Test of the ΔS = ΔQ Rule and CP-Invariance in Kₑ₃ Decay Citation Gallivan, John Daniel (1971) Test of the ΔS = ΔQ Rule and CP-Invariance in Kₑ₃ Decay. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/4ZWR-J504. https://resolver.caltech.edu/CaltechTHESIS:09272017-154622661 Abstract The complex quantity X = (amplitude of the ΔS = -ΔQ process K -o → π - e + v/amplitude of the ΔS = +ΔQ process K o → π - e + v) has been measured in a counter-spark-chamber experiment at the LRL Bevatron. Assuming CPT invariance, ImX ≠ 0 implies CP-violation in the decay. K o - mesons were produced in two brass targets by 2.85 GeV/c pions. A series of veto counters and hodoscopes selected neutral decays into two charged particles. The electron and pion were identified by (1) pulse height in a Freon 12 threshold Cerenkov counter, (2) visual appearance in three radiation lengths of lead, and (3) pulse height in a set of fourteen shower counters. From 240K pictures, 1,079 events were isolated with a (2 ± 1)% background level. A maximum likelihood fit to the π - e + and + e - time distributions gave the result: ReX = -.069 ± .036 ImX = +.108 ± +.092 -.074 This result is within two standard deviations of X = 0 and therefore consistent with it (relative probability = 0.25). It is, on the other hand, more than four standard deviations from the existing world average (+0.14, -0.13) and therefore inconsistent with it (relative probability < 3.3 x 10 -4 ). Sensitivity of the result to a large number of possible systematic effects was investigated and it was concluded that any systematic error was small compared to the statistical error. 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): Peck, Charles W. (advisor) Sciulli, Frank J. (advisor) Thesis Committee: Unknown, Unknown Defense Date: 14 July 1970 Funders: Funding Agency Grant Number Atomic Energy Commission UNSPECIFIED National University of Ireland UNSPECIFIED Record Number: CaltechTHESIS:09272017-154622661 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:09272017-154622661 DOI: 10.7907/4ZWR-J504 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 10465 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 28 Sep 2017 21:49 Last Modified: 20 Jun 2024 22:46 Thesis Files Preview PDF - Final Version See Usage Policy. 47MB Repository Staff Only: item control page

TEST OF THE 6S = 6.Q RULE .AND CP-INVARIANCE IN Ke 3 DECAY Thesis by John Daniel Gallivan In Partial Fulfillment of the Requirements For the Degree of Doctor of Philoso~hy California Institute of Technology Pasadena, California 1971 (Submitted July 14, 1970) :LL /\CKNO WL~DGBMEN'm The experiment described in this thesis was a major effort, even by the standards of high energy physics, and its success depended on a large number of physicists, technicians, prograrrrrners and scanners. In the course of this work, the author was influenced by many people. It is a pleasure to thank Professor Charles Peck, as academic advisor, for his patient and sympathetic guidance, and Professor Frank Sciulli, who supervised most of the research described herein, and who taught by example as much as by persuasion. The author also acknowledges the stimulating environment of the Caltech User's Group, in particular Professors David Binnie, Ricardo Gomez, and Alvin Tollestrup, and the cooperation of Michael Mallary as fellow graduate student on the experiment. The Bevatron operations staff and members of the Lofgren Group at the Lawrence Radiation Laboratory gave invaluable assistance during the preparation and operation of this experiment at the Bevatron. A. Lake, D. Sell, W. Friedler, H. Grau, S. Sedleniek, and D. Toomer contributed to the design and construction of the equipment. Messrs. D. Chu, P. Walden, K. Young, G. Murata, and J. Stanley assisted in the setup and running stages of the experiment. Messrs. C. Lam, D. Molodowitch, J. Tam, and L. Young assisted materially in the data analysis. The scanning and measuring staff was supervised by J. Ferrari and included J. Edwards, M. Jolli.f f, M. Jordan, J. Lyon and G. Martin. The staff of the Caltech Computing Center gave the iii author much acs is tan cc in progranuning and computer opernt:i.onn. 'J'hc contribut:i.ons of Dr. Bruce Sherwood who des:i.gned. the PDP-II progrrun EXPO, and Dr . James Van Putten who designed and built the lead plate spark chambers, are sincerely appreciated . Finally, this manuscript is evidence of Virginia Franklin's typing skill. The author thanks the United States Atomic Energy Corrrrnission and the National University of Ireland for financial support during the author'sgraduate residence at Caltech. iv ABSTRACT The complex quantity X = (amplitude of the 68 = -t::.Q process ~~ ~-e+v/amplitude of the 68 = +6Q process K0 ~ ~-e+ v) has been measured in a counter-spark-chamber eXJ>eriment at the LRL Bevatron. Assuming CPr invariance, ImX I 0 implies CP-violation in the decay. 0 K - mesons were produced in two brass targets by 2.85 GeV/c pions. A series of veto counters and hodoscopes selected neutral decays into two charged particles. The electron and pion were identified by (1) pulse height in a Freon 12 threshold Cerenkov counter, (2) visual appearance in three radiation lengths of lead, and (3) pulse height in a set of fourteen shovrer counters. From 240K pictures, 1,079 events were isolated with a (2 ~ 1)% background level. A maximum likelihood fit to the ~-e+ and ~+e- time distributions gave the result: Rex = -.069 ~ .036 +.092 I.mX ~ +. 108 -.074 This result is within two standard deviations of X = 0 and therefore consistent with it (relative probability= 0.25). It is, on the other hand, more than four standard deviations from the existing world average (+0.14, -0.13) and therefore inconsistent with it (relative 4 probability< 3.3 x 10- ). Sensitivity of the result to a large number of possible sys~ematic effects was investigated and it was concluded that any systematic error was small compared to the statistical error. v T.f\.BLE OF CONTENTS PART I. II. III. TV. v. TITLE INTRODUCTION (A) Theoretical Background of the £:::.S = b.Q Rule (B) Ke 3 Decay (C) History and Current Status of the £:::.S = b.Q 0 PAGE 1 1 6 Rule 9 (D) Experimental Measurement of X 13 (E) This Experiment 15 EXPERIMENTAL APPARATUS 19 (A) General Features of the Apparatus 19 (B) Triggering Components of the Apparatus 23 (C) Data Recording Components 26 DATA ANALYSIS AND BACKGROUNDS 32 (A) Scanning 33 (B) Measuring and Event Reconstruction 42 (C) Final Selections 50 (D) Estimation of Remanent Background 58 EFFICIENCY CALCULATION AND MAXIMUM LDCELIHOOD FITS 71 (A) Ke 71 (B) Maximurn Likelihood Fitting of Data 3 Efficiency Calculation CONCLUSIONS AND OUTLOOK 85 100 t ( tt I ! vi ~ l TJ\.DLE OF CON1.PEN1rS (Cont l. nucd) PAI~r '1~I'l1Ll~ Pf\Gl!: VI. APPENDICES 103 VII. REFERENCES 173 I f \ vii APPENDICES NUMBER TITLE PAGE 1. Theoretical Supplement 103 2. Pion Beam 110 3. Targets and Target Counters 114 4. Spark Chambers 119 5. Freon Cerenkov Counter 124 6. Hodoscopes and Shower Counters 129 7. Fast Electronics and Trigger Logic 135 8. Slow Electronics and Computer 140 9. Data-taking Procedures and Checks 142 10. Scanning Procedures · 143 ll. Measuring, Reconstruction and Track Fitting 157 12. Monte Carlo Program 163 13. Smearing of Time Distributions Used in 170 Maximum Likelihood Calculation viii LJ S'r 01" FIGURE[; FIGURE CA.Pl'ION PAGE 1. SU(3) Properties of Currents 5 2. + Terms I, II, III of N-(t) 14 3. The Nine Experimental Measurements of X Sunnnarized in Table 1 17 4. Experimental Apparatus 22 5. Block Diagram of Trigger and Data Recording Logic 27 6. Shower Counter Distributions of Electrons and Pions 34 7. Electron Pulse Height in Shower Counters for Three Electron Energy Regions 35 8. Average Individual Scanning Efficiency of Production-Decay Region Scan 41 9. Distribution of Xt 10. M 11. X Per Degree of Freedom for All Tracks 48 12. Distribution of !:iXve rt ex = (Xp l a t e - Xf.t) i 49 13. Decay Position Distribution of All Events Passing Reconstruction 51 14. Decay Position of Events Rejected by Quantitative Selections (1) - (7) 57 15. Decay Posi t:i.on Dl.ctr:ibutions of Events Re;jccted in ShO\·tCr Chamber nccca.n 59 16. Comparison of rec Srunple with rcrc Sample 2 pre and M rcrc rac k in Decay-Shower Measurement Distributions from Each Target 2 45 47 ix LIST OF FIGURES (Continued) FIGURE CAPI'ION PAGE 17. M + - Distributions from Lead Converter and 66 e e rce Sample 18. M Distributions for e+ and e ep Events 68 19. Sketch of K - production Distributions 75 20. Comparison of Calibration Data and Monte Carlo for Momentum and Angle Distributions from Each Target 76 21. Comparison of Decay Position Distribution for Calibration Data and Monte Carlo from Each Target 77 22. Mean GC Pulse Height as a Function of Position for Tl rce Data 81 23. Efficiency Functions at 2.8 Kg 82 24. Comparison Between rce Data and Monte Carlo for Pion Momentum, Electron Momentum, and rce Resultant Momentum 83 25. Comparison between rce Data and Monte Carlo for m , the Invariant Mass of the rce rce 84 26. Decay Position Distributions of Final rce Sample 88 27. The Best Value of X from This Experiment 89 28. Likelihood Contours for Fit to Sum 97 29. Likelihood Contours for Fit to Asynnnetry 98 30. Sketch of re Beamline lll 31. Block Diagram of Berun Electronics 112 32. Number of Vees on Film and rcrc Trigger Rate for Different Target Materials 116 0 x LIS'l' OF FIGURES (Continued.) FIGURE CAPTION P/\.GE 33. Block Diagram of Target Electronics ll8 34. Sketch of Gas Cerenkov Counter 125 35. Block Diagram of Gas Cerenkov Electronics 128 36. Block Diagram of MH Electronics 130 37 . Block Diagram of RH Electronics 132 38. Block Diagram of SH Electronics 134 39. Block Diagram of Trigger Electronics 136 40. Computer Scan .Analysis of Ke 144 41. Electron Pulse Height in Shower Counters for Four Segments of Decay Region 145 42. Pion Pulse Height in Shower Counters for Four Segments of Decay Region 146 43. Horizontal Separation Between Pion and Electron at Shower Counters 148 44. Shower Counter Pulse Heights of e and ~ for Different Charges 149 45. Electron Acceptance of Computer Scan as a Function of Electron Energy 150 46. Shower Scanning Criteria 152 47. Production-Decay Region Scanning Criteria 154 48. Special Cases in Production-Decay Region Scan 156 49. Production-Decay Region Measurements 158 50. Comparison Between Calibration Data and Monte Carlo for Y-profile of ~ 165 3 Trigger xi LIST OF FIGURES (Continued) FIGURE CAPTION P/\.GE 51. Comparison Between Calibration Data and Monte Carlo for Z-profile of re 166 52. Comparison Between rce Data and Monte Carlo for Z-profile of e 168 53. Comparison Between rce Data and Monte Carlo for Z-profile of re 169 54. Difference in N+(N-) with Various Corrections for Higher Moments of pK- Spectrum 172 x:Li LIST OF TABLES TABLE TITLE PAGE Measurements of x, 1963-69 16 2. Effect of Quantitative Selections on ~e Sample 56 3. Back~rounds 4. Corrections to Ke Efficiency Function 79 5. Fits with Variations in Fiducial Volume 93 6. Fits with Variations in Mean Momentum, Mean Production Point and Ke Efficiency Function 94 7. Fits Made Investigating Background and Biases in Data 96 8. Fast Logic Signals 138 in ~e Sample 3 70 3 i 1 I. t i l INTRODUCTION I In the past decade, one of the most spectacular dcvclopmcntc :tn r t t ! particle physics has ·been the uGc of internal symmetrJc:: Jn irndcrstanding the interactions between elementary particles. The most prominent of these symmetries, SU(3), combines isotopic spin and strangeness, both of which are conserved in the strong interactions. I' 'f I I f The weak interactions conserve neither isotopic spin nor strangeness and so violate SU(3). However, as will be shown, the most elegant way of breaking SU(3) implies certain selection rules in weak transitions. One of these is the 6S = D.Q rule, which applies to strange- ness-changing semileptonic transitions where 6S is the change in strangeness and D.Q the change in charge of the hadrons involved in the transition. The rule was first proposed in 1958 by Feynman and Gell-Mann and has been the subject of theoretical speculation and experimental investigation ever since. This thesis describes an experiment which studied the leptonic decay of the K-meson, K ~ ~ + e + v and measured the parameter X, the ratio of the D.S = -D.Q amplitude < ~ - e+ v 1:-::0 K > to the 6S = +D.Q amplitude < ~ - e+ v IKo >. A. Theoretical Background of the 6S = D.Q Rule In 1958 Feynman and Gell-Mann(l) formulated the presently accepted notion of the weak interaction as a current-current interaction, for which the interaction Lagrangian density has the form: 5 Lwk (x) = -G J,t(x) ·J, (x) where G "' l0- m- 2 and J, (x) is a current int rv .J2 I\ rv I\ rv p /\ rv I I 2 which ho.o contrlhutiorw from o.11 partlcleo huving weo.k :Lrrtcrr.J.ct :!.orni. J)\ ha.o a vector po.rt and an o.xln.l vector purt which obey current con- servation laws of varying degrees of validity. Up to the present, there is no evidence for scalar, pseudoscalar or tensor contributions to the currents although they are allowed by Lorentz invariance. If wk one separates J'/\ into a leptonic part and a hadronic part, then Lint ! I1 becomes: ! The first term involves only leptons which do not have strong interactions. Matrix elements involving this first term can be accurately calculated by first order perturbation theory and experiments on the purely leptonic decay µ ~ e v v are consistent with the current: I I I I i \ in the usual relativistic Dirac spinor notation. Of the terms involving hadrons, the first ~hadr ~ept + t lept _hadr . . __hadr J'/\ ~i , offers most hope of understanding, since ~~ occurs only once and its matrix elements are easier to handle than those of Jt'/\hadr Jhadr '/\ • The b es t k nown t erm in . ~i _hadr is . the A~- decay t erm in. volving nucleons, ¥pr'/\(l + cr 5 )~n where C ~ 1.2. In isotopic spin formalism this can be wri ttcn 'FN I _/'f\ (1 + Cy 5 )~N where ~N is o. general nucleon spinor, and I is the isospin raising operator. Meson decays + are accounted for by introducing terms containing meson fields into the hadronic current. The conserved vector current hypothesis pro- 3 vides an elegant prescription for adding the vector part of the rneGon current. For pions it is pion ( vector part ) = :i.[I!> * I JA 1( where I!> ~ operator. + o,!Ji - (o,<I> ) *I II> ] " 1C " 1( ·I· n is the pseudoscalar pion field and I is the isospin raising + With this addition the vector current of nucleons and pions is conserved. n+ -+ :rr0 + e + + v is an example of semileptonic pion decay and its experimental rate agrees well with that predicted by the above pion vector current. The decays considered so far do not involve strangeness change (6S = 0). To account for strangeness-changing (6S f 0) decays of hyperons and K-mesons, terms involving these particles are introduced similar to the nucleon and pion terms. Still considering semileptonic processes only, the current ~pyA(a + by 5 )~A will give rise to A ~-decay, A -+p + e-+ v, and a combination of pion and K-meson fields similar to the pion current will give processes such as K+-+ n0 + e ++ v. Other possible terms in the 6S f 0 current are (abbreviating the bilinear form): All the currents have been written with 6S = +l, but the first set has D.Q = +l while the second and third sets have D.Q = -1 and D.Q = 0 respectively. So the first set of currents provide for the D.S = -tl':.Q processes + j, + v - -+ n + j, + v A -+ 'P L: + - -+ :rr + j, + + v (v) K 0 K 0 -+ :rr - + p,+ + v while the second set provides for the f:::S = -6.Q processes The third set cannot play a role in semileptonic processes since there are no known neutral leptonic currents. Feynman and Gell-Mann noted that f:::S = -6.Q tenns like (n, L:+) were not needed to account for the observed hyperon decays and would lead to unobserved processes, L:+ -+ n + .R, + + v • f:::S They also noted that ·f:::S = -6.Q in conjunction with = + 6.Q tenns would lead to decays such as :s- -+ :rr - n with f:::S = +2. With the advent of SU(3) symmetry for the strong interactions, the f:::S = 6.Q rule appears in a very natural way. The pion and nucleon currents involve isospin through the I operator which transforms like + an object with III = 1, I 3 =+land hence has the same SU(3) trans~ : + formation properties as the :rr If the rules !t::SI = l and f:::S = 6.Q are true for strangeness-changing decays, then the simplest SU(3) properties for the strangeness-changing current are those of the t K -mesons. This is illustrated in Fig. l(a) where the SU(3) spin 5 (a) l6Sl=1 Currents 6S •0 Cu rronts • (b) Ko rr+-rr 0 a+11 ----.;;;_ _,__G----.. rr+ ., .8 (c) Ko n - \) 8 • .r..*+ ;:;*O • - 10 Fig. 1 • 6S = -6Q currents - . 10 • • • SU(3) properties of currents : (a) j6Qj = l currents in the octet; (b) transitions caused by currents in (a); (c) 6S = -6Q transitions and their currents. 6 operator F + iF 2 CI) is identified with the re+ and the 6S 1 6S = 6Q SU(3) operator F4 + iF is identified with the K+. 5 = 1, The current is represented by an arrow from the origin of' a multiplet to the position of the particle having the some GU(:5) tro.ncformation properties. The octet current hypothesis, proposed by Cabibbo, ( 2 ) consists of the proposal that all hadronic currents in the weak interaction are members of an SU(3) octet of currents. The currents shoYm in Fig. l(a) are all charged; the remaining currents, vlhich correspond to 0 the re , ~' 0 ::-:0 K , K , are all neutral and hence do not take part in semi- leptonic decays. In this scheme, the semileptonic decays can be seen as transitions in the particle octets induced by the currents of Fig. l(a), as shown in Fig. l(b). or~+ .... n + e+ + v require 0 Decays such as K .... re+ + e + v transitions caused by currents which are not members of an octet, and so violate the 6S = 6Q rule. In fact, the lowest SU(3) multiplets admitting such a member are 1,5) or lO as shown in Fig. l(c), vlhere the currents correspond to 6- and t;+- • B. 0 K Decay -e3 ___ ,_ Measuring the magnitude of the 6S = -6Q amplitudes in hyperon decays,~ +-.n + £+ + v, -0 ~ _. ~ - + £+ + v, involves direct measurement of the branching ratios for these processes. ferent for neutral K-mesons due to the KT, The situation is dif- - K8 phenomenon, vlhereby K- decay occurs from states which are almost eigenstates of CP and so arc not eigenstates of strangeness. This means that K°-. re- + e+ + v can interfere with K0 ..-. re - + e + + v and by studying the interference 7 one can meaGure the phas e of any 68 = -1:::.Q amplitude pres ent r elative to the 68 = -t6Q ampl:Ltude. f\ s ohown in Appendix 1, there are four diotinct am1)li tlJCl.cs J'or Ke.).,. Jcco.y f, the amplitude for K0 ~ n - e +v f, the amplitude for ::0 K ~ n+e - v- g, the amplitude for K0 ~ n+e --v 68 = -1:::.Q g, the amplitude for ""'° K ~ n - e +v and one defines X = g/f and X= g(i. All of these functions involve 2 a form factor which depends on q , the square of the 4-momentum transfer between the K and the n. It is known (S) that this dependence is small and it will be neglected from now on. The discrete symmetries C,P and T imply relations between these amplitudes as shown in Appendix 1. CPT-invariance implies conjugate) -f = -f* and g = -g* so that X = X* • (* is complex T-invariance in the transition implies that f, f, g and g are relatively real so that ImX = ImX = O. With CPT-invariance, ImX CP-violation in leptonic K-decay. f 0 therefore implies direct 3 Sachs( ) has suggested that such an effect could be the source of the CP-violation seen in ~ ~ 2n decay. This matter is discussed more fully in Appendix 1. In Appendix l the leptonic time distributions are derived for a pure K0 beam at t obtains = O. As suming CPT-invariance, so that X = X* , one 0 - 4 ImX . Sin 6mt e -}(r L + r s)t} ~ where rs and rL are the KS and K total decay rates and 6m is 1 l ( ' - I\:S). t I In the detailed derivation, CF-violating effects in ~ I the ~ - K 8 states are taken into account. order 2 x 10 -3 Such effects are of the , well below the sensitivity attainable with present + experiments and are omitted in the expression for N-(t). the above expression becomes N+(o) = 4jfj that N-(0)/N+(O) = IX! 2 2 Fort = O, 2 2 , N-(o) = 4jf! !xj 0 , as one would expect before the K interference comes into effect for t > O. - K° so t I • 9 c. History and Current Statlls of the 6S = /\Q R11le Most checkr: of the AS = 6Q rule hnve b1.~cn .! n >~ · and K ·; 1 e.1 decay. 0 K ./ dcc1iy 111 c1)n13Jdc1·ul>Jy more d:L:l'l'i,'.UJt; 11. J 111 1n1hlilc d1mnlic:rr1 there src posclble churge acyTllmetries in. µ- 1)1J. - i.dcntJ l'.l.cuti<m, awl in counter experiments one has to operate at fairly high energies to filter µ's from hadrons. K s -)re+ +re There is also serious background from , with one of the re's undergoing undetected re--) µv decay. The first experimental evidence on the 6S = 6Q rule was 4 reported at the 1962 CERN conference( ) and it placed the rule in serious doubt. First, an example of L + --) n µ+ v decay was reported 0 and, secondly, two Ke 3 experiments found evidence for large violation. 5 The L+-event was found in an emulsion stack exposed to K--mesons ( ) and the authors were well aware of the danger of drawing sweeping conclusions from one event. They did not report any examples of the allowed L---) n µ-~decay mode which would have been helpful in . understanding the L: + --) nµ +v event. The Ke 3 5 experiments( ),( 7 ) had 28 and 22 events respectively and the data was analyzed in terms of r 1 + x Total K leptonic rate)= 1 _ X 1 1 2 lmX was fixed at zero. r1/r2 = lL 9 +7. 5 -5.6 1 /r 2 = (Total K1 leptonic rate/ 2 • GP-conservation was assumed, i.e., If 6S = 6Q then r and 6.6 +6 • 0 -4.0 1 /r 2 = 1. respectively. The results were The first experiment separated the data into re +e - v and re - e +v events to distinguish between 10 + .OU X and 1 I X and enve X ::: 0.55 _ .J;] The second exper:lment could not do this but, tuldng the value of X wh:lch wuu lcso thon 11nJty, they +0.12 obtained X = 0. 1ltt -O. 20 • Crawford, in hlo rapporteuro t1:ilk to the 1962 conference summarized: is probably wrong." "The conclusion is that the 6S = b.Q rule However, admixture of K -+ n+n - background in the 8 leptonic decay sample gives r 1 /r 2 >land it is noteworthy that both of these results are in that direction. In the seven years that elapsed until the 1969 Topical Conference on Weak Interactions at CERN, the 6S/6Q problem was attacked with great energy on both the L:+ and Ke 3 fronts, the Ke 3 case being given considerable impetus by the discovery of CF-violation in KI, -+ 2n decay. At the 1969 conference, Filthuth(B) reported a L:+-+ n e+v event and two more L:+-+ n µ+v events, all three being from H bubble 2 chambers. 9 The electronic event( ) corresponded to a bubble count 3.6 standard deviations from that expected for a pion, with a 1% probability that the track was not an electron. For the exposure yielding the muonic events, (lO) it was calculated that 0.3 background events of the type: r:+ -+ n n+ "/ followed by n+ -+ µ+v (with decay vertex undetected) would be present in the sample. Thus the probability of the two candidates being due to this background is ~4%. These new events gave totals of 3 L:+-+ µ+/177 L:--+ µ-and 1 L:+-+ e+/931 L:--+ esponded to a branching ratio which corre- r ( L: +-+ n.Z +v /r( L: --+ n £ - v ) ~.o3. On the 11 bnoiu of thcoe cventG :1.t should ·1,c noted thut the (L\~.; '-' -f\..Q rntc) / (N> = +L.Q rutc) L'or muons lu l!) time a that l'ur cl(!Ctronn where o.B o. naive theory would predict the same ratio for muons and electrons. Rubbia, (e) at the srune conference, discussed Ke 3 decay and from eight ~ experiments done since 1962, compiled a world average for X: Rex = +0.14 + o.os ImX = -0.13 + 0.043 This world average clearly contradicted the evidence for a gross violation displayed at the 1962 conference. The experiments con- tributing to it are tabulated in the next section. One other test of the 6S = !::::.Q rule is experimentally + re +re +e -accessible; the decay K+-+re+re - e +v being allowed while K-+ v is forbidden. The 90% confidence limit for this process is + re+re - e +v ) < 0.04 based on 264 Ke 6S = +6Q events r (K+-+re+re +e --;re v K-+ 4 with no 6S = -6Q candidates seen. (Rubbia's talk, Ref. (8).) This completes the discussion of the direct checks of the bS = L:.Q rule and the conclusion in 1969 was that the 6S = -1::::..Q amplitudes were < 20% of the 6S = + 6Q amplitudes. Two indirect impli- cations of 6S = -1::::..Q currents will now be discussed. If the current-current picture has bS = -6Q currents as well as bS = +6Q currents, then these can combine to give 6S = 2 processes with amplitudes which are first order in the weak interaction coupling constant. Examples of such processes are .~: :. observed branching ratio for ;:::: -+ n re - and K0 t t :-:0 K • -> n re - is < 1.1 x 10 - 3 (ll) and it The 12 is well known that the ~ -K mass difference, which is proportional 8 to< K0 jH!K° >, is second order in G (6m ~ r /2) indicating that K0 ttK° 8 transitions are forbidden in first order. The current-current picture would thus need modification to accomodate 6B = -.6.Q currents, if they -were found . The jL:>I! = t rule for semileptonic decays states that the change in the total isospin of the hadrons in such a process is one defines °il' a 31 , and a 33 t. If corresponding to isospin changes (6I, 6.1 3 ) = ( 1/2, 1/2), (3/2, 1/2) and (3/2, 3/2) then the jL:>Ij = t rule 31 = a 33 = o, whereas the weaker 6B = 6Q rule states that 0 alone. Evidence from K+ and IS, semileptonic rates gives (see states that a a 33 = Rubbia's talk, Ref. (8)): = (3.4 + 13) x 10- 3 • . J3a33 Since ~ 4.2 X, a violation of 6B = 6Q corresponding to ReX 2 'C$ °11 would require a subtle conspiracy between a 31 and a 33 to maintain the above relation. The conclusion from all available data in 1969 -was that there -was no definitive evidence for 6B = -.6.Q currents in the weak interactions but the experimental limit on such amplitudes -was fairly large. In view of the implications of non-zero X just mentioned and the importance of measuring ImX accurately to help understand CP-violation, an improvement in the measurement of X by at lea.st an order of magnitude was called for. D. Experimental Measurement of X + If the expression for N-(t) is rewritten with Quadratic terms omitted and rLt = o, one obtains: 1 - 4 ImX sin 6rnt e ~ rs t III In Fig. 2 the features of terms I, II, and III can be seen. 6m ~ r s Taking /2, the wavelength of the periodic terms is 4n/r s which is roughly 12 K s lifetimes. As they are damped by an exponential these terms are essentially constant a~er 5 K lifetimes. The best way to + measure the coefficients of the terms in N-(t) is to collect a sample s of leptonic decays in flight within the first 10 or so lifetimes, separate them into the two charge states, and fit the parameter X + using the time distributions N-(t). Since leptonic decays occur at ~10 -3 times the rate of the usual K ~ n+n - one would expect backgrounds from K decay to be a s s major problem and to be most competitive at short lifetimes. Thus the effect of such an excess of events on the measurement of X should be + considered. From the expression for N-(t) one finds: (:r-.t + N-) o.t t = 0 (N+ + N-) ut t "' oo t ,,_, 2 , hence an exceos of events ut 1 - 2 Hex = 0 will give ReX > O for both K0 and K° initial states, e.g. a 10% excess of K ~ n+n - background vdll increase ReX by .05. s 14 -e-Q.5 i 1 { - 0 .5 TERM ill for Im X = -+ .2 I f t t 1 ' I r ~ ; 0.5 i I' I ! TERM Il for Ra X = + .2 I ii r 3 I TERM I in N..a+ 2 TERM I in N..e- 2 0 3 4 r (in K 5 lifetimes) Fig. 2 + Terms I , II and III of N-(t). 5 6 7 15 A compilation of all experiments done since 19G3 is given in Table 1, w-lth the same results shown on an Argand plot in Fig. 3. It is interesting to note that 7 of the 8 experiments give ReX > o. Each of the experiments suffers from a smaJ.l number of events and so has serious difficulties in investigating systematic errors. Therefore, one should not place much faith in an average derived from them, but if this is done for the first eight experiments, the result is ReX = +0.14 ~ 0.05, ImX = -0.13 ~ 0.04. Ref. (20) measured 2 2 (1 - jxj )/ll - x! from the amplitude of oscillation of the charge asymrnetry following a regenerator in which the phase was measured. The strongest conclusion to be drawn from these experiments is that IX! ~ 0.2. E. This Experiment In order to place a better limit on X it was desirable to do a high statistics experiment for which the systematic errors could be estimated well within the statisticaJ. error. of CF-violation in the K 0 In view of the importance -K° system, it was decided to aim for equal sensitivity in ImX as for ReX and so it was necessary to reach high acceptance well within the first K is greatest. s lifetime where the charge asymmetry It can be shown that the statistical error on X, for X = o, depends on the number of events approximately as follows: o~eX ~ .8/n' a~mX ~ 1.1/n' where n' O, dN dt 16 'fABLE 1. UnitG of B.C. ,K+n ~ K°p :515 .47 ~ .20 do. 152 Mc ·-th o d Paris (1965) Freon/Prop. Colwnbia/ Rutgers (1965) Penn. (1966) l6ml in Keo-z E•vent s Group Padua (1965) ME.A:3UREMENTS OF X, 196:7i - 19G9 - r • x ImX nc1'. 035+· 11 -.30 -.21+.15 -.11 12 15+.35 -.50 .06 +.18 -.44 -.44+.32 -.19 13 -.08+.16 -.28 .24+.40 -.30 14 +.16 -.35 .oo-.::. 25 15 8c i::: • H BC p-p 2 109 = .5 Sp. Chamber ;Cp ~ Ko/\.. ll6 ? 335 = .5 .17 ± .10 -.20 ! .10 16 242 (includes Kµ 3events = .47 • 22 +.07 -.09 -. 08-: • 08 17 Brookhaven / Carnegie D~C K+n~ K°p (1967) .17 Berkeley (1968) -o H BC K- p ~Kn 2 CERN/ Paris (1968) H BC p-p 2 121 = .47 .09 +.13 -.11 .22+.29 -.37 18 San Diego (1969) Sp. Chamber K+cu ~ K° 686 = .46 .09 +.14 -.16 -.11+.10 -.ll 19 .14 ± .05 -.13±.043 - Average CERN/ Colwnbia (1969) Counter Reg. ~ Beam ? = .469 l-jxj2 _ 11-x12 - (= means input, not a free para.meter in fit) • 96-.:: • 05 20 17 ' •' I 0.6 I I I I I I 0.5 0.4 I I I 0.3 I 'f • 0.2 'r' I i I 0.1 I I r Im X ! 0 ------ -0.1 -0.2 -0.3 -0.4-0.5 Constraint of Ref.20 -0.6 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 Re X Fig. 3 The nine experimental measurements :of X summarized in Table 1. 18 = 500, the being the total number of events per K lifetime. With n' error on ReX is :1:: 0.04 and on ImX it is + 0.047. The sensitivity to s background is such that a rd c..p admixture of K s ReX = +0.01 for X = O. ~re +re - giveG Im.X = -0.0l, So :in an experiment wlth n' "' 500 it Jo enough to 1-:.eep this background below 'Z1/o. The method, which is described in detail in the next chapter, was to produce K-mesons in an apparatus that could detect Ke from 0.2 to 7.0 K lifetimes. s 3 decays The K-mesons were produced by pions in small brass targets in front of a large aperture magnet in which the decay secondaries were momentum analyzed. Sensitivity to electrons and rejection of heavier secondaries was achieved using a combination of gas Cerenkov counter, visual shower chambers and shower counters. The experiment involved taking pictures of some 240K candidates from which a final sample of 1079 Ke level of (2 t 1)%. 3 events was isolated with a background The value of X estimated from these events is: ReX = -0.069 :1:: 0.036 +0.092 ImX = +0.108 -0.074 • The error on ImX is larger than expected because X is sufficiently far from zero that the above error analysis is only approximate. This thesis is divided into four more chapters. Chapter II discusses the experimental method and apparatus, Chapter III describes the procedure used to isolate the final sample of Ke 's, Chapter IV 3 clculs with the Monte Carlo efficiency calculn.tion ancl the mn.x:Jmum likelihood fits to the data and Chapter V finishes the thesis with conclusions and outlook for the t:S = 6Q rule. 19 11. EXPElUMI~'N'l AL J\PPJ\W\'J.'Uf~ 1 The experiment wac executed in 19G8 at the Devatrori, u r; CcV vieal~ focusing proton synchrotron at the La'Wrence Radiation La1Jorti.tory ln Berkeley. As stated in the previous chapter, the object of the experi- ment was to acquire a sample of Ke 3 decays with known efficiency in time over the first 7 K lifetimes and to extract the value of X from s this sample by fitting it with the time distributions N+(t) and N-(t). This was achieved with an apparatus which was sensitive to decays of neutral particles into an electron and a pion and which determined the charges of the decay products. sections. This chapter is divided into three The first describes the general features of the apparatus, the second gives a more detailed description of the triggering components, and the third describes how data were recorded for the events that satisfied the trigger. A. General Features of the Apparatus Since a major goal of the experiment was to get more events 0 than the previous experiments, i t was decided to produce the K -mesons from dense target material rather than from hydrogen. This meant that the kinematical constraints of a proton target could not be used to identify the K •s as was done in the bubble chamber experiments. e3 Instead, the t1vo charged prongs from , a neutral decay were identified, one as an electron by its production of Cerenkov radiation and its showering properties in lead, the other as a non-showering, nonCerenlrnv-radioting particle which had to be a rriuon, a pion or a proton. By u process of elim:Lnation, the only neutral decays het.ving euch a 20 :i'l nnJ. ore /\ -> p + e e to tc - 0 + v nnd K + - t T( - + e + 1- V. 'L'hc rnornento. of the ~ccondarle:..; were rneaeurcd Ln a large :.:pectrornuter :1u one w110 111>.l.c to eliminate A events by a cut on the (p e) invariant mass. 13 The · technique was based on achieving three goals: (1) The ability to isolate neutral decays. The triggering system was designed to favour neutral decays and these could be seen in spark chambers placed throughout the decay region by observing the characteristic two-prong vee of a neutral decay. (2) Good differentiation between electrons and heavier particles so that one particle in the final state was an electron and the other a heavier particle. This distinction was made by the pulse height in a 1 atm. Freon Cerenkov counter, by the visual appearance of the particles in three radiation lengths of shower chambers and by their pulse heights in a set of shower counters. (3) Enough mass resolution to make necessary mass cuts. The decay secondaries traversed more than 100 Kg-inches of magnetic field, with spark chambers to determine the trajectory. Negative The momenta were determined with 6p/p ~ 5%. pions were used auction from braes targets. to produce K01 s by associated pro- A beam momentum of 2.85 GeV/c was chosen. It was determined that this momentum was roughly optimum for the experimental configuration by consideration of the following four effects: (1) Available beam intenuity, which decreases with momentum, (2) K -production cross section, which also decreaoes with 0 t t i !i ! I 21 i ! l momentum, ~ ( 3) Apparatus acceptance, which increases with K° -momentum, (4) Electron identification by showering, which is better, the I f higher the electron energy. At this momentum the beam intensity could be as large as 400K/accelerator pulse with about half of the circulating proton beam striking the target used to produce the pions. A general sketch of the apparatus is shown in Fig. 4. The largest component is the M-5 spectrometer magnet which has 60" diameter poles and an aperture of 108" (horizontal) x 22" (vertical). The field value at first was 2.0 Kg, and later in the run it was increased to 2.8 Kg. Most of the other components were either attached to the magnet or else placed as close as was physically possible. The pion beam, through 83 .and 84, impinged on two brass targets placed inside a set of thin plate spark chambers. Production of a neutral particle was demanded in one of the two targets by the signature C.V. J. in either target. J. The counter, 85, placed after the decay region, was used to trigger on decays occurring in the region. A Freon gas Cerenkov counter, GC, which detected electrons, was placed inside the magnet. There were two hodoscopes, MH at the center of the magnet and RH at the back, which demanded two particles through the magnet aperture into the shower chambers. A set of four spark chambers, SC, inside and at the rear of the magnet was used to record the particle trajectories through the magnetic field region. Finally, at the back of the RH, were the shower chambers and shower counters, in which the showering properties of the decay secondaries were studied in five 22 40 inches PLAN GC 53 MH SC I ELEVATION TARGET DETAIL GC MH 1----i I inch Fig. 4 Experimental apparatus •')'L ,._.:J rndiation length::; of' lend. J\.ll of these cornponcnto wLLL now be de::;cribed in the remainder of this chapter. Detailed discussion oJ' the apparatus is contained in Appendices 2-U, and only those features directly affecting the physics will be included here. B. Triggering Components of the Apparatus Approximately 1 in 10 targets led to a Ke 3 7 of the pions interacting in the decay accepted by the apparatus so it is clear that selective triggering was needed to reduce the number of events to be recorded for subsequent analysis. This section deals with the components that played a role in this selection process. Before entering the production region, the beam particle traversed four small ,counters Sl, S2, S3, S4 and a large veto counter S4V which had a hole for the beam and removed off-axis beam particles. A good beam particle had the signature S3.S4.S4V. The selection of neutral particles was achieved by producing them in two brass targets Tl and T2, 1. 2" long, and placing a veto counter 2.0" in diameter immediately downstream of the target. A pion was required to enter a target by the counters c or c imme1 2 diately upstream of the targets so a neutral trigger from either target had the signature C. V., i =l, 2. l l A scintillator 7" x 18" x 1/8", SS, placed 13" downstream from the second target ensured that a decay took place in the region viewed by spark chambers. The first target produced K01 s that could decay over seven decay lengths which is where + the time distributions, N-(t) reach a constant level, whereas the second target had only two KS decay lengths available for decay, but 24 K01 s produced in it had three times more likelihood of being accepted 0 by the apparatus than K 's from the first target. to maximize the counting rates in C 1 and c 2 . The beam was tuned About 99"/o of the beam impinged on c1 and, after multiple scattering and interacting in the first target, about 36% reached c 2 • The selection of two charged particles through the magnet aperture was effected by two hodoscopes, MH and RH. The multiples hodoscope, MH, was a horizontal hodoscope at the center of the magnet consisting of fifteen l" wide counters and the rear hodoscope, RH, had thirty-two 4" wide counters arranged vertically. The MH was helpful in reducing the contamination from small angle electron pairs which did not open out very much in the vertical direction since the magnetic field was in that direction. For the Ke 3 trigger it was demanded that the two charged particles be separated by at least one counter, i.e., at least l" in space. The RH ensured that two particles reached the rear of the apparatus and had a high probability of entering the shower chambers and shower counters where their interaction in five radiation lengths of lead could be studied. There was no separation requirement here, and the RH trigger was satisfied by any two counters firing. Decays where one of the decay products was an electron were selected by a threshold gas Cerenkov counter which had a radiator of Freon 12(CC1~ ) close to atmospheric pressure, with a pathlength of 2 30" through the gas. The counter was placed 1)etween the poles of the magnet as close to the decoy region as possible and had thin mylar windows at both entry and exit. Since the threshold for pions at this 25 prenuurc :Ir; nl>out 3 CcV/c, the counter wuu unl.qucly :..:erniltJvc to elcctr011n and coulu only count J>iono -which -vwrc 11ccompu11Jed by 1J. xconversion or a fast o-ray. 'l'he mean pul:.;e height from electron s in the counter corresponded to about five photoelectrons in the RCA 8575 phototubes which gave an operating efficiency > 93%. From studies of the pulse height spectrum of electrons from different sections of the decay region, it was concluded that the efficiency varied by at most l.'C'/o over the decay region. The Cerenkov light was reflected by spherical mirrors into two lightpipes, one on each side of the beam. Each lightpipe had three RCA 8575 phototubes. The discriminator threshold to satisfy a GC trigger was set at a very low level to ensure high efficiency. The separate sides -were also pulse height analyzed and the pulse heights stored on tape if the Ke 3 trigger was satisfied. This concludes the discussion of the components in the Ke 3 trigger which was defined as: S3.S4.S4V.(C.V. from either target).85.(two MH counters fire with l l at least one counter separation).(two RH counters fire).(pulse from GC, set at very low bias). At the typical intensity of 3 x 10 5 effective pions per pulse (i.e., usable by the electronics) this trigger gave 0.9 triggers per pulse. The contribution made by the various elements can be judged from the following rates (there are, of course, correlations between the rates). 5 With 3.0 x 10 pions per pulse, 2G C3 u <"'A C' Av cl vl ••) 'J· ou't 05 • lllO/pu.loc ou 220/pulce 4 GC 1. 4 x 10 /pulse S3.S4.S4V.S5.MH 1. 0 x 10 /pulse S3.S4.S4V.S5.RH 2.6 x 10 /pulse 4 4 10./pulse Ke 3 trigger = II .GC 0.9/pulse Another experiment to look for interference effects bet•reen +-o KS ~ ~ ~ ~ +-o and ~ ~ ~ ~ ~ ran simultaneously with the Ke taking and had a trigger rate of 1.0 per 3 x 10 deadt:i.me with these two triggers was 3c;/o. 5 pions. 3 data- The overall A general block diagram of the triggering and data recording is shown in Fig. 5. C. Data Recording Components Having considered how the apparatus was triggered, the next topic is to describe the remaining components that recorded data from triggering events. These were three separate groups of spark chambers and a set of fourteen shower modules. Production-decay region chambers In the region where the K01 s were produced and in which they later decayed, there were seven spark chamber modules, each 4" x 8" x 18". The targets were placed in the gaps between the first and second, and the fifth and sixth modules. The modules after the targets were pla ced as close as possible to the veto counters v and v , so that there was 1 2 27 Counter groups Gas Cerenkov Be nm counter a countors counter Mii RH Shovor llodoacope llodoscope Module a decision logic BS-1,Buffer SPHA' a. Pulse height analysers storage Slov logic control Spark chamber trigger Read into PDP-8 i f trigger vas OK PDP-8 ' Productiondecay Momentum Shover/ Magnetic tape record Spark chambers Fig. 5 Block diagram of trigger and data recording logic ·1 28 an active gap about 3/4" from the end of each target. The decay point of a neutral particle could be seen within l" of its production. At 0 the mean K -momentum of 2.4 GeV/c, this corresponded to 0.2 KS lifetimes. The length of the fiducial volume along the beam in which decays were visible was 34" for the first target and 10" for the second target, corresponding to 7 and 2 K lifetimes respectively at PK = 2.4 8 GeV/c. The transverse spatial resolution attained with these chambers was .l" and an angular resolution "' 10 track. This led to a resolution for the longitudinal coordinate of mr for an average length a typical decay vertex of "'O. 3", which is to be compared with the un0 certainty of 0.4" in the K production point. The multi-track effi- ciency of these chambers viascrucial to the detection of neutral decays with uniform efficiency throughout the decay volume. Extra tracks from a target most often tended to be present in the first 5" of chamber after the target. If the chambers were inefficient, decays occurring in this region would be difficult to see, due to the robbing effect of the extra tracks. From looking at the pictures, it appears that the chambers could support up to three tracks well, but four or more tracks became difficult to see, with some tracks robbing energy from the sparks in other tracks. Momentum chambers The next chambers encountered by the secondaries in the:i.r passage through the magnet was a group of four chambers referred to as momentum chambers because of the:i.r momentum determining role. ~he first was 811 x 24" with six -~- " gaps and it was placed between the S5 counter and the entrance window of the gas counter. The second was immediately aJ't(.)r the MH and WU G <.>O" x 10" w:t th J'our ., /1•" gapri. , ) I Fina lly, ut the rear of the magnet, at 1 6° to the norma l to the beam, were two 36" x 60" chambers, each with six 3/8" gaps, on.e chamber on each side of the center line. These chambers were viewed by excellent optics rigidly bolted to the magnet yoke and gave spatial resolutions of the order .05". Shower chambers The interaction of the decay secondaries in three radiation lengths of lead was studied in shower chambers which consisted of a total of six modules, three on each side of the center line. module was 4' x 6' and had nine plates with A t" gaps. The plates were formed of an Al-Pb-Al sandwich, .02" Al on either side of .02" Pb, giving 0.1 radiation lengths per plate. The chambers had six active gaps per module so a shower could be studied in eighteen gaps if it penetrated to the back of the array. Shower maximum is reached after three radiation lengths by 0.7 GeV/c electrons which is a fairly typical energy for the electrons of accepted Ke 's. 3 Since the ability of the chambers to distinguish between ~·s and e's depends on the scanning criteria used, discussion of the identifying power of the shower chambers will be postponed until the next chapter. The optics used in the photography of these chambers was not as good as that used in the other two sets of chambers since it involved very large mirrors mounted at awkward angles. The spatial resolution attained was "'0.2" i n transverse position and "'20 rnr for angle s . This was quite ade - quate for preliminary track r e construction which was then refined by :50 including the momentum chnrnlier rneanurerncntt; i11 Llil' 1.nt<'I\ J'jtLi111;. Shower counters The final detection components of the apparatm; were the fourteen shower counter modules placed immediately behind the shower chambers. Each consisted of a scintillator-lead-scintillator sandwich, the scintillator slab having dimensions 52" x 10" x 3/8". The lead sheet was two radiation lengths thick, so that electrons traversed a total of five radiation lengths of lead in the apparatus. This is shower maximum for 3.1 GeV/c electrons whereas electrons from the accepted Ke 's had an energy spectrum which fell to zero at 2.0 GeV/c. 3 The 28 scintillators were paired in front-rear pairs, with phototubes at opposite ends, and the summed signal from each pair was pulse height analyzed and stored on tape if the Ke 3 trigger was satisfied. It will be seen in the next chapter that this shower pulse height information was used before scanning to reduce the number of pictures looked at by a factor of 4. As will be shown, this reduction took place by use of a complicated computer program. It would have been advantageous to apply this selection in real time to reduce the triggering rate. However, duplication of the program by electronics is a complicated problem in fast logic, and besides, one would not have the advantage of trial and error if one were to apply the selection in real time. Magnetic tape recording 'l'he :;p:.ir·l\ the eh~ctro11ie chru1il>(~l' ,111t11 wu:c recordl~d l>y three <'nllll~rns wlli . ll~ dutn l.':r'om tilt~ coirnteru WL!n..~Gtore<l on 111u1:~11,;tic tape. The tYJo llUC s ti o nc naked ~:>:f.' the c01mt c r :::; in tll v r :yr~ t l~ 111 w1: 1.·v : DiG .i .tal -- wh.i.ch counterG :l':i.r c d, and (l>) J\rm.l.011, "What 'Wa[; tho ( 11) -- J'or ('vrtoi11 co11nLt~n;, mnpl:LtuJc o:I.' the pulcc J.n the co unters Jn cw; c (11) U1e fast logic output corresponding to the signal in q_uestion •1ent to a buffer storage circuit (BS-1) from which it was read into a PDP-8 computer after the spark chambers had fired. For (b) the pulses were analyzed by slow pulse height analyzers (SPHA's) and then read into the computer in the same -way as the BS-1 data. After several events had been accumulated the information in the computer was read out onto magnetic tape . A program, EXPO, controlled the movement of information through the PDP-8 and also histogrammed any desired quantity. These histograms could be observed directly on an oscilloscope while running and provided a very direct check on the performance of the apparatus. This completes the description of the apparatus. A total of 900K pictures -were taken in January-April 1968 of which 240K were with the . Ke 3 trigger. The magnetic field -was reversed twenty-five times during this data-taking period, with equal amounts of data taken at each polarity. A discussion of running procedures and checks on the stability of the apparatus is given in Appendix 9. The next chapter will discuss how these pictures and magnetic tape records -were analyzed to obtain a sample of Ke 's. 3 32 III. DATA ANALYSIS AND BACKGROUNIX.~ Of the 210K pictures taken, it wac expected that .-vJ.5K were good K 7 e.:.i ' c. This Chaptr~r describes the filtcrine; -proccr;c whic..:h extracted these K ·z' s from the raw data and then discusses the backeo ground remaining in the sample. Such a process must be able to reduce the background level to "'1% and at the same time introduce no biases, with respect to decay length, on the accepted Ke •s. 3 As usual, one started with the simplest and crudest selections available and then, with a smaller sample to work on, applied more complex and precise tests to the events. In this case, the first step involved ~ualitative selections designed to isolate neutral decays from region pictures) other triggers and ~-e (using the production-decay from other final states (using the shower chambers and shower counters). To ensure that the ~-e seen in the rear of the apparatus came from the decay seen in the front end, the surviving candidates were next measured and their trajectories reconstructed through the magnet. Quantitative selec- tions could then be made on these measurements, e.g., only events that reconstructed reasonably were retained, mass cuts were made on different invariant mass combinations, etc •• This chapter is divided into four sections: (B) Measuring and event reconstrliction, (c) rescan and (D) Remanent background in sample. (A) Scanning, Final selections and A. Scanning Examples of qualitative features that one would expect a 0 priori of good K ~ nev events are: (a) A vee visible in production-decay region. (b) A showering track and a non-showering straight-through track in the shower chambers. (c) In the shower counters, a large pulse height for the electron and a minimum ionizing pulse for the pion. The 240K triggers were examined for these features in the order (c), (b) and (a). This order -was chosen since it ~rent in order of in- creasing difficulty and sensitivity to biases, e.g., a scanning inefficiency in the decay region is much more direct in its effect on X than a pulse height dependent inefficiency in examining the pulse heights in the shower counters. Each of these steps will now be described and further details are contained in Appendix 10 on scanning procedures. Tape Scan The magnetic tape record for each Ke 3 trigger was analyzed by a computer program which examined the pulse heights in the fourteen shower modules and looked for a combination consistent with an electron and a pion. The pulse height distributions of electrons and non-showering tracks, identified in the shower chambers, are shown in Fig. 6. Fig. 7 shows the electron pulse height response for three regions of electron energy. It is clearly reasonable , the average response increasing with P e although the distribution i t 34 t l ! ' eo !f ~ ! I ! I 60 I' i 895 TOTAL U) r- z 40 i I i II :J I u I LL ! 0 I I 0 I 20 b89 0:: w co 2! ~ z 0 0 10 20 30 PION PULSE HEIGHT 11 ELECTRON ~ 20 40 11 895 TOTAL ~ +317 0 F ig. 6 10 20 30 40 ELECTRON PULSE HEIGHT Shower counter pulse height di s tributions of electrons and pion s II I I I I I I I 35 1.0 < Pe 200 EVENTS -.I,> +23 CJ') I I- .5 < Pe< 1.0 GeV/c z w > 20 w 340 EVENTS l' I i I f LI.... 0 a:: w CD ::! ~ z O < Pe< .5 GeV/c 20 369 EVENTS 0 i I 20 40 60 ELECTRON PU LSE HEIGHT Fig. 7 Electron pulse height in shower counters for three electron energy regions. 9 80 broadens with energy. Thie lotter effect :Ls due to the fact that the shower counters sampled the shovrer at three and at five radiation lengths only and for higher energies, the effect of correlations increases. In the computer scan, an "electron" was defined as a pulse height> 1.7 I . in a pair of adjacent modules. min A "pion" was defined as a pulse height between 0.5 I . and 2.6 I . in a single min min module with< 0.6 I . in the modules on either side. min For a given RH counter triggered, three pairs of sho-wer modules behind it were searched for an "electron". If either RH counter in a trigger had an "electron" behind it, then three single modules behind each RH counter -were searched for a "pion". The trigger was accepted if an acceptable "electron" - "pion" combination was found. If the RH counters for the trigger -were within 4 RH counters of each other then the search for a "pion" was not made and the trigger passed the computer scan with just an "electron". analysis of a sample Details of the tape scan and event are given in Appendix 10. Events passing the tape scan had their serial numbers and other relevant information printed out in the form of a scanning list to be used in the next stage of scanning. From a sample of 524 Ke 1 3 s obtained without any pulse height selections, the tape scan accepted 396 events, giving an overall efficiency of 75%. This should be regarded as a lower limit because many of the 128 events mj.ssed are dubious, the K . ,. sample e.::. being preliminary. A more crucial question is whether the 37 acceptance of the tape scan is a function of decay length or electron charge, thus biasing the Ke 3 time distributions. These matters are investigated in Appendix 10 and no evidence for any bias is found. The tape scan accepted 67,205 out of the original 240,000 triggers. Shower Scan The 67,205 remaining candidates were scanned in the shower chambers for an electron and a non-showering particle. The trig- gering tracks were distinguished from other tracks by using the RH information which was on the scanning list and also visible on the film. The scanner simply found those tracks that were headed for the triggered RH counters using a scanning template, which had the rear hodoscope marked on it. The tracks were classified as 11 1( 11 or "e" according to the criteria: 11 1( 11 (a) Straight through track. (b) Track scattering at a definite point, with straight segments. (c) Track with an interaction where a number of straight tracks emanate from a definite vertex. "e" Any track which satisfies none of the 11 1( 11 criteria and is not an obvious stop. The criteria were 1{cpt simple and liberal the "e" criteria will nccept mnny low energy pions and .p rotona nnd many pion and proton intcract:i orw. HoWl~vc:r, the crl teria have hl.gh efficiency 30 for good Ke 3 events and it wa s planned to have all final candidates rescanned by physicists in the shower chambers. If the picture had an acceptable "re" - "e" combination it was retained, events which were "rc" - "rc" were also accepted in a different sample to be analyzed in parallel with the rce sample. Throughout the thesis, this sample is referred to as the rcrc sample but, of course, positive identification of the rc was not made and such events could also be rcp or rcµ. Most of the events rejected at this stage were 2e events which easily passed the tape scan. The efficiency for K e3 's was checked on an independently acquired sample and found to be 96%. Most of the events lost were cases where the pion had extra sparks along the track, leading the scanners to interpret the event as a 2e event. One might well ask about the possibility of bias in the events lost. ~' The most likely source would be a correlation between the decay length, and 6ZSh' the horizontal separation of the e and rc in the shower chambers, with the scanners tending to miss events when the e and rc are beside one another. This matter is investigated in Appendix 10, and no correlation between ~ and 6ZSh was seen. Another possibility low energy electrons. is that the scanners missed However, the electron energy spectrum does not change much with position in the front end so any bias would be second order . It was concluded that any dependence of the shower scanning efficiency on the decay vertex position was negligible. The number of events accepted was 14,613 rce and 6,005 rcrc. 39 Product :l.on-dccay Rce;:lon Scan 'rhc U1 I.rd phaoc o.f' qunl"l tat:l.ve LJ(~.l.cctJon w111; to semi the decuy region p.Lctureo for the two-prong vce charncterL:tic of a neutral decay. Since the aim of the experiment is to measure the decay distribution of the Ke 3 decay, it is clear that this scan should be highly efficient so that any position dependent biases will be negligibly small. (a) High efficiency was obtained by leaving the scan until last so the scanners could spend more time on fewer pictures, (b) using the MB: information to identify the triggering tracks in the decay region picture, and (c) having the pictures double scanned. The MH information was used by having a template of the appropriate magnification with the MH marked on it. The scanner found those tracks which headed for the triggered MH counters, and the candidate was accepted if these two tracks formed · a consistent vee in the plan and elevation views. The scanners noted in which plate the vee first appeared and this was used in comparing scanners and, later, in checking measurements. More details on the decay region scan are given in Appendix 10. Vees with more than two prongs or with opening angles less than 2° were rejected. This opening angle cut was designed to reject electron-pairs, the major triggering background. From the Monte Carlo calculations, discussed in Chapter 4, it was determined that (.06 ~ .03)% of the Ke ' s have Q . < 2°, this fraction opening 3 40 increasing to 11~ for G . openinr~ < 4°. Hence 2 0 is a sofe cut to make, any posc;j.lJle binc bel.ne; smaJ L. 1':xarnpJ.cc of trie;e;c ri: Tailing the pro<luct ·1on -de cny :reg Jon i- ccan are (a) Scanner finds a vee, but one of its tracks is not directed at either of the triggered MH counters. Such triggers iI are probably due to a conversion outside the decay region lt or else an extra track,visible in the decay region, I ' i triggers an MH counter. (b) Scanner fails to find a vee anywhere in the decay region. A y probably converted in 85 and then triggered the gas ! II counter. (c) An electron pair (which does not separate into two distinct t tracks) and an off axis beam track trigger the apparatus. For the sample of Ke 1 3 s finally accepted, the individual scanning efficiencies were (96.4 ~ 0.5)% and (97.3 + 0.4)% for the I I i two scanners. ! The average individual efficiency as a function of decay position is shown in Fig. 8. There is clearly no systematic position dependence so that scanning biases are negligible. If II there are no correlations between scanners, so that one is 97% efficient on the 3% missed by the other, then the overall efficiency of the double scan is 99.g%. Correlations were investigated using a previously acquired sample of Ke 1 3 s and the double scan missed 1 event out of 300, consistent with the above overall efficiency. I 'Phis does not close the question since there might be a class of patho- I Ii II lI I 41 1.0 ~ 9 ~~ o~ ..... (;f --.a: i t >(.) z ! I I > I .8 :I w - i I ( .) I I I LL. l.J.. w (!) I .6 2 -z z <( u CJ) .4 _j <[ FIRST TARGET x SECOND TARGET 0 :::> Q > a .2 z 0 --~~~~---~--~-------~~~-----~~----'I 0 10 20 30 40 DISTANCE FROM T1 IN INCHES Fig. 8 Average individual scanning efficiency of production-decay region scan "' .•. , 12 logil:al cvcnto that o.ll scanner::; 'Would tend to rnJuu. Ji'rom knowlc:dp;c of the efficiency of the Gpark chambers and the geometrlcal diGtribution of the Ke 3 vees, however, such low visibility vees can only form a minute fraction of the total. The number of ~-e events surviving this scan was 3,395. B. Measuring and Event Reconstruction It had to be established that the electron and the non- showering track identified in the shower chambers came through the magnet from the vee in the decay region and did not interact or scatter on the way. Before entering the shower chambers, the secondaries of a typical decay in the front end had encountered 12.4% of a radiation length, 6.'C/o of a collision length and lost 6.7 MeV of energy if they were minimum ionizing. To check the continuity of tracks, the 3,395 surviving candidates were measured and the decay secondary trajectories reconstructed in space. The reconstruction was first done using only the decay region and shower frames. Events which fit reasonable trajectories through the magnet were then measured in the momentum chambers and the fit repeated, using this extra information. Details of the measuring and recon- struction process are given in Appendix 11 and only features affecting the analysis directly are included here. The pictures were measured with digitized protractor measuring machines, digitizing the angle and the position of some point on the track. The rccolution on the measuring tables wuo -t 0.01" in position and l mr. :Ln angle. In real space, this corre- 13 s-ponded to -_: 0.03" for. -posit Lon measurements and, again, 1 mr. for angular measurements. The angle and the two coordinotes were each encoded and digi.tized into 5-digit decimal numbers ancl punched on cards by an IBM 526 Summary Card Punch. In the decay region picture, the incoming beam track and the two decay prongs had their angles and positions measured in the -plan and elevation views; in the shower chambers, the two triggering tracks were measured in the plan and elevation views and the electron was identified. These measurements were then analyzed by a checking -program which verified by reconstruction that the tracks were consistent with the MR and RH counters triggered by the event. This check actually duplicates the MR and RH checks in the decay region and shower chamber scans. However, it was very useful in isolating events where the scanner or measurer had made a bookkeeping or measuring error. The decay vertex positions calculated by the program were checked for consistency between the plan and elevation views and also checked against the plate number noted by the decay region scanner. These checks were effective at finding mismeasure- ments and such events were remeasured and passed through the program again. Three passes through this program were sufficient to clean up incorrect digitizations. The measurements were then combined with the PDP-8 data tape record and analyzed by a track reconstruct ion program. A prc- lim:lnary tent wns made to sec H' a line, drawn between the pol.nt r:J digitized in the decay rcg :ion and the shower region, intersected the 41 the triggered MJ{ counters within a certain tolerance. 'filis chet:k ic more demanding than the MH checl< previously mentioned b e cau:.:;e j t ties together information in the decay region and the r;r1ower region by interpolating between them, whereas the previous check merely extrapolated from the decay region to the MH. Tracks which headed for the triggered MH counter, but subsequently scattered in the vertical direction, for example, would fail this test. side Events out- the tolerance, "-'23°/o of the total, were removed from the sample. The successful tracks were fit to orbits in the magnetic field and constrained to intersect at a unique vertex in space. This pro- cedure found reasonable fits for 76.5°/o of the measured events, the remainder almost all failing the MH test. The distribution of x 2 for a track is shown in Fig. 9 for all tracks; there were three degrees of freedom per track. All events 100 2 for which the X of each track was less than were then measured in the momentum chambers. The momentum chamber measurements were checked for consistency with the MH and RH counters and mistakes corrected. These measurements, along with the results of the decay region-shower reconstruction, were submitted to a fitting program and the trajectory fit performed using all chambers in which the track was visible. This more refined fit used up to five segments of the track, whereas the previous fit used only two. The tracks vrere constrained to a unique vertex in space, as before. If the fit could be Lmproved by dropping any of the chambers (except the decay region, ,.,,hlch was needed to reconstruct the vertex), 1!5 I I I I +I • I I I . 1. •'• +: + + 1+ + . + +' . I I +: • II . ; ' ! ·~ . . -...... 0 0 ""0 I' i' •• •·• •!. •1• •.• 1- '•"' . ,.., i , u I +! . +,••• I' ... ' I l •• · ; . i !- ' + 1• • • ,. ..:-x u I I,,. 0 0 0 ... 0 0 .,, w "' "'>::::> z ,g I >< "'O ·o . -. "' !w ,a z wo lC .... ' 0 0 u w I ...z• « ... .5 .......-..... ... . ,., "' ·o x ; « z 00 0 x u ..__ "'.. u"" .JX ~: ... :r"' ._, .... ::: Fig. 9 2 0istribution of X in decay-shower measurement track then thiG was allowed. The geometrical reconstruction was checked us ing a large sample of straight through tracks, photographed with the magnetic field off. The momentum fitting procedure was checked with K ~ n+n- 8 and A ~pn events, from calibration data, by looking at the Kand A masses calculated for the 2-body decays. Fig. 10 shows histograms of these masses separately for each target from a sample of success- M. is the invariant mass pn calculated assuming that the positive particle is a proton, the f'u.lly reconstructed calibration events. negative a pion. events. The distribution in this quantity is shown for all Then a cut of M. > 1.160 GeV is imposed and the M dispn nn tribution of the remaining events shown. This order was chosen since the K-background under the A peak is less than the A background under the K-peak. Almost all events are consistent with K or A decay. 2 Fig. 11 shows a histogram of x /degree of freedom for all tracks of the ne sample. 2 This quantity, rather than x , is plotted, as the number of degrees of freedom in the fit depends on the number of chambers from which measurements were used in the fit. This plot shows that for good tracks above the flat background, the assigned errors in the reconstruction program were reasonable. The flat background contains, for example, tracks which interacted in the apparatus and poor fits resulting from attempts at fitting uncorrelated tracks to the same trajectory. Fig. 12 shows a hi s togram of the difference in vertex poc i tion along the b eam, ao calculated by the fitting program (Xfit) 17 H-H.f. V· .l ... l I H. lir .. ·~·rl .f. -fl~-l -f.l ll .:' :1 r:·:·1T1lr·1-, ·. ·1 ·,·1·r·.·,· ·r·: ::r ·r· ···,· ·r· ·1·[·1l1 ·rr ·:· .·:·;.·r·····~···~·(·' ···l·~·r·r· ·[·r· ·r·· ..i. ... J..... .,.~ ..,...... ,.,.,.., ... . l I I 1 I i .1r · · _1 _ • • • I I I f I ' I I I 1 ·1· I I I ,: I ,I . r I I ' ; I I I .~i:!I : : : I I\ I, !I I !<., ., I . ',!I' I l I I I I II I, lI :, 'I .I , I I '! I • i , I 1 ' I I I . l·r··' ·I·[··· ·· :1!,·1· .......... ·t·r···~·~. · ; ···,· •·,.·.·~·~·· ! ~~ ; ! I~'I ~ ' l': I I I I , ,,. l I Tl I ' I ' I ! 2 ~~ ' c~ II ~1·r·r·~· ·t···~· ·1··.·r· .. l. ·r· . ·I- ·~ ~.· s,f,! ·· ···r.l·····r·····"·"· , , ,1 1 I , 1 •••• ' !1l: 1 . ·~· . ·t·t·~·~·l·~·r·t I ·~·r·~ I 1 e: I ~ u: t ' l. I • 2 j.~. 1 ·r·~·~·~·~· ·r·1 · .. ·r· ... ···t ....... ~ . . . . . -~ ·r · . ····· r-"I , Ir I . I I I II s ~·~•I ~ !- . ~.~.~·I· : : I ! I . .l. r.r. .~. r. ~ ... s . . .I. ....r.l.. .~. ~. r.. .L. ! s= ~!-': !! ' II I s I I .' I I I I ~: I f I I II iI l I I ! ~~ H·r·r·f ·r·1·~F·~· ·~· .l.r·r· ·r·r ·1·r·~ i. ·1·r· ..,.. l.l .. ·r·~···~·l., ·r·r·~·~ I < - J . l I I r. 11 I ! I ! ! II ;r a 11 1 " li!. E -' E <' I I I : T2 I c . I r ••• 5 u I ! I I •t i l 1~ 1 l iJ21 :' 1 l 1~.e=l~ :il1.'1 l .·l.. lll1 . , . ~ .•.I ~~. · I 11l· I l . I I •~ _, I ' .,,E·.1..l.~ ..... =s= ..• .l. ···' ·· .... ~ 1. .r .. . ···r· L ··· ~ I I • ~.. ' ' ~ 1 r I I I I e.. II ' ' r ;e~ 'I 1 i f' ! :e~ I I i 1 ! i g : ! I I , § "! .! I '·~· I , . ~' 1 .5. 1 111· ' 1 1 'f ;1, = !: :·= I I~ ·!I- ·~· ···•·•···· I 'r .:e:c.1 ,I I 1 i' . :• .... , .. l.r.c···l·l·~·'. ·1· ···t·L·p·········~·-·L. ·•···r·~·r·r·· •E••~ · 1 I b :• ~: •·e·•• 1 1' I I l · I1 · I ~:-:s. ~ . :b • :• ••: ~ • •••• .s 1·• c:• •:ea1 .: · ~ I .I •3 • ••• .• ..i:.f,. • ~ , :••••·~. • ••• ;: , .E. ·"· r · .p • • • • • • • • S. -~-= I ~J ............ ,..b c ••• ~ ...... e _.l. ! -~-'- -~: .. r.~-~- !~- ··---~~E---~ . -~--1 _-~---~!E~ -~-~-~1~-~-~-~-~l~-~-~ I • I· i:, , o I 1 1 -:.• I I I 1 1 .......... . I! 1 • 01· j :! ..,: . • ... ~ ... • • ~MM ~ I I• i : -~- ~ J ::1oe'! t 1 ~ • I. • • r I 1 .• ! ' ~ ~~~. ~f -.· • • I 1 : I l . I ~ ~ .. ~ ... I I 1 I. ! M~MH .. • • i · )oC"'>C ·:"' ,:;,,,,_, "' ,.,,,,,~ :·~T ,,,:,,, '""''':':''.'~"···:·, M .. A M M 1 1 ·r· · - M -.4MA ~r· : ·~· ·r.·r· ···r·r·[·t· ·r·1· ·r·· ~ ~ · , · t ·· "r · r ·:·r·r·r·r· l·r · ~ · :·~ · r · r·· · r·r !c I I I II I fI II II " I i I. . I .I I .I I . !I I : ! 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I iJ ; 11 I : ~=~= · : : . • ~• i •· = • ~:e:~~===~:: "'r~ ~ :=::: .~ :· ~;iii 1 ~~i~ : it~ iii~ i i I l ·:~~ii i 0 \.~.i 1~~ ~ ~ ~ J-i·~·~SiEIF.:~ 1 -1 M • Fig. 10 M W M M TITI W • • W • " • W W W TITI MpTr and MTl'Tr distributions from each target w?W•W ... I . . . . . . r ...... ·1 , , .,.L.l. l ' . : ' ' . 0 I I : I I : ' .I ;' · I. ' I l ! .. . I : I I : : I I : ~: ! ' I i ! I . r2 . ! . .t .....•...... ···~··· ~ · ~ . .. . . . ·~·r · ·····p·r···I... ............ . ~:: = , I I : . : r , I I ' I . i . I : : I I :: M.. I I I : I II ~ I .; ' ' ~1 .....•.•. L.1. . ·~·~===··r·~·t· . ~ .. I ~ 1 ... ~.~···~· .!..~ ••••• ~ ••••• ~.~ •••••••••• · :C• !! ij lI J' I· 1:g:1 1 !'1' I'·! ~ ' ' ' =·= I I I 'I :'! l~:,l l'l1· I E" • . I I . c : . 0 I I • . , '~ I ·1 ·I - " ~ '"" :::; ..... 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The width of the distri- bution implies that the resolution in longitudinal vertex position is ~ • 3", which is what was expected from the transverse position and angular resolutions. Of the 3,395 Ke reconstructed reasonably. 3 candidates measured, 2,226, i.e., ~66%, Of the 34% rejected, 23% were previously removed by the MH interpolation test. where the X shower fit. 2 The remaining 11% were events of either track was greater than 100 in the front endSome of these events "Were traced by hand, and it was seen that the separate track segments were at angles such that a single orbit could not fit the segments consistently. Such events arise from scattering in the horizontal direction or from fitting track segments of different particles to the same orbit. The discussion will next center on the selections made to obtain the final sample used to fit the Ke C. 3 time distributions. Final Selections Fig. 13 shows e + and e decay position distributions from each target for the 2,226 events which survived the reconstruction. It is evident that there is a substantial charge asymmetry, characteristic of a Ke 3 signal if!XI ~ .2. This meant that the back- ground was at a fairly low level and it remained to make the final selections to reduce it even different kinds of buckgrounu: further. It consisted of two basically '"':! t:1 I-'• Ul J.5co ~ . • • • • • • • • • • . _ • _____ 0 ID 'i 0- 0 o' C1> ~ I-'• c: n ...... ;J Hi P> n C1> O'Q :;:) I-'• (/) Ul P> 'O Cll " ;J OJ P' (tl < ro ::.1 I-' I-' 0 0 I-' ;J ()q I-'· n CD n ;J c+ Pl I-'• Ul 0.. 0 :;:) :;:) n () ...... n ...... Ul 0 'O '< ...... c: 'i n Cll ;J "' Q z. .. -- -- __• _ • • _ __ _L l2. 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H t • t : : ; ~ . -. -+ - - :.- i~:~~g-~~:;~~;~;~~;~~~.~~~x~xx~~x sec· -ix iiiX"i.l..xxXxX_x_x-xiiX£iXiXUX-. - - -----. - 5co- x£Xiixxxxx Xxxxx.x(x£xx·x·ixii _J;:~~~-~~~~;:;~;;;:~~;;; _ z._ 23. ~cc u:ux:x.xx:r.xxxxxxxxxxxxxx + • 5CiL H.l\XXHXHXXXUXXXXXUXX!XU __+_ _ _ _ _ t _ __ • .u. xxxx:un.x uxx .x xxxxxxxxx _ll~xxxx• 21. soo • • • ~!Jl...A!llllAX..U.J..!XXXX _ ~Q. _ K,~-~-•..U!U'l-VQXXUHXMQ • • • • XXXXi<XXlXXXXXJl!..!..!!..~ t • • • 17.S<O CXXXXXXXXXXXX XXIX IXXX.UX t t t t 17.~0 XXXO.XXXXXXXX t _ _H. 5QC _ugxXUAXXM!.XJ\lLUXA~H)\l(Qll__ _ _ • - -· _ _ _•_ _ _ _ _•_la. 5QQ_J(XXl\XHXXXX _ _ __ ~ 19. sec xxxxxx.u:o;xxxxx.uxxx + .• • • 19. 50'J xxxxx.oxx:axxx • 1e:., co • • • ~AUAJLll!.!.UJ\ZJ!H UXH 9. 500 ' · !l-00 - • 11.500 xuxxxxxxxxx 41 \). 50-0 X:X..OXXXXXXXXXXXXXXXXXXXX + + • __l~JQQ__!A.q~~~!_:q_x;<_XX_!~. ~i':t.~X,U~ ---- - · - - - - · · ! __ _ _ _ • _ _ _ __ LL'L 5CQ . x;.;x~xx. _ - -~- -· t 5. ~Ct; - x :o.x xxxxx.o: xx xx xxx xxxxx:uxxx u;xx • • • 15. 500- x xxx xx uxxx - • 11.~co t }CQ_~.q:x~~:\~J:- ~XX. X~X~~:O.:t;XX~X:t;;t;_:\!~~..!~:t;!_~~~~l;XX_X xix.:uxx:u.xxu:xxx.uo.:x.uxxxxxxx __ll~!.\_l\.!JL\M~AAll.AXll UXMlll\!A!AMAQ.!!MUUX q_ 5. s.:.o- P> 3.soo 1.s.oo () • • __ ,.___z.,,OQ. ..---- ~-- - -- 40 ..t_----10......Q. ..t__ _ _ _ t ____ _ 10 0 0 • + • • • Q () • • • •. 20 --?:Rt~t~~~:~--=:)t{~:=;~-=~~-;--~ ~- -:-~==~~N:Ht-1:---;-:~;--:~~~:-s.:c xaxxxxxu.xxxxxxxx.u:n::uxxx.u.xxu:xxxx:oxxxxxxxx • • xxxxxxxxxxxxxxx • • • • • • • ! ._ 0 t::J __ __ 10 ·-----........ ·-- ..... -----·-· ---- ................................ ---- ........... ·-- -- -· _ ___ _.____ . ~c~ XI J 1 o... t__ __ . 'i • • • _• ... ... ... ... ... ~sea • • • • __ - ~ -- - - ... ..t _ 20...Q___lD..._o___ ~Q .. fl_ _ _ -'..O.....Q _ _ _JO w l.t.~.:i~ - ~L ... 1.sc.o l C 0 ·---- ·--.... -...... . ...................... ---- ...... ·- -- -.. -..................... -- • ...___. ___.. ....... + _c. 5.:1:0-J . ____ _ ___ , _ _ _ ----• ___ _.llll . ...... 00 CJl 1--' 52 (a) Events which still show feature::; in their r e construction, not characte ristic of tracks conL.Lnuouo thruu1~l1 the 111ngnct aperture. (b) Events where the "re" and "e" in the shower chwnbers both come from the vee in the front end without interaction or scattering, but where the 11 1! 11 or the "e" is misidentified, i.e., the event is really 2rc or 2e. To reduce (a) and (b), quantitative cuts were first imposed and then all survivors were rescanned in the shower and decay region chambers. Quantitative Cuts The following seven cuts were imposed on the 2,226 remaining candidates. Of these cuts, discussed below, (1) - (5) were directed at eliminating (a), while (6) and (7) were aimed at (b). (1) Charged prongs were required to be contained within the production-decay chambers over their length because if they exit through the sides they would encounter an excessive amount of material. This requirement was actually imposed at the scanning level for later data so it is not meaningful to quote how man~ measured events were rejected by it. It is clearly a reasonable cut, particularly since, on one side, an exiting particle would encounter the dense material of the spark chamber electrical hardware. (2) From the Monte Carlo calculations of the electron and pl.on momentum distributions (Fig. 24, in Chapter 4), it can be ,_. .._, ,.),) seen that there are few events with either secondary momentum. above 2.0 GeV/c. A cut at 3.0 GeV/c is reasonable and any decay secondary with a momentum. > 3.0 GeV/c is probably a result of a scattering which gave a smaller apparent bending angle. (3) The reconstructed position at the MH and RH counters was required to be within one counter of the triggering counters. The MH and RH information has already been exploited in checking the tracks. However, for a small number of events, it was possible for the vertex fitting procedure to move the orbit outside the counter in its attempt to find a unique vertex in space. If the reconstructed orbit is con- sistent with the orbit actually followed by the particle, then the MH and RH counters intersected by it should be those triggered by the event. The resolution for this was determined by looking at the distance of all reconstructed tracks from the center of the triggered counter, in the appropriate dimension. This requirement demanded that the reconstructed track be no more than l" from the edge of the triggered MH counter and no more than 3" from the edge of the triggered RH counter. (4) 2 The x per degree of freedom of all tracks in the sample was required to be less than 5.0. From Fig. 11, where this quantity is histogrammed, it is evident that a cut at 5.0 is conservative for the signal which peaks at 0.8. 54 (5) The trnclrn were rec1u:ircd to have oppool.tc cliurp;eo u:Lncc Jt WM lrnpooolllle to tell which charge was wrong when o.n event crune out of' the fit with both secondarJes having the cnmc charge. (6) The pulse height of the electron shower in the shower counters was required to be greater than 1.2 times minimum ionizing. Now that the electron trajectory was exactly known from the reconstruction, its position at the shov~r ,,. counters could be calculated and the pair of counters containing the showe~ knovm precisely. This requirement simply demanded that the pulse height in these counters be consistent with the computer scan. n-n events, where a I ' low energy pion was accepted as an electron, would tend to fail this test. (7) The gas counter trigger configuration was required to be consistent with the orbits of the electron and pion. The counter had two mirrors, each reflecting light into a set of three phototubes, and the pulse height• of each set was separately recorded. Most orbits had the electron shining its Cerenkov light into one side only and for these it was demanded that the pulse heights be consistent with the orbits. Electron orbits were chosen for which the tangent at any point of the trajectory, when extended to the plane of the mirrors, did not intersect within l. O" of the other mirror. For such events, it was demanded that (a) the side I I I I r 55 reccJv:i.ng the. Cerenkov light have ·puloc he:LP,;hL > 0 nnd thu.t Ho m;-1 bJt 1ic on (cec 1\pp<~rnllx !..i), urn! (b) thnt the pulse height of the side not receiving Cerenkov light be < 3. or its BS-1 bit be off. This test removed e+ - e events where the electrons were separated enough to shine on opposite sides and rt+ - rt events where one of the pions was considered an electron in the shower chambers but the opposite side of the Cerenkov counter had the trigger. Table 2 shows the number of events removed by each of these cuts separately and also the number removed by one cut, but passing all others. Selection (1) is not included in this table. reduced the sample to 1,673. These cuts Decay position distributions of the 553 events removed are shown in Fig. 14. Shower Chamber Rescan In order to establish conclusively that the two tracks in the shower chambers were those of a rte ( pe) event and to reduce backgrounds of type (b ), the l, 673 candidates were looked at by a physicist who had access to all parameters of interest from the computer reconstruction of the event. The appearance of the electron and the pion was carefully scrutinized. The electron was scanned for any large angle tracks characteristic of a strong interaction, the pion for excessive multiple scattering which is characteristic of low energy electrons. 'rhc :.;howcr counter puloe heights -were next checked to sec if o.ny extra trucks actually gave o. pulse height :in the counter into which the tro.ck extrapolated. If so, it could ue in ! )(j TA.BLE 2. EFFECT OF QUANTITATIVE SELECTIONS ON THE 1r-c SJ\MPLB Number which would get into final sample if' this Rejection Total rejected cut were dropped but all Criterion for this reason others kept 2 I x /d.f. > 5 ' (4) 129 25 i Sa.me charge ill 9 II (5) I I I Either momentum greater than 3.0 GeV/c (2) 65 6 I I I i Misses MH by more than ! counter (3) 52 3 106 7 Misses RH by more than ! counter (3) Electron pulse height < 1.2 I min . (6) 124 8 I I I I II I I I GC pulse height inconsistent with orbits (7) i 163 16 I I I t ~ I !' II I 57 e- EVENTS 10 (/) f- z w 10 > w 30 20 40 30 t t 9 Ll.. T1 0 0:: w 40 T2 ~ a:i e+ ~ ::::::> EVENTS z 10 10 Fig. 14 20 30 40 DISTANCE ALONG BEAM (inches) Decny position of events rejecte~ quantitative selections (1)-(7) by 30 40 50 coinciclcnce with the n-e and tltc event wuo rcjcctecl r;:lricc the extro. tro.ck coulcl be due to the uecowlaries intcro.ctin{!; on their wo.y through the apparatus. Most of the extra tracks visible were, of course, within the 500ns. live time of the shower chambers, but usually not within the 50ns. gate opened for the shower counters • .As a result of this scan, 289 events were removed from the n-e sample, some of which were put into the 2tt: sample. Fig. 15 shows the decay position distribution of these rejects for each charge state and each target. There is clearly not much asymmetry between e+ and e indicating that the rejects are largely background. Decay Region Rescan All remaining candidates were examined in the production decay region by a physicist. Dubious vees or events with more than 2 prongs from vertex were removed. A total of 47 events were rejected leaving 1,337 in the sample. D. Estimation of Remanent Background. In this section the following backgrounds will be considered: (1) Neutron stars (2) KS ~ tt:+:rr - , A ~ ptt:- (3) e+ - e pairs ( 4) A t3-decay ( A --7 pe -v) (5) 1. K°- production in the targets Neutron Sta rs The material density in the decay region was kept low to 59 e- 141 TOTAL 10 (/) f- z w 0 > w 10 30 40 30 *v LL. a::: w 40 T2 T1 0 A l + CD ~ e• 148 TOTAL :'.) z 10 0 10 20 30 40 30 DI STANCE ALONG BEAM (inches) Fig. 15 Decay position distributions of events rejecte<l in shower chamber rescan. 40 GO avoid background from neutron stars and )'-conversions. The material was mostly aluminum with som1~ epoxy and mylar gas seals. It corre- sponded to .003 collision len~ths and .01 radiation lcne;ths per K,. L) lH'etime. In order for a neutron to produce an event in the final sample, the vee must contain an electron and a pion with no visible evidence for another electron. The two charged prongs must in addition be energetic enough to get through the magnet (p ~ 150 MeV/c). As an experimental check that neutron stars •~re not a background in the final s8!11ple, it was determined that the excess of accepted vees, produced in the first target, that appeared to decay inside the second target was 0.5 ~ 2.0 events. By extrapolating to the spark chamber volume, correcting for relative densities and solid angles, the total neutron star background from the spark chamber plates was estimated to be 0.05 ~ 0.20 events per KS lifetime. 1.0 ~ 3.0 events from all sample. This gives about material in the decay region in the final In the data used to fit the time distributions it was re- quired that a space of at least one spark chamber gap separate the target veto counter from the visible decay vertex. This excluded any events which might have materialized in the veto counter. 2. + - ' A __, p:rc - ~ __, :re :re KS __, :re+:re - and A __, p:rc have decay rates 10 3 times that of K __, :rcev and to reach a background level of 1%, it is necessary to have a rejection ratio of ~10 /1. 5 sources: This rejection came from three 61 (a) Gas Cerenkov counter, used in the trigger. (b) Shower counters, pulse heights examined in the computer scan. (c) Shower chambers, scanned for an electron. In more detail: (a) The gas counter was used in the trigger as described in the last chapter. The pulse height threshold was set as low as possible, just above the noise. From the number of Ks--? 1(1( in the Ke 3 trigger relative to the number in the more general calibration trigger, where GC was relaxed, the rejection of the gas counter was estimated to be (69 ~ 7)/1. (b) The computer scan discriminated against 1(1( and p1( final states since, without interacting, these would give two minimum-ionizing pulses in the shower counters. If the RH's were separated by more than four counters, there would not be a pulse height acceptable as an electron to the program. From a sample of KS ~ 1(+11'. - and A~ p1l - picked up in the general trigger, it was calculated that the rejection of the computer scan was (3.7 ~ 0.3)/1. (c) The visual shower scan gave the largest rejection of the three. A series of runs with the general calibration trigger wan scanned and measured with no requirements on the appearance of trncks in the shower chrunbero. Evcnto were chosen which had invariant mnoses cono :l.otent with either KS -> 11'. +1( - or A -~ p1( hypotheses and these were scanned 62 for ree by the same criteria used in the Ke 3 chower s can. A total of four events survived f rom a sample of 504, giving a rejection or (146 ± 73)/1. The fact that the rejections (b) and (c) may not be independent has to be taken into account if the three are combined to find the overall rejection. For example, a pion which is shower- like in the shower chambers is likely to give a big pulse in the shower modules. So the overall rejection will be a bit less than 4 the product of (a), (b), and (c) which is (3.7 ~ 2.0) x 10 • However, there are more direct ways of estimating the K and A background, as will now be seen, and the preceding was just to give a feeling for the discrimination of the apparatus against this background and show that it had the correct order of magnitude. Direct measurement of the K and A backgrounds was performed by comparing the re-e sample to the re-re (re-p) sample collected in the shower chamber scan. Fig. 16 shows comparisons of different dis- tributions for these two samples. The re-re events peak at low GC pulse height and have prominent K and A mass peaks, whereas the rc-e events have a broad GC distribution and show no evidence of K or A peaks. In order to measure the small K and A contamination in the re-e sample, it was necessary to make selections which enhance such backgrounds. This was done as follows: (a) Select events with GC pulse height :S, 8, and (b) select events with decay lengths< 10". 63 -rr-e 200 60 - (al (d) 1390 EVENTS TOTAL 1105 EVENTS TOTAL 100 40 + 26 EVENTS 20 f-+62 Cf) 1- z ~ w ~ 50 a:: w (bl :::> 0 200 (el a:: w £l) ~ LL. £l) ~ 25 :::> z 100 f-+514 z f--+31 01...----1:-Wtl.J.Oo-.w...i~.:=iA...:l~z:L...~~~~--J K.XX) 1100 1200 1200 1300 1300 Mp,,.-(MeV) Mp ,,. -(MeV) (cl . 1180 EVENTS TOTAL Mp,,. >1160 MeV (fl 535 EVENTS TOTAL Mp,,. >1160MeV 100 50 600 200 400 M17+17-(MeV) Fig. 16 Comparison of Tie sample with TITI sample. 600 800 M,,.+,,.-{MeV) The shaded events have GC <8 and are within the first two K lifetimes. s The absence of ev.ents with pulse height <2 in (a) and (d) is due to the trigger bias. G1 Sixty percent of nre events Gatisf'y (a) and (b), whercno only Z'/o of the re-e eventn fall in this region, giving an enhancement factor of 30. Histograms of m and m for such n-e events arc shovm as ren pre shaded histograms in Fig. 16. It is reasonable to assume that the mass distributions of good n-e events satisfying (a) and (b) are the same as those for the total sample, since there are only weak correlations between mass and GC pulse height or between mass and decay length. Using this assumption, a subtraction was made to isolate whatever K ~ nre or A ~pre signal was present. For the m pre spectrum an excess of (-3.1 ! 4.3) was found in the A region and form rere an excess of (7.8 ~ 4.3) in the K region, giving a total of (4.7 ~ 6.1) events. Since the procedure is 6CP/o efficient on back- ground, this leads to a total background in the sample of (7.8 ~ 10.0) events. This number was independently estimated from the total number of nre events picked up in the Ke 3 trigger (af'ter the tape scan) and the measured rejection of the shower chambers. This gave 1164/(146 ! 73) = (8 ~ 4) events, consistent with the (7.8 + 10.0) estimated above. The K, A background can be reduced f'urther by a factor of 3 by demanding GC pulse > 8 simultaneous with m pn > 1160 and m nn < 440. The sensitivity of X to this cut will be discussed in the next chapter. 3. Electron Pairs This background falls into two categories: (a) External convcroions: (b) Duli t:c. conver::d.ons: y + Z 4 e+ + c + z followed by G5 1l 0 4e + +e +y. For (a) and (b) the expected invariant mass distributions of the electron pair peaks at very low mass. Fig. 17 shows the invariant mass distribution of the 1!-e sample under the hypotheses that both charged particles are electrons. For comparison, the m + e e dis- tribution is shown for events taken with a 0.25 radiation length lead converter placed in the decay region and where the two charged particles in the shower chambers showered (process (a)). The shape of the latter implies that there are < 9 events from process (a) in the uncut sa..-nple. A cut of 30 MeV on me +e - reduces this background by 30. Data taken with the lead converter were scanned in the shower counters and shower chambers like real data to determine the rejection of the 1!-e scanning fore+ - e pairs. that the rejection of the scanning one+ - e (43.5 ~ 11.3)/1. It was determined pairs was Using the Monte Carlo program (described in Chapter 4), it was calculated that 880 events of type (b) would be in the final 1!-e sample with no shower or mass selections. Using the shower rejection of 43.5, this number reduces to 20 Dalitz conversions before cuts on me +e - • A cut at 30 MeV reduces this to 12. In order to demonstrate sensitivity of the final result to such background, a cut of 60 MeV can be imposed to reduce it further by a factor of 4.8, as will be done in Chapter 4. 4. Lo.mb cla Beta De cay A --) p + e + v gives e events at early times where X = O 66 150 I I I I I I Electron · pairs from lead converter I 100 .; '· . 1 I I t1/x10 I 50 I I CJ) I I- z w > w I 0 0 ...., 100 300 Me+e-(MeV) LL 0 100 0:: w m 2 ::::) z 80 Tie sample 60 40 20 o._______.._______._____ 0 100 200 ~....._ _____,_______ 300 400 __J--J 500 Me+e-(MeV) Fig. 17 M + - djstributions from lead converter and Tie sample e e 67 pre<'licts few events. events, for decay lengths < 5" to enhance the t. and e This signal was expected to be visible in the n e m < lll5 MeV. ep for c + op oignul. li'ig·. 10 shows the diotribution of rn 0 distribution for The n + distribution was used to calculate the e number of events with m < 1115 MeV if there were only K 1 s in ey e3 the ne_ distribution, with no A~ contamination. A subtraction was then made as follows: Inserting numbers from the histograms gave Correcting for the fact that the histograms are for the first 5" from each target, this gave a total of 19 sample. ± 6 A~ events in the ~e To ensure that this background was eliminated, it was required that Mep > lll5 MeV, the maximum p-e mass possible in A~ decay. The cut was imposed on both charge combinations to preserve charge synnnetric treatment of the data. 5. K°- production It was estimated from ~-p bubble chamber data(2l) that the 0 total cross section for K°- production is less than lCP/o of K duction at 2.85 GeV/c. - pro- The momentum distribution of the K° will peak somewhat lower than the K0 and its angular distribution will be less peripheral. I I I iI I From the acceptance of the apparatus as a 0 function of K - momentum and angle, it was estimated that the average 0 relative acceptance of K° to K into thu apparatus was < loo/a. This I 68 50 10 e- EVENTS A{3 REGION~ --c> +15 (/) f- z w > w m 0 p (MeV) LL 0 a:: w CD ~ :::::> z 255 e<- EVENTS 10 -{l;> +136 900 1000 1100 1200 m 0 P (MeV) Fig. 18 m distributions fore+ and eep events with decay lengths < 5 11 1300 69 mco.no thut lcoE:J them l°/o of the K . do.ta co.me from p1on production e.3 of K°. f\.s mentioned in Appendix 2 on the pion l)com, the K- con- tamination in the beam was measured to be ~0.1% of the pion flux. ~ n ) is estimated to be 500µb. ( 22) whereas a ( n - p ~ K0 /\. )~100µb. a (K - p ~ K at 2.85 GeV/c. This means that ~o.5% of the events come from K- produced K°. This gives an overall limit of 1.5% to the K°- pro- duction fraction. As will be seen in Chapter 4, when a fit is made 0 with the fraction of initial K° relative to K as a free parameter, 9 the 3-parameter fit gives K°- fraction= 0 6% +l. % , consistent • -0.6% with the above estimates. In su:rmnary, the following background-reducing cuts have been made in this section: (a) M > 1115 MeV, 163 events fail. ep (b) M > 30 MeV, 8 events fail. ee (c) At least one spark chamber gap visible upstream of the decay vertex, 34 events fail. The total number of events after these cuts was 1,137; a sun:nnary of the background analysis is contained in Table 3. This Chapter has shown how a sample of Ke 3 events, with background < 2 %, was obtained between 0. 2 and 7. 0 K lifetimes. 8 It remains to calculate the acceptance as a function of decay length for these events and to fit them with the parameter X. 70 TABLE 3. BACKC:-ROUNDS IN TRE rc-e SAMPLE Type of Number -present Cut imposed on Estimated back- Background before cut final sample ground after cut Neutron stars 1.0 + - 3.0 NO cut 1.0 + - 3.0 KS~ 21L, A~p1L 7.8 + 10.0 - NO cut 7.8 + 10.0 < -9 me +e _> 30 MeV < 0.3 - Electron pairs: a) External Conversions b) Dalitz pairs Lambda beta - - decay,A ~ p + e + v 12 ~ 3 20 ~ 5 24 ~ 16 - m ep > 1.115 o.o GeV K°- -production - a) 1( p ~ K°K0 n -0 b) K-p ~Kn < 11 < 11 ""5 ~ 2 NO cut ""5 ± 2 Total background 26 ± 11 in 1137 events < 11 from K°Ko product ion 71 IV. EFFICIENCY CALCULATION AND MAXIMUM LIKELIHOOD FITS The last chapter concluded with a sample of 1137 Ke events. 3 In this chapter, these data are fit to X, the !::::S = 6Q rule violation parameter. The function used to fit the data is a product of the decay distributions derived in Chapter 1 and EK (xK), the e3 efficiency for Ke 3 detection at a given decay length, xK. This (~) chapter first discusses the Monte Carlo calculation of EK and e3 ~ i [ l concludes with the maximum likelihood fitting of the data. '. A. ~ 3 Efficiency Calculation In fitting the decay position distributions to X, the likelihood function that is maximized has the general form: = rr. l f(x. )E(x.) l l where f(x) is the decay distribution function and E(x) is the acceptance efficiency for an event whose decay length is x. In the Monte Carlo calculation of E(x) for Ke 3 decay, it is necessary to know the momentum spectrum and angular distribution of the decaying K01 s. Alternatively, one could reconstruct pK and QK for each event and then use EK (pK' QK' x) e3 in calculating ~ , where EK (pK' QK' x) is the efficiency cale3 culated at fixed pK and GK' without folding in their distributions. 0 The K - momentum in K e3 decay can be calculated up to a quadratic arnbigui ty by measuring QK and the momenta and angles of the decay secondaries. In most cases, this ambiguity can be resolved by 72 uppco.llng to Jrnicpenc.kmt Jrnowludi:.i;c of tht' ovectrum of pl<° However, Jn this experiment, the rneasuremeut of GK was poor and it was not possible to find pK' as indicated, for each event. This meant that one could not use EK (pK' GK' x) to weight e3 the events individually in the maximum likelihood calculation. The approach taken was to find the production distribution of pK and GK' D(pK' GK ) , from K 8 for each event. 4 :rr+:rr - events for which pK and GK were known D(pK' GK) was then used as input in the Ke Carlo calculation of E 3 Monte (x) where: Ke3 EK (x) e3 For a large sample, little information is lost by using the latter approach except that it involves more dependence on Monte Carlo calculations. This section will first discuss how D(pK' GK) was extracted from the K:rr 2 data and then show how the final Ke efficiency was arrived at. 3 Details of the Monte Carlo program are contained in Appendix 12. 1. I Calculation of D(pK~) 0 The production distribution of K - mesons from the brass targets, D(pK' GK)' was assumed to be the same from the two targets, any differences in observed distributions being due only to the acceptance difference between targets. It was further assumed that 'PK and GK were uncorrelated :l.n the lo.borntory so that D(pK' GK) = f(pK) .g(GK). These as:.;urnptiom; are justified by the consistency 1· l I[ !l .i I t ! f I I i I 73 achieved in fitting momentum and angle distributions from both targets with the single distribution f(pK).g(GK). For fitting, f and g were parameterized as follows: i(p-A)2 f(p) = e""2 B • R(p; _J;.(G-8)2 = G.e 2 T c, D); 4 parameters ; 2 parameters where R(p; C, D) is a ramp f'unction, designed to make the pK- spectrum fall faster than a Gaussian at the high momentum end: R = l; p < C R = (D-p)/(D-C); C ~ p ~ D R = O, p > D In the actual six para.meter fit the momentum resolution S(p-p') 'Was included; its Gaussian para.meter a is .16 GeV/c for Tl, .30 GeV/c 0 for T2 at p = 2.4 GeV/c, the mean K - momentum. K A sample of clean K 8 _, 2n decays was obtained from a set of calibration runs by demanding: (a) The same reconstruction criteria that were imposed on the final sample of Ke 3 's. (b) m (c) m pn nn > l.160 GeV > .440 GeV. Since KS _, 2n is a 2-bocl.Y dccuy, pK o.nd GK can be calculated from the momenta ancl angleo of the! ::iccondaries alone, unlilw the case of 74 3-body Ke 3 • The observed pK' GK distribution of this comple was then fit to u cHctribution function of the t'orrn: where ~ (p', GK ) -was calculated by generating KS ~ 2rt decays rt2 exponentiall y in time. The fit gave the best values: .03 - .08 + A= 2.48 B = 0.82 + .13 - .03 c = 2.68 +- .04 .07 + D= 2.86 .Ol - .oo .9 s = -l. O +- l.4 T = 9. 0 °2: .6 A sket ch of the resulting f (p ) and g (G) is shown in Fig. 19. The procedure was checked by generating KS~ 2~ decays wit h f (pK) .g (GK ) from the best fit as input. The Monte Carlo and data were compare d for pK and GK distributions. Fig. 20 shows t hese comparisons for Tl and T2. Fig. 21 shows the comparis on for KS ~ 2rt decay position distributions. In all cases the agreement is good. The decay position comparison gives a non-trivial che ck on the calculation of ~ (pK' GK' x ) as a f'un ction of x. rt2 75 5.0 g(e) Cf) 1- z ;:) >0:: <X: er: 10 BK (degrees) 1- co er: 20 <l: >- 1Cf) z w I- z 1.0 f ( p) 1.0 2.0 PK (GeV/c) Fig .19 0 Sketch of K -production distributions, f (p) and g(B) 3.0 20 01 01 0 ::> 20 Z IT ~ ro w 0 0:: 40 LL z w > w 60 ~80 z I l 15 2 PK (GeV/c) T 0 3 (d) (c) for momentum and angle distributions from each t a~ge t --·---- . . ,. -. . . -. -~ -~. .,-...-._..-. . . . . ._..__...._._,. Comparison of calibration data (points) and ~onte Carlo (histogra os) 20 0 ·1- ~ BK (degrees) I 10 I 5 T2 (b) l .rl --~--------------------------.._.....-·-·---'"':""---:----- ..,,._..--...-......--r--· ..··~.-~-..-..~ -~--------·---r---,.··-·· Fig. 0 I • • 0 Tl ::> 20 -1•1.i-n Tl T T.l I 1 • {a) ---1 ~ ffiro 40 0 LL z w > w 60 ~ 80 100 c,. ....,....,.... .._....._.,.,.,........,.~......,.......,.,.,...,......,_ • .._..,.._,....,. (J) -..J 77 400 300 2 ND TARGET 200 T .! (j) r-z w > w 100 80 60 50 40 T 1 ST TARGET 0 T0 1 30 LL 0 20 0:: Il T T w co ~ ~ z 10 8 0 0 I 6 5 4 1 3 l. I 0 2 10 15 20 25 30 35 40 XDECAY (inches) Fig. 21 Comparison of decay position distribution for calibration data (points) and Monte Carlo (his .t ogranw) from each target 78 2. ~) Calculation of EK e3 The distributions of f(pK) and g(GK) were then used as input in generating K 7 1 S to determine EK . e3 e0 decay position, x. (x) at fixed values of For the first target, six positions were chosen at 5" intervals and for the second, two positions were chosen, also 5" apart. In order that the conditions producing these M.C. events be the same as those that produced the Ke 3 data in Chapter 3, it was necessary to make extra selections whose effects are sunnnarized in Table 4. (a) The selections were: As seen in Appendix 10, Fig. 45, the computer tape scan had an energy dependent efficiency for accepting electrons, since it demanded a l~ times minimum-ionizing pulse in the shower counters. This efficiency was imposed on the Monte Carlo successes. (b) For events where the electron shone its Cerenkov light on a particular part of one of the gas counter mirrors, it was found that there was a deficiency of events in the data compared to the Monte Carlo. This effect was corrected for in the M. C. events. (c) The mass cuts m > l.115 GeV and m > 30 MeV were imposed ep ee on the M. c. successes. From Table 4 it is evident that these corrections mostly lower the level of the efficiency anu only make slight chanc;es to the slope as a fUnction of x. High, T2 High, Tl Low,T2 (Target Center 32.2") Low,Tl _ (Target Center 8 .0") Field, Target 40 35 10 15 20 25 30 35 40 35 40 40 35 10 15 20 25 30 .0837 .0934 .0224 .0267 .0393 .0442 .0539 .0621 .0691 .0941 .0997 .0242 .0294 .0393 .0475 .0578 .0662 .0739 Decay Position Efficiency x Without (inches) Correction TABLE 4. -2'C'/o +3% +5% +3% +'C'/o O°/o +l°/o (11/; +l°/o +3% +3% +5°/o +'C'/o +1% +1% -'C'/o +'C'/o -1°/o +1% Gas Counter Mirror (b 2 3 -14% -14°/o -14°/o -10°/o -11% -10°/o -16°/o -13°/o -15°/o -14°/o -13°/o -13°/o -14°/o -13°/o -13°/o -14% -15% -14% corrections (c2 Mass Cuts .0565 .0640 .0155 .0191 .0277 .0313 .0354 .0416 .0457 .0630 .0683 .0165 .0204 .0265 .0326 .0380 .0428 .0485 Final Efficiency EFFICIENCY FUNCTION %change due to these -24°/o -25% -20°/o -21°/o -21°/o -21% -24°/o -25% -24°/o -25°/o -25% -23°/o -24°/o -25% -25°/o -21% -20°/o (a2 Electron Pulse Height CORRECTIONS TO Ke -32°/o -31°/o -31°/o -28°/o -30°/o -2go/o -34% -3 3°/o -34°/o -33°/o -31°/o -32°/o -27% -33% -31% -34°/o -35% -34% Overall % Change I -;:,% -5cb -11% -1C/1p -=-cf, -11% -l4Fj; - -1 51, IJ -13% -7% -5% -10% -v,~ o:I -12;~ -14% -17% - -1 5'b I -ll% Lc1'-er f(p) by 100 1·'.eV I c -..J <.D 80 !\ possible ar:Lcc :U' Ji':i.f~. the f:'/lC position-dependent bins in the rqrp:.i.ra.tuo woulcl co1mtcr cl.'f:ic :i.cncy were dccny poc:li;:ion dependent. ;!i:! r~howu U1c men.n 1)1Jlou hc~Le;ht decuy position. 1'or Tl K ·~':::; n.s a l'unct:lon of co The sol id line is the best straight-line fit. From the mean and width of the pulse height distributions, it was estimated that the overall efficiency of the counter for Ke 's was 3 > 93%. From the straight-line fit, it was est imated that the variation in this efficiency between the extremes of decay position was -l.C!1/o and so of negligible effect on the Ke 3 efficiency. The efficiency functions for the two targets E (x) and 1 (x) were derived by fitting the data in the seventh column of 2 and E (x) to E (x) was fit to A + ~ x + A x Table 4 2 2 0 1 E 2 Bo + Bl x. The efficiency was cal culated and fit at the two mag- netic field settings, 2.0 and 2.8 Kg; Fig.23 shows 2.8 Kg fit, also fit when f(p) was displaced by 100 MeV/ c in calculating E. Comparisons of data to M.C. were made for: (a) pion momentum distribution, (b ) e l ectron momentum distribution, and ( c) rt-e resultant momentum distribution. These are shown in Fig. 24, the pion M. C. histogram has been corrected for pion decay, which has a visible effect for p rt < 500 MeV/c. Fig. 25 shows the comparison of data to M. C. for the invariant mass of the rt-e combination, m • rte The agreement is good in all cases. Further checks on the Monte Carlo calculations are discussed in Appendix 12. The efficiency f unctions El (x) and E (x) wlll now be used 2 in the maximum likelihood fitting in the next section. l I I I t ' I I !f 81 40 I- :c <!) 30 w :c w Cl) ..J ::::> £l.. (.) <!) z <( 20 ,. T ~ T l ... 0 10 0 .I. 10 20 30 40 50 Xv (INCHES) DISTANCE OF VERTEX FROM BEGINNING OF FIDUCIAL VOLUME Fig. 22 Xcan GC pulse height as a function of decay position for Tl ne data. Smooth curve is best straight line fit. targ~t, Second T2 .06 / .05 / / / fit with >- .04 (.) / / E ( X) z w (.) / / / / / First target, Tl / / LL. LL. / / w .03 / Dashed curves are / ~ / fits obtained when / / input f(p) lowered by / / .02 /-' 100 MeV /c (data / / / points for this fit omitted as they confuse figure) / / .01 10 20 30 x, DECAY POSITION (inches) [i'ig. 23 Efficiency :f'unctions at 2.8 Kg. Errors are from M.C. statistics. 40 83 T (a) PION 80 40 - I 00 2.0 (/) z w 120 > w rt P7f(GeV/c) . ( b) I- 3.0 ~ r ELECTRON 80 I I 0:: w GJ ~ I 't II LL. 0 It I I T 0 40 l. :::::> z 00 1.0 (c) 80 I! 3.0 I Pe 1(GeV/c) MOMENTUM DISTRIBUTION OF ACCEPTED K0 •s RESULTANT MOMENTUM t . I ; I ' I j. 40 rI I 0 I 0 1.0 2.0 PRES (GeV/c) I t I t I I Fig. 24 Comparison between Tie data (points) and Monte Carlo (histograms) for : (a) pion momentum, (b) electron I I momentum and (c) TI-e resultant momentum. I I ! f ! 84 i I I ! ! I t ~ f I lr 1079 EVENTS 120 (f) ~ z w > w lJ... 0 I 0:: I :2! :::> z f ! II w CD t I! 1 80 - I 40 I i I I I I I r [ l 200 300 400 500 Mve (MeV) Fig. 25 Comparison between ne data (points) and Monte Carlo (histogram) for the invariant mass of the Tie I I i r I' ~ t I I I I I' 85 B. Mnxjnnmi I..ihclillood FittJnc; o.t' Data ThJu ~;ect:lon vll.l .l' . i.r~:t outline U1e f'j ttJ.n1.o; J>rucedurc, th<m make fit::> to the data and finnlly investigate the sensitivity of the result to variations in input parameters and to cuts on the data. 1. Details of Maximum Likelihood Calculation The best value for the parameter X was determined in a program that maximized the likelihood f'unction i=l i=l i=l i=l where, for example N+(t.) l / 2 e: 1 for e+ events from (t.) l (N+(t) + N-(t)) E 1 (t) dt the first target, T1 + N-(t) are the time distributions discussed in Chapter 1, e: 1 (t) is the Ke 3 detection efficiency from target 1 at proper time t, at the appropriate field value, n~ is the total number of e+ events from target 1 T and T are the fiducial volume limits from the target in 2 1 question t . is the proper time assigned to event i. l The proper time for an event is related to the deca y position by the relation t ~ = XD _ _- K __ . ~ , where ~ is the pro- px c OG duct:Lon point, XD the clecuy vo:Lnt, uncl p~ project ed i n the x direction. Jo t11c K-111u111<:nturn The target length of 1. ;:?" and K- momentum spectrum FWHM of 900 MeV/ c cause an uncertainty in the proper time for an individual event, which is usually, however, a fraction of a KS lifetime. This uncertainty is minimized if one takes for xp the center of the target and uses the average < l/p~ > for l/p~ in calculating the proper time of each event. was 2.28 GeV/c for Tl and 2.22 GeV/ c for T2. l/<l/p~ > The smearing effect + of the xp - and PK - distributions on the time distribution N- ( t ) is + investigated in Appendix 13. The time distributions N- (t ) used in calculatingi. were corrected to take i nto account moments up t o the second. It is shown in Appendix 1 3 that the effect of higher moments changes jxj by< 0.01. In calculating time distributions, the following ~uantities were taken from Ref. ll: -rs = 0.862 x -rL 10 = 0.538 x 10 -10 -7 sec. sec. 6nl-rs = 0.469 The maximum l ikelihood procedure was checked by generating K 7 time distributions with different values of X and then using eo them as input to the fitting program. The resulting fits were: 2000 events, w-lth input X = ( -.069,+.108); 080 +. 0113 ) fit go.ve X :::: ( - 060 +. 021 • - • 032 ' • - • 041 87 2000 events, with input X = (o.o, o.o); 024 0 000 +.o 35 ) -.038 ' • -.034 fit gave X = (0.000 +· which are within the expected limits. 2. Fitting of the Data The 1137 events which survived all the selections of Chapter III were reduced to 1079 by a fiducial volume cut which removed the last 2" of the downstream end of the decay region. felt that vees from this region were in the scanning and hence prone to bias. It was more difficult to identify When these 1079 events were fit by the maximum likelihood program, the result was: Rex = -.069 : .036 ImX = + 108 +.0 92 • -.074 Fig. 26 shows the time distributions of the data with smooth curves corresponding to a) best fit, b) X = o, c) X = (+.14, -.13), the world average given in Chapter I. A notable feature is that the error in ImX is more than twice that for ReX, in apparent contradiction to the statements made in Chapter I, where it was stated that n' = 500 would give errors of ± .04 for both ReX and ImX. This larger error occurs because there are non-linear terms coming into effect as one moves away from X = 0 and the estimate of errors given in Chapter I assumed X = O. The likelihood contourc for the fit are shown in Fjiz. 27. The relative probability of X = O, relative to the best fit is 0.25 88 .08 .04 .' 't l' i X=BEST FIT --X=(O,O) ---- x =( +.13, -.14) 20 N 10 ·TGT. 30 FIRST TARGET I t SECOND ~ TARGET N+ 20 10 TGT. TGT. m 0 10 20 30 0 10 Xv (DECAY POSITION IN INCHES) Fig. 26 Final decay position distributions of ne SGrnple. (a) Efficiency functions; (b) N- distribution from each t tI ~ t li [ . I target; (c) N+ distributions. I I 89 BEST VALUE THIS EXPERIMENT 0.4 0.3 I 0.2 0.1 I -0.1 T @ ~ 1 -0.2 -0.3 PRIOR WORLD AVERAGE .Oii .1 4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 Rex Fig. 2 7 The be st v a lue of X from this experiment. Al. s o shown arc th e contours correspond ing to the 1,2,3,4 standard deviation limits, showing the probability relative to the best result. 90 whJ le that of U1c world average relat:l vc to the li e ot J':I t :Lu < e -0 == 3. ::> x Hence, the best fit und the world overage a.re inconsistent with one another but both are consistent with X == o. If one assumes CP conservation in the decay (ImX == O in the fit), the best fit gives Rex == -.036 +.036 -.044 Conversely, if one assumes maximal CP-violation in the breakdown of 6S == 6.Q, i.e., ReX == 0 in the fit, the best fit gives ImX == +.02 +.058 -.060 Both of these results are clearly consistent with X == O. 3. Sensitivity of the Result In this section the sensitivity to variations in the input parameters and cuts on the data will be investigated. (a) ~~ mass difference The mass difference~- m was allowed to vary as a free 8 parameter in the M.L. fit, giving: ReX == -.081 +.034 -.036 ImX == +. 101 +.094 -.088 + . 052 6ln-rs == +.424 -.048 The last is in good agreement with the accepted value of (ll) +. 469 +- • 01'_ ;:>. The tlrnc dC"pcn<lencl! of N+- N-, the dlJ'J'<..!rcn c' : cf fhe...- c time dictributions, dcvcnds only on -r , 6rn and c ( t J , 8 + N (t ) _ - N ( t ) "' e -t/2·r S • cos l:Jnt • E( t ) . It. \>nr> hoped that a X2 fit of. N+ - N- to this ti:::e d. 0-:;:.r;r,r} r; ;, r;<; ·,:r;.;J. r1 place some restrictions on E(t) and hence make a direct check on E(t) from the data. However, the fit is relatively insensitive to c(t) since N+- N- goes through zero at L.mt = ~/2 which corresponds to about three K 8 lifetimes. A wide range of slopes in E(t ) will still give a good fit to N+ - N- • (b) K° fraction ::-:() As an independent check that produced K 's were not a prob - lem, the fraction of K° at t = o, ~j?:l , was allowed to vary as a free parameter by using the time distributions i ~ N+(t) = (1-~j?:l) N~o (t) + ~j(° i NRo (t) N-(t) = (1-~j(°) N~o (t) + ~j?:l NRo (t) [ where, for example, N~ (t) is the same as ~o (t) except that the term with IrnX occurs with an opposite sign. The best fit gave: ReX = -. 056 +. 036 -.038 ImX = +. 116 +.082 -.080 .006 +.019 -.006 in agreement with the fraction estimated in Chapter III. ! f. I l 1. I I I r 92 (c) Fiducial volume variation Table 5 shows a series of fits in which the limits of the fiducial volume were varied at both the ' upstream and dovmstream ends of the decay region. The variations are consistent with statistical fluctuations and the limits finally chosen were 9.28 11 (Plate 2) to 41.00 11 for Tl and 33.43'' (Plate 2) to 41.00" for T2. (d) Mean momentum, mean production point and Ke 3 efficiency function Table 6 summarizes the effects of varying these inputs. The mean K-momentum of accepted Ke 's was varied by ±50 MeV/c, 3 corresponding to ~ times the standard deviation on the mean momentum calculated from the KS ~ 2~ data. The mean production point was changed by :!: O. 25", corresponding to a position distribution of production points which falls to zero at one edge of the target. The latter is an extreme assumption and it is hard to conceive of a mechanism which could give such a strong 0 variation in K - acceptance between ends of the 1.211 targets. Sensitivity to the efficiency function E(x) was investigated by 0 varying the parameters of the K momentum and angle distributions u::;ed as input in the Kc._. Monte Carlo program. f'(J)K) wus din- placcd by 100 McV/c and g(GK) was derived from each target TJ\I3LE !:) • FITS WITH VNUATIONS IN FIDUCIAL VOLUME The standard fiducial volume is defined from Plate 2 -- 4l". In this table it is varied at both ends. Conditions Number of Events Rex ImX -- 42" Pl.2 -- 41.5" ll23 -0.053 +.0 34 -.036 0 064 +· 092 + • -.074 ll02 -0.06l +· 032 -.038 . 0 096 +· 091 t- • -.078 Pl.2 -- 41" l079 -0.069 :t .036 0 l08 +· 092 + • -.074 -- 40. 5" Pl.2 -- 40" l05 4 -0.069 +· 034 -.036 0 l28 +· 088 + • -.080 l024 -0.066 +.0 34 -.036 0 l53 +· 082 + • -.084 Pl.2 -- 39.5" 978 -0.065 +· 036 -.034 0 l32 +- 084 + • -. 090 Pl.2 Pl.2 Pl.2 -- 39" 949 -0.065 +.0 34 -.038 0 156 +· 082 + • -.096 Pl.2 -- 38.5" 919 -0.065 +· 034 -.040 0 168 +- 084 + • -.092 Pl.2 -- 38" 880 -0.065 +· 038 -.036 0 172 +· 080 + • -.102 Pl.3 -- 4l" 1061 -0.06l +- 036 -.038 +0.096 +.086 -.072 Pl.4 -- 4l" l047 -0.053 +.o 4 o -.038 +0.099 +.080 -.072 Pl.5 -- 4l" 1034 -0.052 +- 036 -.042 +0.108 +.092 -.080 94 Tf\13LE r;. FI'l'S WITH VJ\.lllf\T):ONG IN MJ•:J\N MOMEN'J'UM, Mfi:J\N Pl\ODUCTION PO:lTI'r .1\ND K '" J•;Jo'J.<'ICJl•:NGY l•'IJNC'l'lON e'"> Conditions of Fit Increase < l/pK >- 1 by 50 MeV/c ReX ImX -0.078 +· 034 -.036 +.080 +0 •112 -. 088 -0.061 +· 034 -.036 +.086 +0 • 108 -. 080 -0.049 +.034 -.036 4 +.092 +0 • 10 -.074 -0.085 +.032 -.038 +0.096 +.o 92 -.078 -0.066 +.036 -.034 0 104 +· 092 + • -.078 -0.065 +.032 -.038 0 132 +· 080 + • -.092 -0.042 +· 034 -.036 0 0 2 +.llO + • 7 - • 070 -1 Decrease < 1 I PK > by 50 MeV/c Move Average Production Point Upstream 25" Move Average Production Point Downstream by • 25" Use T2 Angular t0 Q) Distribution ~ 0 +' Cl) +' ::I p.. >:: » () >:: ·rl Q) ~ •rl 0 ·rl •rl Cl) Cr; Cr; >:: 0 •rl +' Cll ·rl H cu :> Q) Use Tl Angular Distribution Lower f(p) by 100 MeV/c in Efficiency Calculation Ge'Po.ro.tely and u:::cd ao Jnput. In all cusco the vnrJationo ure small compared to the statistical error. (e) Cuts on the data Table 7 shows a summary of additional fits made in an attempt to demonstrate the presence of background or some systematic bias from the apparatus. for reference. The final result is shown The second and third entries are fits to the being independent of efficiency. Fig.'s 28 and 29 show the likelihood contours for these two fits and they are clearly consistent. As mentioned in Chapter III, in the discussion on background, there are extra cuts which can reduce the K ~ 2rr, 8 A ~ prr and Dalitz e + - e backgrounds by substantial factors. These are made in the fourth and fifth entries and show no effect, confirming the estimates of background made in Chapter III. Possible charge asymmetry was checked by dividing the data into the two magnetic field polarities used. are statistically consistent. Entries 6 and 7 The effect of a position depen- dent bias in the gas counter was investigated by dividing the data into two samples, one with GC pulse < 18, the mean pulse height, and the other with GC pulse > 18. In entries 8 and 9 the two srunples give consistent results in agreement with the conclusion reached earlier in this Chapter, that the gas counter efficiency is not position dependent. Entries 10 and 11 show fits for the first and second targets separately, in agreement 96 T.i\BLJ': 7. FI'l'S MJ\DE INVJi:: ;•1 JC!\TING B/\CKCHOUND:; J\NJl JIJ/\.'.:\EG IN lWl'J\ 1 Number of Events Rex Final Result 1079 -.069 :!: .036 +.108 +.092 -.074 Sum Only (neglect charge) 1079 -.076 +.086 -.118 +.100 +.092 -.112 Run Condition ImX ------------------------------------------ ----------- -------------+.110 +.036 Asymmetry Only Reduce K /\.0 ~ 0 ~:rr p + :rr + 1079 -.068 1031 -.065 +.034 -.038 +.092 +.104 -.068 1066 -.069 +.034 -.036 +.108 +.096 -.070 516 -.057 ~ .050 +.099 +.120 -.096 -.038 +.181 -.160 + :rr - - background by ' factor of 3 (see Text, p.64) Reduce Dalitz background by factor of 4.8 (see Text,p65) Magnetic Field Up ----------------------------------------- ---------- -------------+.046 +.140 Magnetic Field Dovm 563 -.081 Large Cerenkov Pulse(> 18) 487 -.037 -.052 +.046 -.050 +.123 +.137 -.116 +.104 -.110 ·--------- -----· ----------------------------· ---------- ~-------------+.052 +.120 Small Cerenkov Pulse(5_ 18) 592 -.085 First Target Only 868 -.053 -.056 +.048 -.046 +.043 +.164 -.086 +.098 -.120 ---------------------------- ---------- ~--------------------------+.056 +.130 Second Target Only 2ll -.045 Positive Electrons Only 672 -.077 ::- .072 -.062 -.004 -.ouo +.016 +.1 60 -.190 ---------------------------- ---------- 1o-----------------------------+.054 +. 0151 n egative Electrons Only 407 -.015 -.068 +.160 -.102 97 0.4 0.2 0.1 .14 -0.1 -0.2 -0.3 -0.4 -0.2 -0.3 -0.2 -0.1 Rex Fig. 28 Likelihood contours for fit to sum 0 0.1 0.2 98 0.4 ASYMMETRY (N+-N-)j(N++N-) 0.3 0.2 x 0.1 1 -0.1 -0.2 -0.3 -0.4 -0.3 -0.2 -0.I 0 0.1 0.2 Rex Fig. 29 :Likelihood contours for fit to asymmetry 0.3 0.4 99 with co.ch other. to c + and c Entr:Lce :i.;~ and L'S i;how the cf'J'cr:t of :f'Jtt:Lnp; clnto. sepurn:tcly. lJeforc CF'.r-invar :lnncc io nocwnc<l, there arc two independent par8Jfleters X and x, one occurring in the e+ time distribution and the other in the e bution. time distri- If one assumes CP:r-invariance these satisfy X = X* From the last two fits Ix - xi = .155 ~ .219, consistent with CPr-invariance. In conclusion, all of these tests, a) through e), show no reason to include any systematic error in the final error quoted for X. 100 V. CONCLUSIONS AND OUTLOOK The final result for this experiment is: Rex = -.069 t .036 ImX = +. 108 +. 092 -.074 The difference in the logarithm of the likelihood function for this best value and for X = 0 is t.::, log £ = 1.38 so the relative probability . correct is . e - 1.38 = 0 •25 • t ht a X = 0 is The previous world average, Rex = +.14 + .05 ImX = -.13 t .043 While inconsistent with the above result (relative probability < e -8 = 3.3 x 10 -4) , is consistent with X = O. If the present result is incorporated into the world average, the latter becomes: Rex = +.002 + .029 ImX = -.080 + .038 which implies that jxj < .16 with 9C/fo confidence. One can be legit- imately suspicious of the errors in the old world average and the 9CP/i confidence limit on jxj would be lower than .16 if the error on IrnX, ~ .043, vrere increased to include systematic errors. At this stage the rc udc r is likely to ask the follo'Wi.ng que sti ons : 101 o.) If the experiment were to be rcp<Hi.ted with the orur1e 1)()und11ry conditiono, e.g., l1cam time, major equipment, etc., what changes would optimize the experiment? b) With existing accelerators and techniques, how should a high precision measurement of X be made? In answer to (a), the following hindsight remarks are relevant. By spending about six months modifying the apparatus it would have been possible to: (1) lower the triggering rate by reducing the amount of material available for /-conversions in the front end, e.g., by using wider gap chambers and (2) increase the acceptance of the apparatus by moving the production-decay region further into the center of the magnet. Of course, there was considerable pressure to finish the run and six months of further work on the apparatus was an unattainable luxury. The question of further experiments posed by (b) is a less academic question. (l) Such an experiment should: + Use a K- -beam which gives a higher yield of K01 s per 0 incident beam particle, lowering the trigger rate per K produced, (2) 0 Work at high energies where the efficiency for K - detection is greater for a given aperture and electron detection by shower technique is easier, (3) Use vrire chambers to facilitate data analysis, (4) Use hodoscapicgo.c Cerenkov counters so that Cerenkov radiation propcrticc of both n and e are examined, 102 (5) Reduce the amount of material in the decay region to the lowest possible level to cut down on the triggering rate, (6) Collect ~100,000 events at which level the systematic errors will tend to exceed the statistical but with careful design should be surmountable. At the time of writing an experiment to collect 30,000 Ke 's is 3 being run at the CERN PS by a CERN-Orsay-Vienna collaboration. Another Ke 3 experiment, of comparable statistical accuracy, is scheduled to begin in late 1970 at the ANL ZGS, to be performed by a University of Chicago group. many of the features These two experiments incorporate (1) - (6) but are sufficiently different in technique that one would hope them to be sensitive to different systematic errors. When these experiments are analyzed, the para- meter X should be known to < .01 in both ReX and ImX for the Ke 3 case. With the advent of high energy, high intensity neutrino beams at NAL, study of the reactions: v + n ~ 2:+ + µ - (68 = -6Q) will become possible in heavy liquid bubble chambers. energies the cross section of the allowed At high v + n ~ ~ + µ + J..S. expected to be no more than an order of magnitude less than the cross sections of the quasi-elastic reactions v + n ~ p + µ v+p->n+µ + is quite feasible. A high precision 68 = 6Q rule test by this method 103 VI. Appendix 1: APPENDICES Theoretical Supplement The notuthm uocd :in dur;cril>.lng ·t;hc) K 0 :-::() nyutcm Jo U111t - K of Le e un<l Wu(;•/,) who define the :;tates: and l 2 0 K > )( . 2 C1 + lr2i )]""'2" IK[, > = cc 1 + E 2 )I K° > - C1 - E2 )l::-:0 <:. CPT-invariance holds and both 5 and E: vanish if CP-invariance is also true. The most general amplitude for K ~ TI + £ + v consistent with Lorentz invariance and a V-A leptonic current, has the form 2 2 2 where f (q ) and f (q ) are Lorentz scalars depending only on (P-Q) , + P and Q being the K and TI 4-momenta respectively. It can be shown 2 (Ref. 24, p. 342) that the form factor f_(q ) enters with a coefficient (mi/11)() and so, for Ke 3 decay, can be neglected. In general, 2 2 0 f_(q ) can have different SU(3) properties from f (q ) and so K + decay could exhibit different behavior from K~ LS = LQ rule. 0 However, study of Kµ 3 µ3 3 with respect to the with counters and spark chambers is very difficult due to the background K~ ~ TI++ TI- v.ri th either TI .::> decay:i.ng to the normal µv mode . It will be assumed tho.t Ke 3 is being 104 considered and f is written f . + In general, there are four distinct amplitudes, writing the whole amplitude as f, f, the amplitude for Ko -t 1( + e+ + v f, the amplitude for K° -t 1(+ + e + v g, the amplitude for Ko ~ 1( + + e + v g, the amplitude for K° ~1( and one defines X = g/f and X= g/f. + e + + v } 6S + 6.Q }~ = - 6.Q 2 The q -dependence of f and f is 2 known to be small (see for example Ref. 8, p. 232) and possible q dependence of X and X will henceforth be neglected. The discrete synnnetries these amplitudes. C, P and T imply relations between Rewriting in full: 2 <rtevjK > ""'- f(q ).(P+Q)µ. ife I µ(l + 15 )'.l'v e Since there are no strong interactions in the final state rtev, the phase difference between !nev >in and lrtev >out is electromagnetic * g = -g* t" CPI'-invariance implies f = -f, so that irtev >. ~!rtev > so that X = X* . The negative sign in f = -f* comes about as follows ln OU (see, for example, Ref. 24, p. 401): the hadronic part of the amplitude transforms like a 4-vector and does not change sign under CPI', the l e ptonic 1x1.rt changes sign s:incc: 1 (CP'r)- (\f 0 'l' ) CPI'""' -(Y 0. 'i'b) for 0 . = V or A. aib u:i. 1 complex conjugate ente rs since T is a n anti-linear operator. The 105 '11 -J.nvar:luncc alone impJ.:Lco that l', :t', g ond. /!. can 1111 be chooen relatively real: OU t < BIHIA >.in = OU t< n!HIB >.in ' statement of T-invariance = in . < BIHJA >*OUt , since H is Hermitian =out< BIHIA >.*in , since 1~ev >in ~1~ev >out " " an d !Ko >j _n = !Ko >out • Hence, T-invariance implies ImX = IrnX = 0. With CPI'-invariance, ImX the leptonic K-decay. 1 0 implies direct CP violation in Sachs has suggested that such an effect could be the source of the CF-violation seen in ~ ~ 21! decay. If one -writes for€ (see Ref. 25 for details), previously defined for the K_r, and KS states: * r 12 - r 12 E = Er + EM =(r S - r )-2ibm + L i * ~2 - Ml2 (rs - r L) -2ibm then the contribution to Er from leptonic decay modes is: 2 r L (leptonic) i ImX 11-x12 = ImX((l.7 + . 1 ) x 10-3)ei(l32.9o + l.Oo) ,, S l nce E "' 2 x 10 -...) an(·i 'rm 6: if one aosumes IXJ :S 0.2, then one hf!s lOG to look to EM if one wishes to attribute the KT, ~2n CF-violation solely to leptonic sources. EM involves off-mass-shell matrix elements whose values are not restricted by experiment. term is also 90 0 The Er(lept) out of phase with the experimental E • Without assuming CPT for the present, one obtains from the KI,' KS states above, dropping terms of order E2 ,.,,,5 x 10- 6 , !Ko>= (l-E 2 )!K~ > + (l-E 1 )1~ 0 !t;pure K at t=O > = (l-E )e 2 0 reexpressing in K , i(-m +IT /2)t i(-Il\,+IT /2)t s s . !Ks> +(l-E 1 )e L !IS:,> K° states From this the transition amplitudes to decay to nev are: _ + <n e v!t; K0 at t=O > = e + e i(-m +IT /2)t s s (f(l+25) + g(l-2E)) i(-~+ir /2)t L (g(l-25) - f(l-2 E)). 107 Next repla ce f(l+25) + g (l-2 E) by f(l+y) where y :::: 20 + X (l-2 c) . Then since: - 4 Imy Sin (a-b)t one finds + 2 f -r t 2 - r t 2 N (t):::: jfj le S jl+yj + e L jl-yj rL +rs . - 2 + e t [ 2(1-IYI 2 )cos(ms-~)t + 4 Imy Sin(m8 -~)t J A similar expression holds for N-(t) if one extracts g and defines y:::: 25 + (l-2E) . (f/g). · Reinserting for y, we get N+;::: jfi 2 { e -rs t jl+25 + X(l-2E)j 2 + e -r Lt jl-25 - X(l-2E)j 2 rs +rL + e- 2 2 t [ 2(1-j20 + X(l-2E)j ) + 4 Im(25 + X(l-2E )) cos(ms-~)t Sin(ms-~)t J } } . lOIJ N = !'fl 2 { e -r 8 t I (1+25) X + (l-2€)1 2 + e -r t L I (1-25) X - (l-2E)! 2· r s+r L.._ v 2 + e [2( 1x1 2 - 120x + (l-2€)1 2 )cos(ms-~)t x* (X25 + (l-2E))Sin(ms-~)t] } + 4 Im If CPI' is assumed for both decay and state so that \'fl = lfl, -"* X = X and 5 = o, these expressions become, -writing 6m = ~ - r11\:S , r = 1 - 2€. N+ = If\ -r t 2 { -r t 2 2 e S ll+Xrl + e L 11-Xr\ rL+r s - 2 t N- = \fl 2 + e 2 } [2(1-IXrl ) cos 6mt - 4 ImXr Sin 6mt] -r t S {e -r t * 2 \x + ri + e L IX* - r\ 2 r L+rs + e - 2 t [ 2( \ X ! 2 -Ir\ 2) cos 6mt - 4 ImXr Sin 6mt] . For t >> l/r S , one obtains . 2 N+ I 1-Xrl N- = 'J(· IX -rl 2 } • . . = l + 4. Re €. 1-IXI 2 11-x12 This quantity has been measured :i.n the KL charge asymmetry experiment s. ( 2 G),( 27 ),( 2e) (1 - r) "' 4 x 10- 3 Since thcGc experiments show tho.t its effect on the time distributions at early 109 times cannot be seen until the coefficients of the tirne-dep1..::mlent terms arc measured to 0.5°/o, well below present day Genr_; Ltivity, whJch :j :; a.n order of' rnn.gn i tucle wor: :c. If r io uc: L to unity, the ·L:Lme distributions become: = lfJ 2 { e -r 8 t Jl+XJ 2 + e -r t L 11-XI 2 -(r s+r L) 2 + 2 e t 2 • (1-IXJ ) • cos 6mt -(r s+r L) - 4 e 2 t ImX • Sin 6mt} In the final fitting of the data from this experiment to the para+ meter X, the above form of N- was used. A more precise experiment could extract X, € and 5 from the leptonic time distributions. 110 Appendix 2: Pion Beam 0 The particle beam used to make K 'c in the a pparatus was an 0 unseparated ~-beam produced 8t o to the internal circulating beam of the Bevatron. spread of ~1%. The nominal beam momentum was 2.85 GeV/c with a nominal The beam was designed to have its first focus between the bending magnets Ml and M2 as shown in Fig.30 with a second focus at the apparatus between the two targets. QlA, QlB, Q2A, Q2B are the usual quadrupole doublets required for each focus, Ml and M2 achieve the overall 17° of bending and Q4 compensates the fringe field of the Beva tron. The beam counters were 81, 82, 83, 84, and 84V. 81 and 82 were 3" x l~" scintillators used for beam tuning; 83 was a 3" x 3" one-quarter inch thick scintillator; 84 was a 0.8" diameter i-" scintillator; and 84V had a hole 0.9" in diameter and was 0.4" thick. All these counters had RCA 7850 phototubes whose last few dynodes were boosted by a condenser bank to handle the high rates. which analyzed their signals is shown in Fig. 31. The fast logic The transistorised fast logic modules used in all fast logic are described in Appendix ?. The useful beam intensity was 3 x 10 steered onto the internal target. 5 per 10 12 protons This intensity was at a level that gave one extra beam track in the production-decay chambers for about 50"/o of the pictures. ning Any increase in intensity would have made scan- these pictures more d1.fficul t. Of vital interest to the Ke 3 experiment is the K contam i - nation in the beam since a K-minus can charge-exchange to K° and give 111 S4 S 40M5 _yf:J I. S3 {/JQ3 Fig. 30 Sketch of n- beamline 112 I _r· 11 ~· "l 1.-'.l L-j !.-\ g 1_1•, i14V 'l'VD -4 Bewn Gate TC- 6 BefON ..JJ:i]j6B 5 c c TC-6 From target r 1ick I (Cl. VJ + v C;> . n)· EM) TC6 Sl.52 s caler &S - 1 d~ad!.1.rne DTG Sevat:- on c.:::int ro l r ooo ..___-_3_o_o_n_s_.~ gene rator S3. S4 scaler S3 S4 Reset scale r Beam dee.dtir::ie generator EM( =S3. S4.54v") BS-1 fast r eadir. ve to scaler -._____ EFF~ r eset s caler To SCEFf3'1 L-3 & PDPEFFEM citts . { Appen.:iir. 7 has a glossary or rast logic modul es. _]-e~~al_e after 3/ 23/68 EFr"l'M ac11ler To Cl ,C ' Eff!J~ on tnrge t r ack ff-15 ocale r' f_g.f5 fh nout. Fig. 31 Block diagram of beam electronics 113 an JnJ t:J nl utntc.: of oppoo :Ltc r;l~rnngcncso J'rorn o K 0 SFr; Ccrenlwv counter \Vl:Hl placed ht the beum. • I\ Lc!n atrnoopricrc By anu:J y'l. I np; the Cerenkov pulse in coincidence with a time of flight system the K contamination of the beam was measured to be (0.1 : 0.01)%. 114 Appendix 3 : Tare>et s and Turr'. et Count ers As mentioned in the_) text, it was de cided at the outset to (! maximize the production of K ' s by u s ing dense targets and to for ego the advantages of hydrogen production kinematics. The usual technique of a coincidence counter before the target and a veto counter behind it was employed to select neutrals in the forward direction. In order to fit the leptonic decay distributions to X using the functions N+ and N , it is necessary to know where t the data used in the fit. = 0 is for A systematic error of 0.4 ems along the 0 beam in the average K production point changes ReX by .01, whereas ImX is not sensitive to this. X is relatively insensitive to the higher moments of the production point distribution. of 3.0 ems was chosen. A target length This was short enough so that the average 0 K -production point could be determined accurately enough and decays could be seen well within the first K lifetime (12 ems). 8 This target length is a reasonable fraction of an interaction length for the denser metals. It remained to decide on the material, the transverse dimensions, and the number of targets. Considerations involved are: 0 (1) Total K -production for a given incident pion flux. (2) Net acceptance through the apparatus of Ke 3's from the s e o, K s. o Different materials may produce K 's with differe nt momentum and angular distributions. (3) Trigger rate given that (1) and (2) are satisfactory. (4) Multiple scatteri ng and attenuation of the beam as it 115 pnc:..:ct; (5) through t}1c turp;etc, caur: l ng .Lt to rn:!L: t: lu t.er tar1J,t:tr1. Shadowing effect o:[' a target on decays occurrl.ng upctream from it. (6) This increases with transverse size of the target. It was desirable to use the same material in all targets 0 so that the K production physics would be the same. From runs with polyethylene, aluminum, brass and tungsten it was found that the number of neutral decays (vees) on the film per incident pion behaved as shown in Fig. 32. factor in the choice of material. So (1) was not a strong It vras found that tungsten caused almost no beam to reach subsequent targets due to multiple scattering. With the same geometry, aluminum gave a higher Ke 3 triggering rate than brass because it converted fevrer of the r's produced in it. These converted elsewhere in the apparatus, triggering the gas Cerenkov counter. The final target configuration, previously shown in Fig. 4, vras t-wo brass targets 1.2" (3.0 ems) long, the first one 1.26" in diameter with its center 72" from the magnet center, and the second one 0.75" in diameter, 48" from the magnet center. An added feature was a disk of lead 0.2 11 (1 radiation length) thick between each target and its veto counter to help reduce the Ke 3 triggering rate by converting r's produced in the brass. The counters c , 1 c2 , v1 , and v2 were all coupled by air lightpipes to a 1.0 11 diameter lucite rod lightpipe which led to RCA 7850 phototubes placed outside the magnetic field reg ion. Air lightpipes were used to reduce the material in the decay region. The phototubes had their last few dynodeo connected to 116 ] I TT - Tr TRIGGERS ~ ~ 16- i 12 I t T UNGSTEN ~ BRASS ~ 1 v <f) 0 "-... 8 w ~ 0:: Q 0·~~~--1~~~~._~~~-"-~~~--~~~-- o 2 3 4 p/Al/ 3 (g/cm3) Fig. 32 Number of vees on film and nn trigger rate for different targ~t materials 5 117 a conde ns e r bank to handle the high counting rate s. had efficiencies > 9go/o. These counte rs The counters were centered on the targets by pins which were placed in holes drilled halfway into the counters. The upstream target was suspended from an adjustable mounting bracket, whereas, to cut down on material in the decay region, the second target was actually supported by the air lightpipes. These were folded from 0.01" mylar and so had good mechanical rigidity . A block diagram of the fast logic analyzing the signals from c , 1 c2 , v1 , and v2 is shown in Fig. 33. Note that the signal from v is split; one half goes to a TVD-4 set at a 1 whose output vetoes c • 2 bias > I . min This prevented interactions in the first target from giving spurious triggers in the second target. 118 Cl @~ TVD-4 8. BS-1 V2 C2 C2 (BS-1 gate) BS-1 l ( BS -1 gate) TC-6 BS-1 V2 EFFJM EFF™ L-3 scaler scaler I!i~5 E.'15 TC-6 Appendix 7 has a glossary of fast logic modules. Tl T2 scaler scaler ® BS-1 TARG scaler All reset cables in TVD-4's are 20 ns. All veto extenders in TVD-4's are 14ns . TARG . Fi g . 33 Block di.agram of target electronics 119 Appendix 4: Spark Chambe rs There were three di s tinct sets of Gpark chambers in the appa ratuc wh i ch will be now r;epurately deG crtbcd. Production-decay Chambers The production and decay of K01 s was viewed by seven spark chamber modules. i- 11 gaps. Each module was 18 11 x 8 11 x 4 11 and had 11 active The first target was between the first and second modules, and the second target was between the fifth and sixth. Each plate had a total of .0015 11 aluminum and was stretched over a window frame shaped brass rod which was filled out in the middle by crinkled • 0015 Al foil. 11 Each module presented 0.01 radiation lengths of material to particles passing normal to the plates. The plates could slide in and out of the lucite box which formed the shell of the module, so that defective plates could be removed by simply opening up the module and replacing a plate. The whole assembly of chambers, high voltage condenser banks, targets, target counters, as well as S4 and S4V were mounted on a cart which ran on rails 8 1 above. This cart could be rolled in and out of the magnet with ease and allowed convenient access to the components on it as well as clearing the way to work on the apparatus inside the magnet. The gas mixture used in these chambers (also in the momentum and s hower chambers) was commercial 90/10 Ne-He mixture which was purified and recirculated. Each chamber was driven with 3.9µf. of capacitance charged to 9 Kv. and pulsed by spark gap in parallel v.-i t h a s horting gap to provide un i formity of spark intensity. The delay J;>o time ut which the chnrnber eff'j cicncy droppcli to 50°/o wnc rneac1u·cd to be 600ns. at the operating clearing field of 60V. The efficiency during operation for two tracks was 9~, but with competition from extra heavily ionizing tracks it deteriorated. The tracks on the film were located in space using two kinds of fiducials: full fiducials and transfer fiducials. The full fiducials were a carefully surveyed set of aluminum strips with notches cut every 4 11 and were lit from behind by luminescent panels. Since these large area panels could not be pulsed at the rate at which pictures were taken, there was also a set of transfer fiducials consisting of smaller panels which could be rapidly pulsed and so photographed on every frame. The transfer fiducials were measured whenever a frame was measured and then the reconstruction program could refer them to the surveyed full fiducials using measurements made when both sets were lit. The full fiducials were securely attached to the magnet whereas the transfer fiducials were mounted on the mobile cart. Because the chambers had only 9" vertical clearance do;,.m to the coil cover of the magnet, it was necessary to split the plan view of the chambers with a V-shaped mirror and combine these two halves at a later stage in the optics. This realistic film format made it easier to scan the decay region for neutral vees. It was felt that high visibility of low intensity sparks would aid in scanning, so an f-2.5 lens was used in the camera which viewed these chambers. The camera was a 35nnn. Flight Research model 207 which 121 coulu pulnc 1:5 tJmes/oec. gJv:i.n1.r, o. dco.dt:i.rnc of "/Orne •• '11hc d1ambcrc were r'Cmovcd nt the end ol' tl1cJ da Lr:J.-tnJ~ :! n1.~ nnu a large 1.llrnninutcd lucJtc chcet, with 0. /," x cur'tes.!mi e;r.·Jci etched on it, was inserted and photographed through the optics in both views at many distances from the camera. of optic axes could be found accurately. In this way, locations Significant distortions were discovered and carefully mapped out by this grid photography. A correction scheme was devised in the decay region reconstruction program and, using this, the position accuracy determined from straight through tracks was ~ 0.08", ~ 0.11" for transverse position Y and Z respectively, and ~ 0.01 radians for angular measurements, which is fairly typical spatial resolution for optical spark chambers. Momentum Chambers These chambers were placed in the region of highest field of the M-5 magnet and provided most of the information used for the measurement of the decay secondary momenta. There were four chambers in all: a front chamber, FM, was 8" x 24" with six-~" gaps and was placed between the S5 counter and the entrance window of the gas counter; the middle chamber, :MM, was at the center of the magnet , immediately behind the MH, and was 60" x 18" with four 3/8" gaps and, finally, at the back of the magnet were placed the rear chambers, RMN and RMS, each 36" x 60" with six 3/8" gaps. The chambers were constructed vlth plates which consisted of an aluminum-styrofoamaluminum sandwich, the aluminum being 0.0005 11 foil and the s tyrofoam 1/8 " thick. Such plates are easy to handle and ·were set into lucite 122 i'ramco without hnvine; to otrctd1 and ma i ntn:!.n tuut lurp;r: are no oJ' alum:Lnum foll. 2 . J :acl1 plo.tc pn~11cnted . 007 gmo I cm to .1nc:l c.lcnt }l1.1.rt.Lc.lcn, 1 so the full set of momentum chambers presented .6<{o 01' u radiation length to particles normal to the plates. The FM chamber was pulsed from 3.9µf . charged to 9 Kv., MM from 2 x 3.9µf. at 12 Kv., and the two RM chambers were each pulsed from 3 x 3.9µf. at 12 Kv •• The gas mixture was the usual 90-10 Ne-He. The fiducials were similar to those of the production-decay chambers, with transfer and full fiducials on all chambers. Each chamber was looked at in the plan and elevation views by optics of high Quality bolted securely to the magnet. The Flight Research model 207 camera was also bolted to the magnet. There were considerable variations in spark intensity for different views on the film and it was felt that making all views eQually bright would make it easier to measure the film. A plate of grey filters was mounted about 10' from the camera to give the desired uniformity of intensity on the film. The transverse position measurements were °:!:° 0.03" in the FM and RM chambers, °:!:° 0.06" 0 in the MM chambers, but the angular measurements were poor ~ ~ 1 , due to the short track lengths and the staggering of successive sparks by the crossed magnetic and electric fields. However, the chambers were primarily used to measure the sagitta of the orbits and the momentum resolution obtained was 6.p/p ~5%. Shower Chambers The sho-wer chambers were used to study the interaction o l' the decay secondaries in three radiation lengths of lead and con- ')'.-: l <-0 sisted of six modules, three on each side of the center line. li1cy were located with the normal to the plates at 16° to the center line so that, on the average, the decay secondaries would be at normal incidence. Each module was 4 1 x 6' and contained nine plates each formed of an Al-Pb-Al sandwich. There were six active gaps in each module, so a non-interacting track would give 18 sparks in traversing the array. The plates had .02" of Al on either side of .02" Pb, the sandwich being glued together with epoxy and pressed in a very large area hydraulic press to ensure flatness. The modules were mounted on a mobile cart which could be moved to provide access to the apparatus at the rear of the magnet. The gas mixture was 90-10 Ne-He and each module was pulsed from a 4 x 3.9µf. condenser bank charged to 12 Kv •• As with the other full fiducials and the chambers, there were carefully surveyed usual supplementary transfer fiducials pulsed for every frame. chambers were viewed in the plan and elevation views. The The optics were not as good as for the other chambers since there were many large area mirrors mounted on a scaffold constructed from steel tubing which was not entirely rigid. model 207. The camera was again a Flight Research The position measurements had resolutions + 0.2" and angles were measured to ~ 0.02 radians. As mentioned in Chapter III, these measurements were of small weight once the momentum chambers were included in the fitting, but did serve as a starting point. The identifying power of the chambers for ~'s and e's will also be discussed in that chapter. 124 Appendix 5: Freon Ce renkov Counter A 1 atm. Freon 12 <;erenkov counter was used for electron detection. At 1 atmosphere nF re on 12 = 1.00105 which g:lves a Cerenkov threshold velocity of ~ = l/n = .99895 corresponding to y = 21.9. This gives thre shold momenta of pe = 11.1 MeV/c, pµ = 2.29 GeV/c, and p 1{ = 3.02 GeV/c . With an incident beam momentum of 2. 85 GeV/c only electrons will directly count in the counter; any othe r particles triggering it through electron generation. For E e >> me , Q~ = 2(n-l) = .0021, so QC ~ .05 ~ 3° The gas was contained in an aluminum box 18 11 x 35" x 60". The front and back panels, which had openings, were 3/4" Al and the other sides were all t" AL The entrance and exit windows consisted of black mylar 0.02" thick. A sketch is shovm in Fig. 34. The mirrors on which the Cerenkov light was first incident were 1/811 thick lucite spherical mirrors attached to adjustable mounts which could be manipulated from outside without opening the counter. The light then bounced back into one of the two lightpipes and ultimately into the phototubes. soaked in fibreglass. The lightpipes were constructed from a synthetic fibre epoxy and cast into shape, the end result being like The sections just before the phototube were parabolic in shape with a focus at the phototube. The parameters of the parabola were optimized using a light ray tracing computer program and a cast of this s ha:pc wac made by spinning a rough approximntion to the c h o.pc o.t n certr.i.ln r,pi;cd o.n<l pourinr:~ epoxy on :Lt. CJ.'h c. eiio:xy then hn:rck n ed to o. parabola whose parr:unetcrc depended on the ve locity of rotation. '' f' ''i 125 l ' ' ! ' ' ! ! ' ! . { . ; ~ f I : PHOTOTUBES TOP VIEW .~ .'. ' : :'. . ' . f . I I . l ' 't f SIDE VIEW LIGHT PIPE ATTACHMENT WINDOWS I I l FRONT ! l VIEW PARTICLE ENTRANCE WINDOW Fig. 34 Sketch of gas Cerenkov counter 126 The phototubes used were RCA 05 75 which had a measured photocnthode efficiency of 21l°/o. There we r.e three phototubes on each side. Tr1cy were in a region of relative Ly high field and were shielded with ), " thick soft steel tubing. The counter was bolted to a set of rails attached to the coil cover of the magnet. The counter was originally tested with 1.0 GeV electrons at the Caltech synchrotron. The counter was not in a magnetic field and so the results of such tests are not obviously comparable to the conditions in the experiment. The best yield obtained in the electron beam -was a distribution ~mich corresponded to a Poisson with m = 9. If one assumes no other broadening, this gives nine photoelectrons from the RCA 8575 phototubes. for the final Ke 3 The actual distribution from the counter data is shown in Fig. 16, Chapter III. To get the narrowest distribution when summing phototubes the gains must be equalized. To do this with the six phototubes of the gas counter , it was necessary to have some well defined reference signal. For this reason, the phototubes had small pieces of plastic scintillator glued on the side of their photocathodes, with a Cs source attached. 137 The gains were equalized at Caltech by moving the counter relative to the electron beam so that all the Cerenkov light t .i shone on one phototube at a time. The gains were adjusted to get 't ! ! the same mean pulse height from each tube, and then the ratios of the signals from the sources were noted. Thus, while running at Berkeley, the gainn could be equalized liy e;ett ing the s ignalc from the sources into that ratio. For example, when the magnetic field polarity of 127 the M-5 magnet wno chnngecl, trn: gains of t}w phototulJcu ch£.rnr:;ccl slightly uncl the source s ignulr; were uoed to bring the a :lx phototubes back to equal gains. The electronic circuitry that analyzed the phototube signals is shown in Fig. 35 . As can be seen, the three signals on each side were first added and then fast amplified (MIX-1 and FA-1) . They ¥rere then separately pulse height analyzed and also the sum pulse height analyzed. After another stage of fast amplification, the signals went to a TVD-4 discriminator set at a very low bias and if either of these triggered in coincidence with the beam a signal GC was generated and sent to the final logic rack. The distributions of pulse heights for the separate sides and the sum were stored in the PDP-8 computer while running. It could be inspected on a CRT display and provided a good check that the counter -was operating normally. 128 Nl N2 N1 GCN Spha. G Q B S - 1 < l - - - - -... i....-----~.- BS-1 - BM5 Appendix 7 ha.a a glossary of fast logic modules. GC to final logic rack ·Fig. 35 Block diagram of gas Cerenkov counter electronics l29 Appendix 6: Hodoscopes and Shower Counters Multiples Hodoscope The multiples hodoscope, MH, was a set of fifteen horizontal 60" x l" x 3/8" scintillators made from Pilot Y which has good attenuation characteristics. The hodoscope was placed perpendicular to the beam 8.7" downstream from the magnet center. Each counter had a 6655A phototube which was mounted in a gap between two sections of the magnet yoke where the field was relatively low and heavy shielding ~~s not necessary. The pulse height distribution, from the end of a counter away from the phototube, was a Poisson for which the mean, m, was greater than 20 and rose to 60 at the end near the phototube. This meant that the counters could be operated with an effi- ciency > 99.sa/o from all parts of the counter. A check of the uniformity of response of the counters comes from the profile of accepted events at the MH, in which no bias along the counters can be seen. A block diagram of the MH electronics is shown in Fig. 36. There are three basic signals: MHGl 1 counter triggered. MHG2 2 counters triggered. MHAC Adjacent counters triggered. The signal Mlf = MHG1.M11G2. BM5 was used in the general VEEM trigger 0 0 . t b c J.ng . . th c PPG· t·rige;er • an d a J.so in ·ror th c K -> re +re - re c:xpcr:nncn rim i n -para llel. For the K03 (PIE) trigger, the signo.l u;..;ed was 130 15 counters MH15 I I I I ·1 I I I I I I I I 15 TVD-4'e BS-1 ,eame for all 15 counters Multi-c o incidence ckt. OUT" (N + l).N MIX-1 MHAC <D--....l BS-1 MIX-1 TM-5 TVD-4 >l TVD-4 MHGl >2 ....__._. MHG2 BS-1 BS-1 ,......---i:os.'15 f i c c lI l l' TM-5 Mli* t To final logic rack I for VEEM & PPG I t c v I TC-6 Appendix 7 has a glossary of far.t logic modules. MH {vithout adj. counter) MH BS-1 to final logic rack for Ke3 trigger MH scaler I I I ! Il Fig. 36 Block dio.gru.m of MH electronics I ! ! t i I ~ MH == MHGLM1IG~! .M!Ii\C. BM5, the Mll/\C c1e;na.l licJn1.'.: ~cricrntcd by n mu.IL:L- channel coincidence c1rcuit -whJch gave an output when nd,jaccnt counters fired. Rear Hodoscope The rear hodoscope, RH, consisted of two sections each having sixteen 42" x 4" x i-" Pilot Y scintillators arranged vertically, with phototubes at the bottom. Each side had its normal at 16° to the center line and was mounted, together with its phototube shielding, on the mobile cart which also supported the shower chambers and shovrer counters. The apex where the two sides met was 84. 4" dovmstream from the magnet center. A block diagram of the electronic circuitry which analyzed the RH signals is shown in Fig. 37. basic signal, RH, is formed thus: As in the MH case, the RH= RHG1.RHG2.BM5. there is no restriction on adjacent RH counters firing. In this case Each RH counter had above it a light, visible in the shower chamber optics, with the counter number on it. This light flashed on when a picture was taken, if that counter had triggered, and was very useful in picking out the triggering tracks when scanning the shower chamber film. Shower Counters The shower counters immediately behind the cho>rer chambers, consisted of fourteen modules, organized in two seven-module sections, one on each side of the center line with their normals at 16° to the center line. Each module had two scintillator slabs, one wJth its lightpipe on top, the other with lightpipe on bottom and with 0.4" 132 TVD-4 South 32 oountero North TVD-4 32 TVD-4'a TVD-4 TVD-4 RHl BS-.<i------' (one ror each r-_.__ _ _ _...___ _ _~----.L.--. RH) 8 MIX-l's MIX-1 MIX-1 MIX-1 TM-5 TVD-4 TVD-4 >2 >l ~ ~BS-1 BS-1 .----.-BN5 BS-1 G C§i) Appendix 7 has a glossary of fast TM-5 logic modules. RH scaler BS-1 g To final logic TVD-4 Fig. 37 Block diagram of RH electronics 133 lcnJ betVJcen the cc:intillotorr;. Ne .1 02 (;c.JntJ.lJ11l;orr; VJ.ith acr:embly cornpnc:t. The olobu were S~.:" x Io" x :'i/11 11 Lle;lll;pipcu r.ittuc:l1ed nt :JO 0 i.<.1 J\ccp U1c 'rhc lightp I puo were pluc:cd o.t oppo~;.i te endn to average over the attenuation of signals along the counter. The 0.4" of lead VJas glued between f.-11 layers of styrofoam backed with aluminum sheeting and the whole assembly, scintillators and lead, was bolted to a frame and mounted on the mobile cart. The electronic circuitry which interfaced these counters is shown in Fig. 38. Since each module was separately pulse height analyzed it was necessary to match the gains of the fourteen modules. Minimum ionizing particles gave a very noticeable peak (see Fig. 6 , Chapter III) in the pulse height spectrum and the high voltage on the 6655A phototubes was adjusted to place these peaks in the same channel for all modules. The pulse height spectrum could be displayed from the PDP-8 while running and this also provided a check on the stability of the counter gains. 134 ~ ;S I F SSIH ••• . • SllllTll ( 7 unit" totnl) Sl'HA Sl'<lA ~ ~ As on ~Orth HIX-1 MIX-1 SPi\A < >---- ~ llLl'S-lC TV0-4 SH."1 < 1-------..J BS-1 Appendix 7 has a MIX -1 glossary of fast logic modules . BS -1 ..i:il- - - ' ~ Fig. 38 ..__-!'.:_. To Sii TVD-4 in final lo g ic r a ck Block diagram of SH electronics Appendix 7: Fn:;t Electronic:; and Trigger Logic. The fast electronics used standard modules built o.t Caltech which have been described in detail in CTSL Internal Report No. ?il. A brief glossary of these circuits will help in understanding the electronics block diagrams: FA-1 Fast amplifier; DC coupled, gain 10, - input, - output, risetime 2.3 ns •• TVD-4 Fast discriminator, DC coupled, input -.05 to -lV, output rise and fall time 2 ns., output length(? ns. + reset cable length). L-3 Limiter, DC coupled, shapes pulses for use in TC-6, risetime 2 ns .• ™-5 DC coupled fast multiplexer for digital signals. TC-6 4-channel coincidence or anticoincidence circuit, resolving time 2 ns .• GM-1 Gated mixer, can also be used as a flip-flop. IN-1 Inverter. MIX-1 Mixer. DLPS-lC Delay line pulse shaper. DI'G-1 Deadtime generator. The fast logic was organized into seven racks: Beam, GC, RH, MH, SH, and Target. Trigger, All except the final trigger rack have already been described in Appendices 2, 3, 5, and 6. diagram of the trigge r rack l.s given in Fig. 39. A block The signals TAHG, 136 'l'ARG QC MH(rulJ. veto) 1111 UH N . S ( f r om Hll ruck) 35' r o oet 14' clip ~t;, ,.~ To V!:lli 'l'M-5 TM-5 'l'M-5 SH Ml! cc TARO TARC MH RH TAHC MH RH CC \; c c c c TAHC scaler N.S RH SH MH" RH Ap pendix 7 has a glossary of fast TC- 6 TC-6 r<§) TC-6 logic modules. sclr· '-~~~~~---' ~ BS- 1 C§"0 BS- ™-5 'i'M-5 VEE scaler VEE _ r+h ~ ELVEE c TC-6 ~ BS-1 ~ BS-1 TM-5 TM-5 TM-5 PIPR PIE PPG TM-5 scaler PDPTAPE To spark chamber trigger Fig. 39 Block diagram of trigger electronics PDPNO-TA.PE l37 GC' MJI, rm, unu : :rr wcrr ~ nJ l ulH.>llL 1.0 no • .IOTl/J, Vlllt~n tl1cy llrr .l vcd 11 I; the trigger rncl~. J\cc..:Jucr1 Lll ~ I r11Lco Jn tbc~ .Log.I c V1erc 11• .~tJ:.l.:le; 11>.Lc sir.ce the beam -was nl-ways < 500K per sec. and was usually -without excessively spiked RF structure. Table· 8 has a list of all fast logic signals. The normal "DATA" run trigger was (PIE +PPG), normal "CALIBRATION" run trigger was VEE before 2/2/68, VE.EM after 2/2/68. The TAPE trigger vms always VEE before 2/2/68, always VE.EM after 2/2/68. TABLE 8. FAST LOGIC SIGNALS "* Indicates that the signal was scaled and logged. ( *81.82 } used for beam tuning and as a control room monitor 83.84 BM = 83.S4.84V BEAM BEAMDT 300ns. generated by (c1.v1 + c2.v2 ) *EFFBM = BM.BEAMDI' *BM5 = EFFBM.85 *C BM 1 = c1 .EFFBM = c 2 .EFFBM *C!M *Tl TARGET *T2 MH \ RH . = c1 .v1 .BM5 = c2 •V2 .BM5 TARG = Tl + T2 *GC = GCN + GCS MHGl = >l counter from MH MHG2 = > 2 counters from MH MHAC = Adjacent MH counters fired *MH = MHG1.MHG2.MHAC.BM5 MH·* = MHGl.MHG2. BM5 (also called MHW08) RHN = signal in RH 1-16 RHS = signal in RH 17-32 RHGl = > 1 counter :Ln RII RHG2 = > 2 counter::; in RH *RH = RHGl. Hl-fGc). BM5 -- (continued) 139 '1.'J\JlL1': 11. l -x-m; = rurn .Hus SHN = sum of North above TVD-4 threshold SHS = sum of South above TVD-4 threshold *SH (SHN + SHS) .BM5 *VEEM = TARG.MH*.RH *PPG = VEEM.SH.NS.Ge *VEE ::::; TARG.MH.RH PIPR = VEE.Ge *PIE = VEE.Ge SH TRIGGER Ff\L;T LOGIC SIGN/\r.~; ( Cont :lnucd) *PDPEFFBEAM = EFFBM. (PDP deadtime) *S.e.EFFBEAM = EFFBM.(spark chamber deadtime) J\ppcndix 0 : Sl•)W Electronic:; uncl Computer. An important part of the electronics was the l.nterfacc between the fast logic and the PDP-8 computer. The fast logic pulses were ~10 ns. long, whereas the PDP-8 was a relatively slow computer with a 4K memory and a l.5µs. memory cycle time. The digital infor- mation was read from the fast logic racks into BS-1 Buffer Storage circuits. The analog counter pulses were pulse height analyzed by 64-channel Slow Pulse Height Analyzers called SPHA's. These circuits were all clamped while the spark chambers were firing. When the electrical noise had died down, the BS-1 and SPHA information was read into the PDP-8 accumulator by a read control circuit. The resident PDP-8 program, EXPO, was then interrupted at whatever task it was engaged in and began storing the fresh data in its memory. When several events had been accumulated, they were written out on magnetic tape on a DATAMEC D2020 tape unit. The tape I/O was double- buffered so that it gave a negligible contribution to the overall deadtime. The EXPO program could histogram any data the experimenter called for through the teletype and display the result on a CRT. This program has been described in detail in DECUS No. 8-161. Besides being stored on tape, some of the BS-1 information was put directly on film so that it would be available while scanning. This was done by having the BS-1 information activate relay switches in series with data lights visible to the cameras. These do.ta light s were lurninc::::;cent panels ;,imilar to thos e uc c cl for the transfer fiducio.ls. The c:lrcu :Ltry for these lights, which involved 11l muny poorly :;IL i~.l.ded c;ulilc:.; around the opurk charn1Jcr::, 1-11w c.l.ec.:Lr.1 cu.U~y isolated from the BS-1 and f:.i.st electronics Ly c.:oupling the two with miniature bulbs shining on LASCH's. The film advance for the three cameras was governed by a camera control circuit which controlled camera deadtimes, etc., and prevented the spark chambers from triggering unless the cameras were ready. In between machine pulses this circuit triggered a loop generator on the cameras whtch pulled out a loop of ten frames so the delicate camera mechanism did not have to pull film directly off the 1200' roll in the magazine. t ! t .t ! Appendix 9: Dntn -tal\ Lng l'rocl'Jurcs nnd ClK!c.:lrn. The usual spark chamber trigger -was (PIE + PPG) ancl the tape trigger, at the beginning of the 4-month run, was VEE, later changed to the more general VEEM. After about 12 hours of data taking with this trigger a short calibration run was taken, triggering the spark chambers as well as the tape on VEEM which gave many K 4 8 events needed for the Monte Carlo efficiency calculations. 2~ While running, a continuous run-by-run log was kept of all rates that were scaled (normalized to the total number of beam particles). Any dis- crepancies in these rates were investigated and the trouble cured before resumption of data-taking. The BS-1 and SPHA information was being logged by the PDP-8 and could be displayed on the CRT. The appearance of these histograms was a good indication of how the counters were working and one could find out very quickly if a counter were maladjusted or totally turned off. The apparatus was visually checked at least every eight hours while running. Spark chamber performance, fiducial and logic lights, and camera operation were all checked. The developed film was also spot-checked for spark-chamber efficiency, burnt out data lights, etc •• The field polarity of the M-5 magnet was reversed every few days, amounting to twenty-five times during the data-taking run. A record was kept so that the total amount of data at each polarity was equal. was monitored to O.l'fo. The magnet current Appcnclix 10: ~konnj_ng l'roced11 reG. Tape Scan The analysis of a tape record is demonstrated in Fig. 40 with the aid of a sample event. and 22. The RH counters triggered ~rere 12 The pulse height in each of the fourteen shower modules is given above the module. The first step is to search for an "electron" -- an adjacent pair of modules with pulse height > 14 (1. 7 . ) • min Pairs 4-5, 5-6, and 6-7 are looked in behind RH 12, and 9-10, 10-11, and 11-12 are looked in behind RH 22. 4-5, 5-6, 6-7, 9-10, and 10-11. An "electron" is found in Next, the "pion" search looks for individual modules with pulse height between 4 and 21 (0.5 - 2.6 I . ) min and< 5 (0.6 I . ) in the modules on either side. min is unsuccessful in 4, 5-, and 6 behind RH 12. The "pion" search It is similarly un- successful in 9 and 11, but finds one in 10 behind RH 22. So, the event is accepted with an "electron" behind RH 12 and a pion behind RH 22. It was stated in ·the text that there was no evidence for any decay-length dependent biases in the tape scan and this will now be demonstrated. Fig.' s 41 and 42 show histograms of electron and pion pulse height for four intervals of decay position (first target only) from the final data: 35" - 45". 5" - 15", 15" - 25", 25" - ~-S5", and The mean pulse height in each of these intervals le 46 .0, 48.3, 50.6, 50.3 for electrons, and 17.1, lB.l, 19.5, 19.1 for pions. Since the var:LutLons j_n the average are well within the vidth of the distribution J'or each caoc, 1 t; is conclw.led tha.t there 144 Computer scan analysis of S.N. 910742, event accepted with electron behind RH 12 and pion behinJ RH 22. 0 . ·· - -=---~ -i 7 r-S HOV\/ER -7 __ 6 . -- -.. _ o . MODULES - . s -......z..... 0 20 ·. . 4 ~ 3 - ·- · ~ - 0 . . 0 . . 2 - .. l REAR HODOSCOPE Search behind RH 22 "Electron" search "Pion" search { 9-10 OK 16 lO-ll OK 16 _ 11 12 NO 0 {l~ NO Search behind RH 12 "Electron" search "Pion" in 9 and 11 search NO 6-7 OK 20 5 NO, 20 in RH6 "Electron" · behind RH12 behind RH 22 Fig. 40 0 6 NO, 17 in RH5 0 "Electron" and "pion" 5-6 OK 37 4 NO 0 OK 16, 0 11 {4-5 OK 17 Computer scan analysis of a K e3 . trigger 35 11 < XOEC < 45 11 1 302 EVE NTS MEA N PULSE HEIGHT 50.3 20 0 25 11 < XcEC < 35 11 1 374 EVENTS MEAN PULSE HEIGHT 50.6 (f) 1- 20 z w > w --l1i> +15 LI.. 0 0 15 11 < Xo::::c < 25 11 , 254 EVENTS MEAN PULSE HEIGHT 48.3 20 ~ +10 0 20~ 11 11 5 < X DEC < 15 ' 151 EVENTS MEAN PULSE HEIGHT 46.0 ~ +3 0 20 40 60 80 ELECTRON PULSE HEIGHT Fig. 41 Ele ctron pulse height in shower counters for four segments of decay region 100 146 ..,, ,... QI .:;;~ 20 V Ll ,,.. II < P\ 02:C < '"}0 MEAN PULSE HEIGHT 19. 1 -"'> +34 0 i....;;.;ii-A...~~---~~~~-F-~~~---'-c.,._;;;;io....i-=;;.;;_;;;;;;;..,..~~ 2,,,...~, < 20 flru (/) I- z :) 0 u O xO::::.C , . . < ~5 7 MEAN 11 PULSE HEIGHT 19.5 -Cr> +45 0 LL 0 0:: w 00 I 5 ll < x DEC < 25 OI 20 MEAN PULSE HE~GHT 18.1 d2 '.:) :z -{;> +24 0 v <l""u S u< "DEC ::> 20 MEAN PULSE HEiGHT 17. I --0-- +13 10 20 30 PION PULSE Fig. 42 HEIGHT Pion pulse height in shower counters for four segments of decay re g ion .. ~· - ·---·- ·· -·- ... .... 40 147 ir; no evhicncc J.'or uny uyfJtcmnt :i.c poc:ition-dcpcndcncl~ in the pul1:c hclg}1t i;pcctrurn uf c :Ltl1cr u.l<)<:tronu or p.10111;. Another poos ible r;ource of bias would o.ricc .i J' the clcctronpion separation at the shower modules were dependent on decay length in the front end. When the electron and pion are near one another, the pion could add its pulse height to the electron giving a pulse height above threshold to events that would otherwise fail, since a pion search is not made when the RH separation is :::_ 4. This question was investigated using Monte Carlo events, dividing the decay region into three segments and histograrrrrning the electron-pion separation in each segment. These are shown in Fig. 43. There is no statistically significant difference between these histograms. Charge biases in the computer scan were investigated by histogramming separately the pulse heights of e+, e , TI+ and TI the final data. from These are shovm in Fig. 44 and there is no demon- strable difference between distributions for different charge states. Fig. 45 shows the acceptance of the computer scan as a f'unction of electron energy. Low energy electrons reach shower maximum •~11 before three radiation lengths and so give a very small pulse in the shower counters. This efficiency was used as a cor- rection in the Monte Carlo program. il+C 200~,r L <6Z>= 4 2.2 I (f) 30 < xDEC< 40 11 100 L r- ---'> z +770 w > w g 0 n:: <! u <6Z>= 43 .4 V 3011 2 0 II <"DEC< w rz 0 ~ 100 LL --z:;;. 0 er: w m +676 0 ~ :::> z <6Z>= 43 .9 11 11 I0 <XDEC< 20 ~ +546 0 20 40 60 6 Z (inches) Fig . 43 Horizontal separation between pion and e le ctr on at shower counters 80 11 149 601 40- ~ 7T t MEAN 18 .8 20- ~ 0 10 20 40 30 60 - MEAN 19.6 40 CJ) 7T ' I- z w > 20 ~~ w LL 0 a::: w CD 0 10 20 PION PULSE HEIGHT 50 40 30 ::2: :::> e- MEAN 47.9 t z 0 60 20 80 100 + e, MEAN 50.I 50 ~ +23 0 I 0 20 40 60 80 ELECTRON PULSE HEIGHT Fig. 44 Shower counter pulse heights of e and TI for different charges 100 150 1.0-; ...... ~ ~ 2 0.8 lL 0 6.L z W<C OU Zif> ~w0. 6 Q_ o._ t5~ ~o:: w 2 1- 0.4 o~ a:°- r- :?! uO wu ci 0 .2 ! I I I I 0.0 0.4 0.8 1.2 1.4 1.8 II 'I [ ELECTRON ENERGY ( GeV/c ) I .1 f t i ' I t Fig . 45 ! Electron acceptance of computer scan as a function of electron energy. Smooth curve is to guide the eye. I 151 The actual scanning in:3tructions given to the scanner are reproduced here, with Fig. 46 for illustration . "Shower Scanning Procedure for K e3 The primary object of this scan is to pick up events in which a pion and an electron have triggered the shower detecting part of the apparatus. If the event is not n-e combination but can be classified n-n, then it is also included and its type noted. Find the RH counters from the computer output and look for the tracks in the shower chamber which extrapolate into the RH counters on the scanning template. +l.. - 2 The tolerance for this is counter on either side of the triggered RH counter. If a unique n-e combination can be found, a pion in one counter and an electron in the other, then the event is accepted. If there is an ambiguity where two pions or two electrons are within the limits of the counter, then the event is rejected as ambiguous (if one of these ambiguous tracks is within! counter but not actually inside, then take the one that is inside and accept the event). Pion criteria: 1. Straight through tracks. 2. 'l'racks scattcr:Lng at a definite point, with straight segments. 3. Tracks with an :lntcraction where a number 01' strale;ht 152 ------------ 1. Straight through tracks 2. Tracks scattering at a- definite point with straight segments ----- 3. Tracks with an interaction where a number of straight tracks emanate from a definite vertex - ---~-- - 4. Example of a shower Fig. 46 Shower scanning criteria ,. 7 J.0.> tracks emanate from a definit e vertex . Electron criteria: Any track which satisfies none of the pion criteria and is not an obvious stop, i.e., a straight track which stops at a definite point in the chambers. In general, an electron is characterized by extra curving tracks coming off at small angles." Decay Region Scan The actual instructions used by the scanners are reproduced here, with Fig. 's 47 and 48 for illustration. "K Scanning in the Front End -e3~~~~~-=-~~~~~~~~~ From the computer output find the two MR numbers and insert the pins in the appropriate holes. Move the strings attached to the pins over the elevation view until the tracks associated with these MR counters are identified. For Tl events the tolerance is ~ 2 counters; for T2 it is ~ 3 counters. If these two tracks satisfy the following: a) Are reasonably straight, with no scatter> 5°. b) Form a consistent vertex in both views, at the same position along the beam within a few gaps (be liberal when tracks are on opposite sides of split in the plan view). c) There are no other tracks stopping or starting at the vertex either from upstream or going downstream (traeks going right through vertex do not affect event). 154 ~r====.======~ ..L consistent -- I - -- I + ... / I / 1 inconsistent -/-r ===- ti~====I + a) Vertex consistency between plan and elevation views ---- ···-·- -· .. ··- ·-- · ·-- - -- .. ·----- . ----- -- -- --··· . ----- ---BAO. .: : ;;,,..------- -c:-.-+ Ti c) Vertex position relative to triggered target (example is a T2 trigger) Fig. 47 Production-decay region scanning criteria 155 d) The vertex must not be upstream (to the left in picture) of the target which triggered. If a) through d) nre catlcf'J.etl,then check the eve nt on the scan list and write down an ectimate of the chamber number and plate number of the vertex. The following special cases are illustrated in Fig. 48. 1. ~ ~ 1 2 or c 1~ 2~2 event s These events are to be treated by the same rules as the regular vees with the addition that if a track appears to pas s right through the vertex then the event is rejected. 2. Small opening angle events For events with vertex upstream of T2, reject the event if there is no opening for at least two chambers in both views. For events downstream (to the right in picture) from T2, there must be evidence of two separate tracks for the event to be acceptable." 156 OK,only 2 came T1 out of target ---o OK,track passed through C2 or V2 NO GOOD,more than 2 out of T2 GOOD,track into T2 --~2':);,. .--------< i<Q QOOD ,_1 in & 3 out 1. Tl events where either C2 or V2 fired ~ I i ~ B.AD BAD ~ ~ + I [S'J I r.33 w+ 2. Small O!)ening angle events Fig. 48 Special cases in productiondecay region scan 157 Appendix 11: Measuring, I\econctruction and Track Fi t·i~ ing. Thie Appendix der;cr jl>eu how mcn:-;urementG from the three 3~)rrrm. f'ramec tukcn for each event were UGe<.l to reconctruct the tra- jectorieG of the decay secondaries in the magnetic field. For each measuring mach:ine a program, COVTUV, was ,rritten to transform the numbers, encoded in the digitization process, into two cartesian coordinates and an angle on the measuring table. The overall calibration of each machine was regularly checked by placing an accurate cartesian grid in the film clamp and digitizing many points and angles. These measurements were analyzed by a checking program using the same version of COVTUV that was being used to analyze the data. Over the period in which the data pictures were processed, no significant drifts were found in the calibration of the measuring machines. Measurement of a decay region picture will be taken as an example of the spark chamber digitization process. Fig. 49 (a ) shows an example of a production-decay region picture; Fig. 49 (b) shows a frame for which the accurately surveyed full fiducials were lit along with the transfer fiducials. The measuring procedure for data frames was to .make twelve position-angle measurements in the order indicated. When measuring transfer fiducials, the position only was measured by simply placing the measuring arm cross-hair at the point to be digitized. In measuring decay se condary tracks, the cross-hair was placed as close as pocsible to the decay vertex. For each run, a fe w ccts of full fiducials were measured in the order indicated in (b). 150 (a) 0 tll fO c::i I/ill CJ Q Q Q cl~ ~ ~- <§J. ~-· ... ...... ·-®_T ...... w - .. ~05~ ··--. t:l Ill Cl g G e Q .. IM 0 v ·--· ·-J»--·--·' @-____ 0 Ji. ....... ' ·-··- ' 1 t f' ! ' Fig. l+9 Production-decay region meuourcmcnts : (a) Normal data f rame; (b) Full fiducial fro.me. indicnte measuring order. Numbers 159 A set of about t en full fiducials was collected by duplicating those measured in adjacent runs. Any variations in the optic s took place on a long time scale relative to the few hours it took to collect a data run, so it was reasonable to combine full fiducial measurements from three adjacent runs. In analyzing a set of data measurements, the first step was to use the full fiducial measurements to calculate for each view the magnification from the table to real space and the location of the optic axes relative to the transfer fiducials. The average over the ten frames ~~s used to avoid sensitivity to single measuring errors. The optic axes for the plan and elevation views intersected rather closely in space. The measurements were analyzed to find the equation of the tracks projected onto the planes containing the optic axes, with the transfer fiducials as a reference. It is then a matter of algebra to calculate the equation of the track in three dimensions. The optic axis locations were known from the surveying so this 3-D equation could be transformed to a standard coordinate system whose X-axis was along the beam, Y-axis in the vertical direction, Z-axis perpendicular to these two and whose origin was located 80" from the magnet center. upstream The procedure in the momentum and shower chambers was similar so that all shower chamber tracks could be geometrically reconstructed in a common coordinate system. The process descrJ.bed so far involved programs consisting of about 3,000 cards of Fortran and used a large number of parameters mea sured i n the s urvey of the t.1.p-poratus at the conclusion of the lGO experiment. There are limitless possibilities for both programming and surveying errors in this scheme, and it is clearly desirable to have enough direct checks to tie the process together. This was provided by runs of straight through tracks, where the apparatus was triggered on interactions in the targets with the magnetic field turned off. Measurements of the track of the same particle made in different chambers were fit to a straight line. Using a sample of 1,000 such tracks, systematic errors in the chamber positions could be found and corrected and the spatial resolution of each chamber measured in the transverse position and angle. These resolutions were used as assigned errors in the trajectory fitting program, to be discussed next, and •rere: Transverse y (vertical ) Chamber Transverse z (horizontal) . 08", 6mr .11", 6mr FM .03", 17mr .03" J 500mr MM .06", 17mr • 06", 500mr RL\1 • 03"' 17mr • 03", 17mr Shower • 20" J 17mr • 20" J 17mr Prod. -de e . The huge 500mr angular resolution in the front and middle momentum chambers, horizontal view, is a reflection of the short track lenGth and the staggering of sparks in the crossed electrical clear ing and magnetic fields. The inforrrntion obtained from the measurements was, at tl-iic stage, in the form of a 3 -D equation of a segment of track at each H:il <.:lw.mucr where n meao1ircrncnt v1u:; made. Trie m:xt ::tcp w1u1 Lo ·1· J nd tlin orbit wh:ich ~ave the best 1'1 t to thcce trncl~ segrncntt: und thence to calculate the momentum of the particle from the known magnetic field. A subroutine was written which could generate a trajectory through the magnetic field from a given initial momentum and direction. In order to fit the measured segments to a common trajectory, an initial momentum and direction were guessed at, traced through the magnet and compared with the measured track at each chamber. The derivative of the position and slope was calculated at each charnber, with respect to the five initial parameters. Using this information, the best fitting trajectory was obtained by minimizing its function of the initial parameters. X 2 as a The five initial parameters of each track were then varied to constrain the two trajectories to intersect at a unique point in space, the decay vertex. With 3- momenta of the two decay secondaries known, the invariant mass of different decay hypotheses was m , m , mee' etc •. rce rcrc calculated, e.g., The following information was then compiled into a 1,000-word record and written out on magnetic tape: 1) Bookkeeping information, e.g., frame number, date measured, etc. 2) Information from the data tape record written during the experiment, e.g., which counters fired, pulse height in gas counter, shovrer modules, etc. 3) Information on trajectories of decay secondaries, e.g., transverse coordinates at places of interest in the 162 apparatus, decay vertex coordinates, etc. 1) Quo.nt:L tiec calculu Leu from the momenta, c ·8·' m , m etc. :rre :rrrc' 5) Error rno.tr:!.cco J'or mer.J.curemento Jn each churn1>cr and oJ:' the final fit. 1G3 J\vpcndlx 12: Monte Carlo Pr.n1'r:111l ])JL;cw;::Jun uJ' tlw Monte Carlo vrup:rum wtll 0 the olmulation (![' K,, -> 21r dccuy n.nd later w.1 th K I' .! rnt cknl -> 1rCV. i,rl-Lli In eucli IJ case it is assumed that pK' GK' and ~ are given. These were randomly generated in the center-of-mass system and then Lorentz-transformed into the laboratory system using pK and GK. The individual decay secondaries had their orbits traced through the magnetic field. If both secondaries succeeded in traversing the field region without striking the magnet poles, coils or return iron, then the Monte Carlo event was subjected to the following checks: 1) Decay vertex within fiducial volume. 2) Tracks are contained in fiducial volume for their length in decay region. 3) One track hits 85. 4) Both tracks hit MH and go through different counters separated by at least one counter. 5) Both tracks hit RH and go through different counters. 6) Both tracks hit shower modules. For K -) 21r it was demanded that both tracks be contained within 8 the GC front and rear windows. The only reason for this demand was historical -- at first it was feared that tracks traversing 3/4" of aluminum would reconstruct poorly, but it was later found that th is was not the case and for the Ke 's the requirement was not 3 1HtT>03cd.. EventG out:i. c fy:i. n 1-~ aJ l the prccerling condit :Lono were Vlri ttrm on mn.c;netic to.pc for ::rnbseque nt exo.m:tnation. lG1 Bcs:ides 1.lcinG a complex s :imulation pro1',rrnn, t;l1c~ McinLc Cur.lo program had as input very many parameters oi' the appurat1 1G -v1}1 i cl1 H<~n~ measured in the survey carried out at the end of the expcrjmcrrt. It is desirable to have as many checks as possible on such a procedure. Besides the checks mentioned in the text -- momentum, angular and decay vertex position distributions -- it was also possible to compare the decay secondary transverse position distribution (commonly called profile) for data and M.C. events at different points. For K __, 2rc, 8 profiles were compared in both Y and Z directions at a) end of decay region, b) MR, and c) RH. in Fig. 's 50 and 51. These comparisons are shown for Tl data The agreement is good in all profiles except that the data have a bigger dip than the Monte Carlo at Z = 0 in all Z-profiles. This is probably due to (1) a concentration of material at Z = 0 behind the gas counter mirrors, and (2) a tendency to miss events whi ch are near the center-line of the shower chambers. Neither of these effects give position biases in the front end so it was not necessary to correct for them. The only inconsistency found in the K 8 __,re+re - data was that the number of events actually coming from T2 was 70% of the number calculated from the Tl rate, correcting for efficiency and beam flux differences. For one set of runs this was: (T2 Beam) (Tl Beam) anu 2'1-1 event~; x (T2 Efficiency) (Tl Efficiency) were actunlly ~;ccn, so the K,, (.7 -~ .l) ol ' Lll<' r11LL' l!X.JH'<'Lt•d. 349 ' 2rc rutc J'rom 'I.' ;' .1 L; I (c) ! m1 - ,~~.Jrfill y ~Fl ~ y (f) ~ z 0 ..__~~-..,I r - 15 ::) - 10 -5 0 l I 5 10 ~L I 15 Y (inches) 0 u (b) ~~ I LL 0 I I 2 Qc......------~-....---_,-------.,~---~ l ---~~~~~-.--~-'1-- -6 -4 -2 0 2 6 4 8 Y( inches) ~+~ 100 (a} I~ E o...._______~~-----....-----..-------r,-----~~---~,------~ 1 -----~ -3 -2 -I 0 I 2 Y(inches) Fig. 50 Comparison between calibration data (points) and Monte Carlo (hi st ograms) for Y-profile of n at (a) End of decay region, (b) MH and (c) RH. 3 166 ( c) I -, I~ (b) tt• 0 ©'ff/d I I I - 10 - 20 I i 20 10 0 Z (inches) (a) 100 - O io..-~-11--~---~---~---~_,-~-.-~___,....~---~-l}o , ~~~ -8 -6 -4 -2 0 2 4 6 8 Z {inches) Fi g . 51 Comparison b etwe en calibrat ion da ta ( p6ints) and Monte Carlo for Z-prof ile of TI (hi~Lo ~rruna) at (a) End of decay region , (b) MH and. (c) RH. .LG7 rrhi~; discrepancy rn:1y 1JC dHC to th e! di l'J'crencc .in between Tl and ·~2. ~~L:ornc:Lry For example, secondaries from T2 mny get into the MH without passing through v , thus vetoing the event, whereas 2 this would be rarer from Tl which is 24" further away from the MH. It was felt that this failure to normalize the targets for K1L 2 data would only affect the physics if one attempted to impose a normalThe efficiency calculations were ization in fitting the Ke 's. 3 checked very thoroughly to be sure that the effect was not due to a progranuning error. 0 K _, 1lev The Monte Carlo K e3 1 s were generated in the E vs. E 1L e Dalitz plot with the spectrum that one gets from the matrix element in Appendix 1 ·with s= ff+ 0 and no q 2 dependence in f + .(29) They were then Lorentz-transformed into the lab, using PK and GK as given. The Monte Carlo events were then sent through exactly the same program as the K _, 21L events without the added requirement 8 that both tracks be within the GC windows. As before, successes were written on magnetic tape for later examination. Fig. 's 52 and 53 show Z-profile comparisons for both e and 1L from Tl events at three locations in apparatus For the Ke 3 and again the agreement is good. data the relative number of events from Tl and T2 is in agreement with the calculated ratio. However, when fitting, the normalization between the targets was still allowed to vary as a free parameter. 168 (c ) 50 0 I -50 0 Z(inches) (/) f- z 100 :J 50 I I r rr I u-'~ 0 u T ! LL. 0 a:: 50 w J- I ff CD ::2: :J z 0 / ( b) I -20 - 10 0 Z (inc hes ) 10 20 -8 ·- 4 0 4 a 100 0 Z (inches) Fig. 52 Comparison betwe en ne data (points) and Monte Carlo (histograms) for Z-profile of eat (a) End of decay reg ion, (b) MH and (c) RH. 100 50 0 -50 I 0 Z (inches) 50 (/) I- z ~ 0 100 (.) ~ LL. 0 I a:: w co 50 ct: """ ~ z (b) I 0 -20 -10 0 Z(inches) 10 20 l 100 (a) ! 0 -8 -4 0 4 8 Z (inches) Fig. 53 Comparison betwe e n ne data (points ) and Monte Carlo (hi s tograms) for Z-profile of 7T at (a) End of decay region, (b) MH and (c) RH. .1.70 Appendix 13: Smearing of T:l111e Dl stributions Us ed in Ma.dmwn Likelihood Calculatj_on + Corrections were made to N-(t) due to spread of production point in targetu and the fin :i.te width of the momentum spectrum of accepted Ke 1 3 s. The latter has already been shown in Fig. 24. In general, the proper time is give by: -c = (~ - ~) ~ p c (~ - ~) = k x where ~ is the decay point, ~ is the production point, measured from the center of the target so that < ~ > ~ 0 and px is the 0 x-component of K momentum. p x The effect of the width in (~ - Y'"p) and was taken into account in a Taylor 1 s expansion as follOYffi: f(k ~- ~) p x 2 + crx ) + . 2f~.e).e °l?~ } p0 2 ~ = < l/p where £ x >and cr 2 = (a 2 + 0 2). x ~ ~ calculated from the reconstruction of each event, cr ~ ' a was ~ was taken as .3 11 corresponding to uniform production in the targets and crp as .38 GeV/c from the pK- spectrum. The effect of the pK- spectrum can be taken into account exactly by numerical integration. + The N-(t) time distributions were calculated for the three cases: (a) Effect of spread in pK neglected. i . ' i 171 (b) Taken into account up to the second moment by the above scheme. ( c) Folded into the dietribution numer:l.cnlly. Fig. 54 chowc the difference of (a) - (b) nnd the difference (c) - (b). If the fit to X is done with the time distributions from (a), one gets +.036 +.08 4 Rex = -.080 -.034 , ImX = +.10 4 -.072 compared to the final ReX = -.069 +- .036, ImX = +. 108 +.092 -.074 quoted from using (b). The effect of (c) on the time distributions change s the relative probability by< 0.5°/o of N+ at .t = O, when compared to the time distribut ions from (b). This is less than the difference between the distributions from (b) to (a). Since the change . in X from using (b) to using (a) is negligible compared to the statistical error, it follows that the effect of neglecting higher moments has a neglibible effect on X. ' ! r' . ' ! I 172 0 -~ II .5] ~N + :z lJ... -.5 0 ~ 0 (.f) <! w u z w w .5 cc lJ... lJ... -0 ~N + I -.51 / Diffe rence between N with ou t corre ction and N corrected up to 2nd MOMENTS Diff eren c0 between N corrected up to 2nd MOMENTS and exactly calculated N 4 N 0 I 0 2 4 t Fig.54 6 (Ks LIFETIMES) , Difference in N+ ( N- ) with various corrections for higher moments of PK-spectrum. for X = 0 are also shown. N+ and N- 8 173 VII. REFERENCES 1. R. P. Feynman and M. Gell-Mann, Phys. Rev. 109, 193 (1958). 2. N. Cabibbo, Phys. Rev. Letters .lQ_, 531 (1963). 3. R. G. Sachs, Phys. Rev. Letters 13, 286 (1964). 4. F. S. Crawford, Rapporteurs Talk, Proceedings of the XIth International Conference on High En~rgy Physics, CERN, 1962. 5. A. Barbaro-Galtieri, W. H. Barkas, H. H. Heckman, J. W. Patrick and F. M. Smith, Phys. Rev. Letters ~ 26 (1962). 6. R. P. Ely, W. M. Powell, H. White, M. Baldo-Ceolin, E. Calimani, S. Ciampolillo, O. Fabbri, F. Farini, C. Filippi, H. Huzita, G. Miari, U. Camerini, W. F. 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