (selection is ma.de via a. jumper). The schema.tic for the pulser, designed by Shun Chan and Chris O 'Grady, a. Caltech graduate student and post-doctoral fellow respectively, resides in the box labeled PULSER.SCH. Test pulse triggers enter the Controller boa.rel, and are used to place a test pulse of a. certain length and amplitude onto the backplane for distribution to the 1/0 board s. A DAC is used to determine the height of the test pulse. Each of the three test pulse lines can be activated independently via Slow Control. The length of the test pulse line is determined via a one-shot, the output of which is controlled by 192 a potentiometer. Since there is only one DAC , only one pulse size may be generated a.t any given time. Various power supply voltages and many of the control and pulser signals are connected to front-panel LED s. All signals to the LEDs a.re collected , and voltage dividers in LED CONN .SCH are used to drop voltages to levels that are accepted by the LEDs. The front panel LEDs in LEDS.SCH provide a visual stat us display for the Controller board. Optocouplers a.re used to float all the Slow Control signals to the floating voltage in SCOPTOP.SCH, a.ncl CMOS switches a.re used in SWITCHES.SCH to switch the Controller board voltages monitored by the Slow Control system . The "Slow Control Ena.bled" signal is generated by the comparator in SCENAB.SCH. Floating currents (from the I/ 0 boards via the .13 backplane) a.re level-shifted clown to Earth ground in DEFLTPI.SCH before they a.re sent off to the slow control ADC to be digitized for monitoring purposes. Floating voltages a.re level-shifted down to Earth ground in DEFLTPVl.SCH and DEFLTPV2.SCH. The edge connectors in EDGECONN .SCH are used to collect (and transfer) all the currents and voltages that a.re to be monitored by the Slow Control system . 193 ; ; ; 8·'' - ' -3- - : ; ; :e : !~ ~ ; : Jlllli 11 LLLll ~l•l'l•lof.l.L.l.bl.l.,l'.L! Figure D.6 : The SCI Controller Board schematic drawing. Each rectangle on this sheet represents a specific part of this board. 194 The I/O boards take the control signals placed on the backplane by the Controller boa.rd , attenuates them by a. factor of twenty, and differentiali zes and buffers them before sending them off to the Recei ver boards which transfers them to the CA MEXes. The P -side I/O boards talks to both CAMEXes and JAMEXes, and thus, two sets of reference voltages a.re required on them. Figure D.7 shows a. schema.tic dravving for the JV-side I/O boa.rd. The connections to the three backplane connectors on the I/O boards lie in the BACKPLANES. The Control signals are read via the Jl backplane, and all the hybrid and CAMEX (JAMEX) power supply voltages, provided by the power supply system, enter through the middle J2 backplane in the same manner as for the Controller board. ·w henever an I/O board is Slow Control enabled, it closes its CMOS switches, thereby placing its monitored voltages onto the J3 backplane. The chips used to differentialize the control signa.ls from the Jl backplane a.re contained in CSDIFF. The attenuation and differentia.lizing reduce the control signa.l's ability to broadcast noise to the components of neighboring subdetectors. Differentia.lizing these signals also improves their immunity to external noise sources . The control signals are buffered in CSDIFFBUFF before they are sent off to the Receiver boards. The address lines and the output enable (OE) are buffered in CSBUFF. Each of the hyb rid and power supply voltages that enters via the J2 backplane is fused , monitored and routed to the appropriate output connector in SWITCH- YARD. Certain voltages are derived from the power supply voltages so that they can only be present if power is present , and a.re adjusted using potentiometers on each I/O boa.rel. The detector bias voltages, or the offsets from floating ground, a.re derived independently on each I/O boa.rd for each detector wafer via four potentiometers. Many of these voltages can be measured by means of test points located just above the Data.Boa.rd connectors along the face of the I/O boards. All monitored volta.ged are brought clown to appropriate levels in VOLTAGE MONITORS using several voltage dividers. A comparator m IOCOMPARATOR is used to determine if the particular board is being addressed at a given time. It is identical to the one on the Controller 195 board. The Slow Control CMOS switches occupy the rectangle labeled SC CMOSS- WITCHES. \i\lhen a board is selected via the Comparator, a "Slmv Control Enable Signal" is sent out and the CMOS switches are closed. The monitored voltages are then placed onto the .J3 backplane. During calibration , each I/0 board takes test pulses off the backplane, buffers them, and routes them to the appropriate output connectors in TESTPULSE. Whenever test pulsing is disabled, the test pulse lines can be grounded by means of a solid-state relay either directly to floating ground, or through a potentiometercontrolled resistance. The grounding mechanism is controlled by a jumper. Some signa.ls are monotored via front panel LEDs in IOLEDMONITORS. The signa.ls are brought clown to levels accepted by the LEDs on these boards in LEDLEVELS. As with the Controller board, the LEDs provide a vis ual status display for the 1/0 boards. The output data from the CAMEXes is sent different ially to the 1/0 boards from the Receiver boards. The 1/0 boards receive these signals, buffer them, and level-shift them in LEVEL SHIFTERS by means of an AC-coupled differential op-amp ( to eliminate any noise between floating ground and Earth ground). The AC-coupling is achieved by means of l/lF, 50 V capacitors. The ga.in of this defloating amplifier is controll ed by means or resistors. This acljustability enables us to optimize the output signal with respect to the Data.boa.rd ADCs. Fina.lly, the CONNECTORS rectangle shows the connections to the hybrid connectors, and temperature sensors monitor the temperature of t he I/0 boards in TEMPERATURE. ~ - Ii) v) (I) f-3 p-"' -1 vJ ;:)) i,-,- (") M- ~ :::; ,_. Ii) ~- M- Ii) (1) v) p-"' :::; M........,. ,_......, .,, ~ vJ W ~ M- ~o ("l 00. Ii) ~ g ;=c; ~ trj ~ () '"v v) ~ vJ ~ ~ ~ "v 8 n h 0 0.... ....., ~ (I) ~ Ii) tj 00. n 0... ~. v) (1) ci.... ;:)) 0 c... i:-: 2: td E v) >---< v o ------0 M-~ o>-+, (en) rT) ~ ~ ,J ) 0..: "v I ~ n > -, ("l (1) "C ~ v) ~o (1) ~(i) ~~ '"rj ..-; Ii) I-- I-- t- E 11 D B C D N N I I EN W<2 .. 1> D01JT<26 . . 1> 7 I I TEMP< . . 1> 6 Tl 1> l LI ____k:;32 . . 1 > Ts3 I GUG I,EDI,EVE::~~ L I II 11 VREF t - - - - - - - - - - - - - - - - - - - - + TEMP CDt - - - - - - - - - - ' ENSW DOUT !RS ENSW DOU SHIFTERµ ENSWE I TOT.F.DMONITORS L...j OUT E~lEI OUT<13 .. 1> U! 8 I .. 1> .. 1> DRAWING TSEN I LAS T_MODIF!EO a:. Thu Sep > IBAK RBEN ~ VBAK I I I 1 11 : 03 : 23 1 994 Ivsrl U266 U26 7 3 I . . 1> I ENG I NEER : GU;d 1> TI<~ - • 1> l> GUG I TI I rvsc I I ROSS/COWEN/CHADHA I PAGE , N -S IDE I \O ROOT r m , s:~4 l TIT~CI 1:EsTem r vscs6 4 r--==~-"-"'--' SCA t-......,.<=..,_,_.a...!.!..a!...._.j GA U2 9 IBAK U2 68 I VBAK CT IBAK<l5 .. l> . . l> ENSWE I-- I-- 11 C 11- II D 1 OF 1 7 BACKPLANES VBAK<l8 .. l> I T<l 2 oooO '"" CEN< VOT,TA~F. MONTTORS VPAS IMON I VPAS VMON<32 . . l>VMON VPA < TM N<2 VREF<27 .. 1> ENSWE 5 t(.D 0) 197 D.4 Printed Circuit Boards For bot h the final SCI Controller and I/ O printed circuit boards (PCB), vve used 9lT board s (366.7mm x 227. :3111111 ). In addition to the top and bottom layers, that were utilized primari ly for the routes connecting the various components, ea.ch boa.rel has eight embeclclecl voltage a.ncl ground planes. 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