A Determination of the Neutron Spin Structure Function gⁿ₁ with the 1995 HERMES Data Citation Bray, Bruce D. (1998) A Determination of the Neutron Spin Structure Function gⁿ₁ with the 1995 HERMES Data. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/pr7a-ed83. https://resolver.caltech.edu/CaltechTHESIS:02222021-234525490 Abstract The internal spin structure of the neutron was studied in deep inelastic scattering of longitudinally polarized positrons from a polarized 3 He target in the HERMES spectrometer at the DESY storage ring. The spin asymmetry was measured at an energy of 27.52 GeV in the range 0.023 ˂ x ˂ 0.8 at an average Q 2 of 2.5 (GeV/c) 2 . The results are evolved to a constant Q 2 of 2.5 (GeV /c) 2 and arc in agreement with the world data for the spin dependent structure function g n 1 . The integral of g n 1 (ʃ 1 0 (x, Q 2 = 2.5(Gev/c) 2 )dx) is found to he -0.036 ± 0.012(stat) ± 0.005(syst) ± 0.003(extrapolation) which is 2 standard deviations from the Ellis-Jaffe Sum Rule and, combined with the world data for the proton, is in good agreement with the Bjorken Sum Rule. Combining this result with the weak coupling constants F and D implies the quarks carry (38 ± 11)% of the nucleon spin and the polarization of the strange sea represents (-7 ± 4)% of the nucleon spin. 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): Filippone, Bradley W. Thesis Committee: Filippone, Bradley W. (chair) Hughes, Emlyn Willard Politzer, Hugh David Weinstein, Alan Jay Defense Date: 23 July 1997 Record Number: CaltechTHESIS:02222021-234525490 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:02222021-234525490 DOI: 10.7907/pr7a-ed83 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 14092 Collection: CaltechTHESIS Deposited By: Kristofer Jolley Deposited On: 23 Feb 2021 23:00 Last Modified: 26 Oct 2021 18:43 Thesis Files PDF - Final Version See Usage Policy. 37MB Repository Staff Only: item control page

A Determination of the Neutron Spin Structure Function g1 with the 1995 HERMES Data Thesis by Bruce D. Bray In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy California lrn;titutc! of Technology Pasadena, California 1998 (Submitted .luly 23, 1997) ii © 1998 Brun~ D. Bray All Rights ReserYc~d lll Acknowledgements First, I would like to thank iny wife, Laura, for lwr support, understanding and love through this endeavor. Earning a Ph.D. required many long days and nights in laboratoric~s or in front of a computer and she ha!-i heeu understanding of these many trials since the day we first met. The Bray and Miller families both deserve special recognition for their support and encouragement during my :-;tudies. Many people have been involved in my education and development as a physicist. I would like to acknowledge and thank Brn<l Filippone for his guidance, time, and support. I would like to acknowledge many of tlw members of the HERMES collaboration who made this endeavor worthwhile with their companionship and example. There are far too many members who deserve to he thanked and I will only mention a few. Allison Lung deserves special thanks for the man:v hours she spent working with and guiding me during the com,truction and installation of the hodoscopes: Art MateoR and Dirk DeSchepper for their work with nw on the NAPA analysis: Ralf Kaiser for the many thankle:-;s hours dwcking partide id<\ntific:ation routines. Finally, a general mention of all the peoplci iu Hmulmrg who made my stay an unforgdtahl<> experience. IV Abstract The internal spin structure of the neutron was studied in deep inelastic scattering of longitudinally polarized positrons from a polari,1,<1d :iHe target in the HERMES :-.pectrometcr at the DESY storage rinp;. Th<• spin a.s~'11mietry was measured at an energy of 27.52 GeV in the range 0.023 < :1: < 0.8 at an awrage Q2 of 2.5 (GeV /c)2. Tlw results are evolved to a constant Q2 of 2.5 (GeV /c)2 and arc in agreement with tlH' world data for the spin dependent stmctur<· fnnctiou yj'. The integral of gf u;: gj'(:c, Q = 2.5(Gev/c)2)dx) is found to he -0.03G ± 0.012(stat) ± 0.005(syst) ± 2 0.003(e:t:trapolation) which is 2 standard deviations from the Ellis-Jaffe Sum Rule and, ~omhined with the world data for the proton, is in good agreement with the Bjorken Sum Rule. Combining this result with the weak coupling nmstauts F and D implies the quarks <·,H-r~· (38± 11)% of the nucleon spin awl the polmizat.iou of the strange sea represents (- 7 ± 4)% of the nucleon spin. V Contents Acknowledgements Ill Abstract IV 1 2 Physics Motivation 1 1.1 Introduction . . . 1 1.2 The Formalism of Polarized Deep hu•lasti<" Scattering 2 1.3 The Polarized Structure Functions . 5 1.4 The Quark Parton Model 8 1.5 Spin Structure Function Sum Rul<~s 12 1.6 Spin Decomposition of the Nucleon 15 1. 7 World Data Before HERMES 16 1.8 Semi-Inclusive Physic.'> 17 Experimental Apparatus 19 2.1 HERA . . . . . . . . . 19 2.2 The Polarized Positron Storage Ring 20 2.2.1 Measurement of the Beam Polarizatio11 22 2.2.2 Synchrotron Radiation 23 The HERMES :iHe Target . . 24 2.3.1 27 2.3 2.4 Tlw Measurement of the Targ<•t Polarization The HERMES Spect.rornd,cr 29 2.4.1 A General Overview 29 2.4.2 Magnet 29 2.4.3 Tracking 31 2.4.4 Alignment 39 2.4.5 Efficiency 39 2.4.G Particle Identification . 42 2.4. 7 Hodoscopes 43 2.4.8 Calorimeter 43 2.4. 9 Cerenkov Detector 49 2.4.10 Transition Radiation Detector 51 2.4.11 Luminosity Monitor .. 54 2.4.12 Gain Monitoring System 55 2.4.13 Trigger . . . . 57 3 Particle Identification 61 4 3.1 Particle Identification . 61 3.2 Particle Identification Cuts . 61 3.3 Likelihood Method . . . . . 63 3.3.1 The Likelihood Functions 64 3.3.2 Hadron Rejection and Efficiew·~- . 66 3.4 Positron and Hadron Fluxes for the Inclusive Measurements 67 3 .;)r: Monte Carlo Comparisons 67 Data Analysis 73 4.1 1995 HERMES Data Analysi:-; 73 4.1.1 An Overview of the Data Anal~·sis 73 4.1.2 Tlw Analysis Chain . 74 4.1.3 Initial Run Selection 76 4.1.4 Particle ID Criteria . 76 4.1.5 Down-shifting . . . . 77 4.1.6 I3urst Quality Criteria 78 1.1. 7 I3eam Polarization 79 4.1.8 Target Polarization 79 4.1.9 Luminosity 81 4.1.10 Live Time . 83 4.1.11 Chamber High Voltage Trip D<'t<'c·tiou 86 4.1.12 Scalers . . . . . . . . . . . . . . . . . . 87 4.1.13 Synchronization and Run Initialization 87 Vll 4.2 4.3 4.1.14 Summary of Burst Cuts .. 87 4.1.15 Secondary Run and Fill Selection 89 4.1.16 Event Selection 90 4.1.17 Y Binning . . . 90 4.1.18 Corrections from the Transverse As~rmmetries 91 Calculating A?e . . 92 4.2.1 Backgrounds. 93 4.2.2 R.a<liative Corrections . 99 4.2.3 The Measured Asymmetr~· .--1?•· . 101 Extracting A'i' . . . . . . . . . . . . . 103 The Measured Asymmetr~· .·!;' 104 4.3.1 4.4 4.5 4.G 4.7 5 Systematic Studies of the Asymml'ti)· . 106 4.4.1 Time Stability of the As~·mmetr~· 106 4.4.2 The Determination of th<• Statistical Errors 107 4.4.3 False Aic;ymmctries 116 Extracting .'I? ....... 116 4.5.1 Evolving the Structure Func:tiou .'I~' to Co11stant Q'2 117 4.5.2 Mea.">urcd Integral of g;1(:r. Q2 = 2.5( G,, l "/ r:)'2) 117 Dominant Systematic Errors . . . . . . . . . . . . . . 120 4.G.l 121 Cut Dcpcudcnce of the ~l<·as11n·d l11t.egral of .'l;'·(:r). Comparison to Tlwory . . . 122 4.7.1 Low :1: Extrapolation 122 4.7.2 High :1: Extrapolation . 123 4.7.3 Total Integral of g\'(:1:, CJ'l = 2.G(G<'\ ·;,-)1 123 4.7.4 The Ellis - .J affo Sum nnl<• 123 4.7.5 Tlw Bjorkcn Sum Ruk . . 124 4.7.G Quark Contributions to tll<' Spin of tlH' >Jnd<!Oll 125 Summary and Conclusion 127 A Design and Testing of the Hodoscopes 128 A.I The HERMES Hodoscopes . . . . . . . 128 ,·iii A.1.1 Introduction . 128 A.1.2 Components and Assembly . 128 A.1.3 PMT Testing 131 A.1.4 Attenuation 131 A.1.5 Detailed Atterruation StudieH 133 A.1.6 Final Gain Tests 134 A.1.7 Y Position Dependence . 134 A.1.8 X Position Dependenc<~ . 136 A.1.9 Particle Identification . 138 A.2 CERN Test, Beam . A.2.1 138 Experimental Setup . 138 A.2.2 Shower Distributions 140 A.2.3 The Linearit~, of th<• Calorimd.<•r 140 A.2.4 The Hodoscope Resporu,e 142 A.2.5 142 Particle Identification . B Merging Independent Results 146 Bibliography 148 IX List of Figures 1.1 Feynman diagram for'lowest order DIS lepton-nucleon collision . 2 1.2 DIS in the quark-parton model 8 1.3 att in the Bjorken Limit 11 1.4 at -l- in the Bjorken Limit 11 1.5 World Data for rr 17 LG World Data for fii 17 2.1 Polarized Electrons in a Storage Ring 19 2.2 Polarized Electrons in the HERA Stornw~ Ring . 20 2.3 Schematic Diagram of the Compton Polarimeter 22 2.4 Polarized Positrons in a Storage Ring . . 23 2.5 Schematic of the T-Shaped Storage~ Cdl 25 2.G Vertex Distribution of Reconstructed Tracks in the Target 25 2.7 Temperature Dependence of :{He Dc\polarization from TeA'3ts at Caltech 2.8 Polarization Mca~urcmcnts in tlw TOl\I all<I Pumping Cell Polarimeter 28 2.9 The HERMES Spectrometer . . . . . . . . . . . . . . . . . . . . 30 2.10 A High Track Multiplicity Event i11 th(' HERl'vIES Spectrometer 32 2.11 Track Finding with a Tree Search at hu:rea.-;iugly Higher Resolutions 34 2.12 Pattern Matching Algorithm . . . . . . . . . . . . . . . . . . . . . . 36 2.1:3 Improving the Momentum Measnrc~m<'nt Through Forced Bridging . 37 2 .14 K~ Mass Rec:onstrnctiou . . . . . . 38 2 .1 fj The Cham her Efficiency Algorithm 40 2.lG Time Dcpcndc~nc<~ of the Chamber Effi<-i1'11c_y for a Series of Fills 42 2.17 Isometric View of the Hodoscopc . . . . . . . . . . . . . 44 2.18 Monte Carlo Calorimeter Response for ;"j GcV /c Particles 47 2. 19 Isometric View of tlH~ Calorirnetc~r 48 2.20 HERMES Cerenkov Detector 49 . . 27 X 2.21 Cerenkov Response for Hadrons . . . . .. . . . . . . . . . . . 52 2.22 Cerenkov Response of Hadrons Below the Cerenkov Threshold 52 2.23 TRD Module . . . . . . . . . . . . . . 54 2.24 Current Dependence of the Luminosity 55 2.25 Luminosity Monitor . · . . . . . . . . 56 2.26 Gain Monitoring Data for One Run 57 2.27 Trigger Timing . . . . . . . . . . . 59 3.1 Particle I<lentifica t ion Detector Sp<~drn for All TI:acks in the DIS Acceptance . . . . . . . . . . . . . . 62 3.2 Particle Id Variable Distributions 65 3.3 PID3: Solid Linc All Particles, Daslwd Lim~ Positrons, Dotted Line Positive Hadrons .. 68 3.4 PID3 vs TRD Plane 69 3.5 Momentum and :1: Distributions for Hadrons and Positrons for a Sample of Data . . . . . . . . . . . . . . . . . . . . . . .. . 70 3.6 Hadron Contamination for the HERMES :1: I3iuning 71 4.1 Off Line Analysis Chain . . . . . . . . . . . . . . . 75 4.2 Beam Polarization \"<'rsus Time Durinp; a Risetime Measurement . 80 4.3 Target Polarization \ ·ersus Time N<~,u a Spin Flip . . . . . . . . . 82 4.4 Luminosity \h~rsns Tinw and Luminosity /Current/Target Density for a Fill . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.f> (a) Live Time Distribution for a Snhset. of Data and (h) Livetime per Burst for One Run . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.G 84 85 Efficiency awl 11<•<·011structed Tracks J><'l' 13urst N<!ar a Detected Trip in the Front Chamh<•r . . . . . . . 88 4.7 Pm,itive Hadron As~·nunetry Af 95 4.8 Electron A:,;ymmc>tr~· . . . . . 97 4.9 Negative Hadron As~·mmetry 98 4.10 Diagram:,; \,Vhich Contribute to the Intnnal Radiative Corrections 100 4.11 A'; Ht, Versus x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 xi 4.12 Primary Part of 3 He Wave Function ...... . 103 4.13 A1 Versus .1: With Systematic Errors (Solid Band) 105 4.14 Time Dependence Plots for Positrons iu the Top Detector: The asymmetry per fill versus fill number, the confidence level of sets of runs within each fill, and the distribution of tlw confidence levels . . . . . 108 4.15 Positron Time Dependence Bottom Detect.or as Defined in Figure 4.14 109 4.16 Positive Hadron Time Dependence Top Dd.<•ctor as Defined in Figure 4.14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 4.17 Positive Hadron Time Dependence Bottom Dc!te•d.or as Defined in Figllr<' 4.14 ..................... . ............ 111 4.18 Negative Hadron Time Dependence Top Detector as Defined in Figure 4.14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 4.19 Negative Hadron Time De~pendencc Bottom Detector as Defined in Figure 4.14 . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 4.20 Positron Yield Versus Fill for the Top and Bottom Detectors 114 4.21 Fluctuation:,; in Positron Yield: Top aud Bott.om . . . . . . 115 4.22 116 Efficiency Distribution U:,;ed in False• Asyrmm~try Checks 4.23 .<J~' v:,; :1: at Measured (.J 2 With Sy:-;tematic Errors (Solid Band) 118 4.24 r1;' vs :r. at Constant Q2 With Systematic Errors (Solid Band) . 119 4.25 Tlw Agrem1wnt B<•twcen Data From \'a.rious Experiments and the Bjorken Sum Rule• 125 A.I Pa<ldlc A:,;sembly . 129 A.2 Hodoscope Paddl<' .-\rrangenwut 130 A.3 PMT Gain Mea~ur<'mcuts 132 . . . A.4 Hodoscopc\ Paddle• ..\tt.ermat.ion T<\st.s 133 A.5 Lip;ht Attenuation in Hodoscopc Pa.dd!Ps 135 A.G Hodoscope Y Dependence After Off-lirw Corrc<:tious . 137 A. 7 Gain Variation During th<~ First 2G Fills 139 A.8 Calorimeter Linearity . 141 xii A.9 I\lean Electron Energy vs Momentum for the Preshower: Both Scales in GeV .. . . . . . . . . . . . . . 143 A.IO Electron Efficiency of Preshower 144 A.11 Pion Rejection in Preshower 145 xiii List of Tables 1.1 DIS variables . . . . ' . . . . . . . . . . . . . . . . . 2.1 Mean number of patterns compared 1wr track as a function of noise 3 (Monte Carlo simulation) for a 4 h:v 128 hi11 detector 33 2.2 Tree Search Parameters. 35 2.3 Bridging Parameters . . 36 2.4 Typical ACE Efficiencies 41 2.5 Physical Properties of FlOl Lead Glass 44 2.6 Momentum Threshold of Cerenkov Detector 50 2. 7 Lorentz Factor for Positrons and Pious . . . 53 3.1 Efficiency and Rejection Factors for PID Cuts 62 3.2 Average Contamination and Efficienci<~s for the PIO Methods Used 64 3.3 Conbuuination Measurement from TRD . . . . . . . . . . . . 66 3.4 Mont<' Carlo Contamination and Positron Effici<\n<:~' for PID3 72 3.5 Monte Carlo Contamination and Positron Efficienc~' for PID3-TR.D and PID2-TRD . 72 4.1 G MS Gain Cuts . 76 4.2 Cut:-. Used in Efficiency Studies 77 4.:3 Fraction of Data Involv<\<l in Down-shift-iuv; 77 4.4 Iluu Quality Summary 78 4.G SPcondary R.1111 Quality Smmnar:v 89 4.6 :1: and .ti Biu Boundari<\s Used in the A11al~1sis . 91 4.7 M<\a.U Depolarization for the :1:,y Bins 91 4.8 A 2 Measurements from El42 [46] 92 4.9 Total Events in Full Run Li::;t (Nominal Cuts) 94 4.10 Correct.ions for Misidentified Positive Hadrons 95 . xiv 4.11 Charge Symmetric Background Correction 96 A?e .... 101 4.13 Partial Wave Decomposition of 3 He . 103 4.12 Radiative Corrections for 'l 4.14 A~1 and A/fr: Top and Bottom Averaged 104 4.15 gj1(:r, Q2 = 2.5[GeV/cf) 117 4.lG Systematic Errors on Aj1 (x) at the :t\foasurecl (J'2 120 4.17 Systematic Errors on gj1 (:r:) at the Mcasurc~d (/2 121 4.18 Systematic Errors on gj'(.1:) at (/2 = 2.5G<,V 2 • . 121 4. 19 Front Chamber Total Tracking Effici<~11c:~' Cut Dq>c\11clence 122 A.l Calorimeter Resolution With and \Vithont L<~a.d Pwshower 140 A.2 Hadron Rejection and Electron ld<\Htifin,tion of tlw Preshower 142 A .3 Hadron Rejc~dion and Electron Idcntific:atiou of tlH' Calorimeter 144 13.1 Averaged Measurement of A/1" .. 146 13.2 A~'· and yj' From the Average A?•· 146 13.3 Averaged :t\foasnrement of gj1 at Mca.-;nrcd (/1- 147 3 1 Chapter 1 1.1 Physics Motivation Introduction 11ud1 of the current knowledge of 11udco11 strndm<' has lw<~ll developed through the deep inela.-.;tic scattering (DIS) of lepton h<'ams frolll unclear targets. In DIS the high energy leptons are scattered hy the constituents of tlw nucleon. The unpolariz<•d nucleon structure functions determiu<•d b~- DIS have revealed the momentum distribution of partons within protons and neutrons. This was compelling evidence of structure within the nucleon. Quantum Chromo-Dynamics (QCD) implies that the uudeon contains three valence quarks held tog<'tlwr hy a sea of gluons and virtual quark auti-quark pairs. The development of polarized lepton l><•ams a11<l polarized nuclear targets has op<~1wd a. 1ww avenue to probe the spin st.ructun~ of tlw 11udeo11. Previous experiments m<•asuriug the spin dependent :-;tru<:ture of the 1111deo11 suggested the surprising result that little of the spin of the nucleon is carri<'d h~- tlw quarks. [1] [2] [3] [4] [5] Tlwsc results have spurred several 1ww cxpcriuwnts to measure the spin structure of the w·utron and the proton more accurntel~-- Tlwse structure functions will be able t.o t<•st pn~di<:tions about the nature of tlw ·s<'a · of virtual quarks and gluons binding th<· uuckus together. The HERMES experiment is part of a. H<'W gc11<'ratio11 of spin structure experiments 11H<lerway at SLAC, CERN, aH<I HERA, awl has 11ia.ny 1111iqn<' features which will allow it to make a sip;nificant contrilmtiou to t ll<' k11owkdµ;c of the spin structure of tlw 11ucleon: • A pure internal target eliminates com'ctious d1w to dilution and minimizes the cxtNnal radiative corwctions • Au open spectrometer design with a larp;<• ,H:<:<)ptauce allows measurements of semi-inclusive asymmetries in tandem with inclusive measurements for further 2 e k q p p p' Figure 1.1: Feynman diagram for lowest ord(•r DIS l<~ptou-undeon collision spin deeomposition • A polarized c+ beam in a storage ring provides significant luminosity in combiua.tion with the internal target • A 11wasurenw11t of H,D, and :1Hc spin strnctm<' with the same spectrometer at the same kiuemati<:s reduces problems from comhiuing the spin structure fnw:tions from different experiment:-; This thesis will di:-.cus:-; the result of the n~n•ut <'XJ><'riuwut to measure the spin<lqwnd<'ut strnctun~ fmu:tion .<J,i at HERMES iu 1!)!);; _ 1.2 The Formalism of Pol~rized Deep Inelastic Scattering Tlw formalism for Uie d<!ep i1wlastic scatt<!riug of l<•pt.ous from a uudeon can be dcscril1<~d in t<~nns of Feynman dia).!;rnms. In tlH' lirsl onl<~r approximation, a virtual pl10to11 is <!Xchanged between the lcptou awl 11m·l<•o11 as shown in Figure 1.1. The qnautiti<~s in the figure and used in this discussion of deq> inela.<;tic scattering are defined iu Table 1. 1. At high energies, the negative invariant mass of tlw virtual photon, the energy transfor, and the invariant ma."iS of the final stat<• haY<~ the following values in the lab frame: 3 Four Vector Lab Frame Components (E,k) (E' ,kr) (v,q) (M,O) (M + 11,q) k k' q p p' Definition incident positron momentum scattered positron momentum virtual photon momentum initial nucleon momentum baryon final state momentum Table 1.1: DIS variables Q'J. = -q'1 = (k - k'? fol, -4EE'si11?((-)j2) 11 = JJ • (j ~I, £ - E' M (1.2) (1.3) Calculating the doubly differential cross s<!dion for tlw process in Figure 1.1 by t.lw standard pm,criptions for QED [G] ~·idds: ,Pa 4a'l. E' dfJdE' Q £ --- = - 1- L '"' lV'"' (1.4) wlwr<! n is tlw fine structun• constant. awl t.11<' tm1sors L,w and W 1"' describe the leptonic and hadronic cmT<!nts. Th<~ leptonic tensor cau h<~ cakulat<!d from qED and tak<!S tlw form of a sum over final spin states: - - 1..1 '~ r,,,,ti,11 + f,i,fi'/L - .<J/IV''/..' • /~'' + ,;,,1·1f ..,n,/(J ' .·,wr,/J•> 1.• 1 '~ ;\ = L 111s , + L,,.,, (1.6) (1. 7) where m, the lepton mass, is iudud<'d to ca1tcd th<\ normalization factor in the spin vector. 4 The spin symmetric and antisymmetric terms are: (1.8) A L /LIi - 1··1nc ' ,o,.1/-J '' /W<l /:J ,', " (1.9) The advantage of lepton - nucleon scattering is that this tensor is known. The stru<:turclc~ss leptons can be used to probe the struct.1m\ of the nucleon, that is detcrmi1w the unknown hadronic tensor l,f//LII from its tensor product with the known lepton tensor L1w. Similar to the lepton current, the hadronic current <:au he decomposed into spin symmetric and spin anti-symmetric comi>01w11ts: (1.10) Furthermore, this arbitrary tensor can be decomposed into four unknown structure fnnct.iorn.;. Parity ai1d time reversal iuvariauc<~ constraints, lwrmiticity, and current conservation determine that thcs<1 are the onl~- iwlepend<\Ut components for electroma.p;nct.i<- scatterinp;. The symmetric term is defined a:-; [7] : awl the a11tisy1mnet.ric term: (1.12) The strnctun~ functiom; nr, and H/2 descrilH' tlw spill av<!raged scattering which is <lescrib<!d iu standard discussions of DIS [8] ..lust as tlw spiu independent portion of the hadronic tensor amplitude cau be descrilwd ill t<!rnts of two structure functions (W1 and W2 ), tlw spin dependent portion contaius two spin dependent structure 5 functions (G 1 and G 2 ). 1.3 The Polarized Structure Functions When the lepton is in a state _of positive helicit.'· (spin parallel to the beam momentum), the difference between cross sections for nucleon polarizations at an angle </> and at an angle </> + 1r summing ov<~r the final l<>pton and hadron polarizations is [9] da t(<i>) da t(,t,+1r) 41rn 2 , • 2 dCJ2dE' - dQ'2dE' = £'2(J 2 ([Eco..,</>+ E ,·o.'i({t - q, )].MG 1(11 , Q ) -2EE'[m.wp - ro.'i(f1 - <f,)]G'l(,/1 CJ2)). (1.13) The angle•.., are the polarization axis (</>) and tll<' scattering angle (0) relative the the directiou of the lepton's momentum. For a. longitudinally polarized target ( </> = 0), which was the case for the 1995 HERMES data.. this reduces to (1.14) For a. transvers<'ly polarized ta.rp.;ct. (<fa= 1r/2). this a.c..;ymmetry can be expressed as (1.15) It is possible to d<\t.ermi1w tlw spin depewfout st.rnctnre fund.ions from these doubly difforeutial cross sect.ions, hut it is lltor<) pnwt ical <'XJ><~ri11t<)Utally to make instead asymnwt.r_v nwas1uenwnts. Tlw systematic errors of tlJC' 1twas11n~ment of these struct.11 re fimctions can IH) rc\dun•d hy calculating a11 as_'\·mmctry as opposed to a difference of doubly cliffor<~ntial cross sect.ions. Tlw parall<'l and transverse asymmetries can be defined a."i: (1.16) G (1.17) These asymmetries can be related to the asymmetries for the virtual photons scattering from the nucleon a ; - a: ; .llf11G (11, CJ 2) - CJ :l G ( 1i, Q2) 1 2 1 2 1 2 A,=----=----------2 rr1;:.1 + rr:1/2 JF, (11 (J ) (1.18) 1 where rr 1;:.1 and rr:1; 2 an• the virtual phot.011 absorption cross sections with the photon and nucleon spins anti-parallel and parallel. (1.19) The relation is a.c; follows: (1.20) (1.21) Where (1.22) ca.u b<! regarded as the depolarization of the virtual photon and ll = rr 1, /rr'I' (1.23) is tlw ratio of lonp;itndiual and transverse virtual photo11 cross sections. The kinematic factor 11 is giwn b_v 'I/= f.jqi-/(E - E'f). For the transverse case th<' kinematic factors arc (1.24) 7 (1.25) and (1.26) lu th<'S<' formulae (1.27) i:-; tlw ratio of longitudinal to transverse virtual photon fluxes. The factors TJ and ( are small :-;o the photon asymmetries are approximately proportional to the longitudinal and transverse a.c,ymmetries. The fador D represents the polarization of the virtual photon for a fully polarized lepton. The photon asymmetries can be written in terms of the measured counting asymmetric:-; hy inverting these equations to give Ai= A11 D(l + (11) 11A.1 A11 ----~d(l + (11) - D (1.28) and (1.29) If A 1 i:-; written in terms of A11 and A 1 , we oht.ain a formula which will be used throughout this analysis. A11 - 1/.4"L· A I = I) (1.30) TlH' photon asymmetry A 1 i:-; bound hy (1.31) while A2 has the restriction [10] 8 k' k I' (I- ~)P ~ P+q Figure 1.2: DIS iu the quark-p;ut,011 model {1.32) 1.4 The Quark Parton Model In tlw quark-part.on model [11] [12], a nudcon is composed of point-like constituents, <'ach carrying a fraction of the total nudc\Oll mouwutmn. Iu the limit of an infinite 111011wut11111 frame, tinw dilation suppresses a11y intc\rnctio11s hc~tween these partons. Considc\r tlw scattering of a virtual photon with four momentum q as shown in Figure\ 1.2. For sufficicmtl:v larw\ Q2 , dnring tlw lifotimc of tll<' virtual photon (1/ '1Q2) tlw coustit1w11t partous <'il.ll IH\ c:ousidcn~d to 1><~ fn•<•. 111 tlw Bjorken limit (Q 2 ➔ oo a11d J/ ➔ oo with :r: = 21:,F constant) we can then considc\r <lee\)> inda.'itic scattering from a uudcon to he dasti<: scattering from a free quark a.11d write (1.33) where m is the mass of the parto11, P is the\ monumtmn of the nucleon, and E, is the !) fraction of the nucleon momentum carried by the struck quark. In the Bjorken limit we neglect terms proportional to m 2 (the mass of the parton) and M 2 (the mass of the nucleon) to observe the behavior of the terms proportional to Q2 and M v. The equation for the momentum fraction of the struck quark then reduces to Q2 f. = - - = :r. (1.34) 2./1,111 The Bjork<'ll :-;caling variable :r: rcpre:-.ent:-; th<• fraction of the parent nucleon mouwntum which was carried by the scattered pa.rton. It i:-; convenient to dcfiue a new set of four dimen:-;ioules:-; :-.tructure functions (F1,2 and .<Ji,'l.) for discussions of this high energy limit: (1.35) {1.36) (1.37) {1.38) 111 tlH' Bjorkcu limit, these new stru<:tur<\ fnndiou:-; arc predicted to be functions of only :r independent of CJ'1-. This behavior i:-. called :-.caliuv;. Experiments are performed a.t iinit<• 11 aud Q 2 when~ scaling violation:-; an~ <'XP<~d.cd and <~xperimental results are pres<~ntcd iu terms of !h and !h· These :-;trud.nn· fuw:tiou:-. ta.kc the following form at finit<~ ct· .l/1 v7JI = - -F1- - [A I + - A'l. ] 2.1:(l + R) {1.39) /I and F'l. .' h = 2.1:(1 + n) [A, 'l. _,1_ n - A 'l· (1.40) Rewriting the ::;tructure function g 1 in t<\I'IBS of the observed asymmetry A11 and A'l., we obtain 10 {1.41) These structure functions can be interpreted iu t<~rms of the momentum distribution of the partons iu the nucleon, written as: Fi (:r:) 1 :2 -'E-J('r)<'· 2 1 {1.42) F-i(:1:) • , T°E-j-(T)/l'i (1.43) t l t 1. • . • , where the index i nms over flavors, ci is the dmrv;c and f;(:1:) is the probability of finding a pa.rton of flavor i an<l momentum fraction :1: in tlw nucleon. In au analogous fashion, g 1 (.1:) and g2(:1:) can be iutnpretcd in terms of the helicity dependent mouwntum distrilmtious of the partous (1.44) {1.45) when) J/ (:1:) is the probability of finding a part.on of flavor 1, with momentum fraction :r: and tlw same lwlicity as the parent 1111<:l<\(>11. In the BjorkPu limit. tlw virtual Compton asymnwtrics .-l I aud A 2 cau be written as ( 1.46) A- - 2M1,j .</I + .'/'l. 2-N F, . {1.47) .4 1 has a simpk interpretation in the Bjork<~n limit. As CJ1 ~ oo, A 1 becomes gif Fi both of which haw interprdations in the part.on modd. Thus, A I can be interpreted in terms of the spin distribution of the nucleon. In the Bjorkeu limit 11 e -+- Figure 1.3: er tt in the Bjorkcu Limit e Figure 1.4: er H in the Djorken Limit Ai = ~ = Ei(J/(x) - Ji- (:1:))f,f ~_.!:__all- - att F1 Ed;.(x)e1 - Datt+ att · (1.48) This a consequence of helicity conservation iu the ultra-relativistic limit. The sign convention of A 1 can be understood heuristicall~· in tcrmi,; of the spin of the quarks that th<' lepton scatters from within the 1111dco11 a~ shown in Figures 1.3 and 1.4. Neglecting the ma.<;scs of the leptons and partons, the positive helicity lepton can 0111~• couple t.o a positiw helicity quark in the <·c•utcr of ma.<;s frame. If the spin of the uudeon is parallel to the beam spin, thiH selc>cts partons with spins opposite the nndeon spin (! - ) (Figure 1.3). \Ve can calculate A 1 for a SU(6) model of the nucleon with three constituent quarks. Given the proton wave function [13]: 12 (1.49) with , 1 <I> Ms = v'6 [udu + d·u·u - 2-u:1.td] (1.50) (1.51) (1.52) (1.53) It is easy to show Af = 4/9(u. t -u .!-) - 1/9(<1 t -,l-l,) = ~ 4/9(u t -·u .!-) + 1/9(d t -d -!-) 9 (1.54) or intcm:hanging 11 a.nd d A;' = 0. These naive~ predictions might be expected to be valid at medium values (~ 0.3) of :r, whc\rc~ the• valence quarks dominate. 1.5 Spin Structure Function Sum Rules Tlw initial motivating factor to measure\ spin dependent structure functions was to test two s11m mies: the Bjorken and Ellis-.Ja.ffo s11111 rnlc~i-;, which relate the integral of th<' spill strnctnn~ functions gf'" to thf' haryo11 weak decay couplingH. Bjorken Sum Ruic• The Bjorken 1-,m11 rule [14] rclatei-; the spin Ht.rnctnr<' finu:tions gf and gf to the ratio of the axial to vedor couplings, !JA/ !Jv obs<\rved in hcta decay. The Bjorken sum Rule is amazing because it relates high energy physic:s to weak nudear decays with only the assumption of isospin symuwtry and cmnmt algebra. In the Bjorken limit it. can be written as 13 l foo 1 9A [gf(x) - gr(x)]dx = -1-1 = 0.210 ± 0.002. (1.55) 6 9v The Bjorken sum rule has been derived in terms of an operator product expansion in order to calculate the QCD corrections at finite Q 2 • For three quark flavors it takes the form [15] 2 1 f [gr(:i:) - g~'(x)]d:r: = !1 .<JA l[l - n.,(CJ2) - 3.5833(n.,(Ci'1) )2 - 20.2153( 0 s(Q ) }3] lo 6 gv rr rr 1r (1.56) The HERMES data is taken at an average (}'1- of 2.5 GeV/c2 . At this energy transfer the strong coupling constant (a.,) is [lG] given by oiQ 2 = 2.5{GcV/<:}2) = 0.305. (1.57) The Bjorken sum rule then has the numerical value [1 [gr(:r:, Q2 = 2.5(GcV/c}2) - g;'(:r., C/2 = 2.5(GcV/<:)2)]d:r, = !1 gA l[0.8506] .lo 6 gv = 0.179 ± 0.008. (1.58) Ellis-Jaffe Sum Rul<~ The Ellis-.Jaffc sum rules [17] wm·e motivakd hy tlw orip.;inal gf experiments. A sum rule relating to jm;t _gf was deriv<)d lwcaus<~ at t.h<\ time 110 neutron data was anticipated i11 the rwar future. The Ellis-.Jaff<~ sum rnl<·s make two additional assumptions to r<'lat.<~ the structure functions of the prot.011 a11<l 11<•11tron to F and D the symmetric mu! antisyrnmdric constants describing haryou octet decay. The assumptions are • <\Xact SU(3) symmetry in tlw ha.ryon octet d<~ca.ys • no net strange :-;ea polarization The sum rules can be written as i 0 i P( )d·_ l.<JA( 53F-D) X - - - 1 +---- 91 .T, 12 !JV 3 F +D (1.59) 14 and 1 1 )dX _ -1-9A ( 5 3F - D) gn( - -1+----. 1 X o 12 gv 3 F +D (1.60) The violation of the Ellis-Jaffe sum rule is often interpreted in terms of the spin asymmetry of the strange sea. Defining a new variable .6.i = .I~ (f/ (:l:) - .fi- (:1:) )d:r: as the total fraction of the hclicity carried by a quark flavor, the integrals of the structure functions for the proton and neutron can he written as: 1 :r d:r - r = -.6.u + -.6.d + -.6.s 1 q;'(:r:)dx - r;' = -.6.'(J, + -!J.d + -.6.::;. I 0 1 0 ll( <11 .J . ) 1' 1 4 18 1 18 1 18 4 18 1 18 1 18 (1.61) (1.62) It is convenient to replace the flavor helkitic.c.; with the singlet (.6.u + .6.d + .6.s), t.ripl<!t (.6.u, - .6.d), and octet (.6.u + .6.d - 2.6.s) terms. These can be related to the haryou octet decay constants hy writing F am! D iu t.<•nns of the quark helicities. .6.u - !J.d F + D = ,.'IA I (1.63) _f/\1 .6.n + .6.d - 2.6.s :JF - D .6.u + .6.d + .6.s (1.64) (1.65) The cmT<!nt hc!st fit for F awl D is [18} F = 0.4G9 ± (l.008 D = 0. 798 ± (l.008 F/ D = 0.57G ± 0.OlG. (1.66) The structure function integrals arc decompos<'d iuto siuglc~t and non-singlet terms to include QCD corrections from an operator-product c\xpansion. 15 whern the perturbative QCD corrections tak<' t.lw form [19]: 2 2 2 Cns = 1- ( 0 •<;J }) - 3.G833(''·'~J ) }1 - 20.21G3( 0 ·•~Q ) ) 3 (1.69) (1.70) These perturbative corrections a.re necessary to make a meaningful test of the Ellis-.Ja.ffe sum rule a.t finite (J2. At an an•raµ;e CJ'2 of 2.5 (GeV/r,)2, these sum rules make the following predictions for the proton alHl ll<'lltron: r;· = -0.013 ± 0.005 (1.71) (1. 72) 1.6 Spin Decomposition of the Nucleon Th<• spin of the nudcon can lie dc\compos<'d into parts due to the quarks, the gluons and the angular monwntum. (1.73) where Lq is the orbital angular mom<•ntum of the quarks, !::i.G is the gluon spin contribution, and L 9 is the angular monwutum of tlw gluous. Since the gluons carry about half the momentum of the nucleon. it would not be surprising for them to carry Hi a significant fraction of the spin as well. DIS alone does not provide enough information for the decomposition of the nucleon spin. However, some additional assumptions and measurements can allow an extraction of !:!,,.q. The proton and neutron integrals can be exprc>ssed a.'i: (1.74) (1.75) where I:,,, Ip,, and / 0 are the triplet octet awl siuµ.;ld t.<~nns from equations 1.67 and 1.68. Solving these equations for l:!,,.q = Cl.n + l:!,,.d + .:\.s, one can solve for the nucleon spin carried hy the quarks. 6.t1 = 2_(f'' _ (F + D C,, 1 12 + :3F - D)C ) :3G "·' (1.76} (1.77) or: (1.78) Assumiuµ.; SU (3) Hymmctr~,, it iH poHsihlc to separate the components of the quarks' spiu with t.lw nwasurerrwut:,; of any three~ of th<' followiuµ.;: r~•, ff, F+D = l:!,,.u - l:!,,.d, and 3F-D = l:!,,.n - l:!,,.d - 26..-;. 1. 7 World Data Before HERMES Since tlw firnt mea.<;urement of gr [20], a S<~rics of ('X))<~riuwnt8 at SLAC and CERN [1] [2] [3) [4) [5) have measured the spin :,;t,ructurc• functions with increasing accuracy. These nieasurements have indicated a 'spin crisis· h<~cause the Ellis-Jaffe sum rules 17 OJ Proton 0.15 ,... "' 0 WJ E- 0.1 5'IC t T j EMC+SLAC 0.05 l 4 a ' 10 11 Q!(GtV1 Figure 1.5: World Data for q' ?\tulron 0 .o.m ..... "' e ..a.o5 r..- !>IC t ,0.075 -0.1 l 4 6 8 Figure LG: World Data for fj' a.ppPar to he violated. Nc~w cla.ta from HERMES and SLAC (E154 and E155) will contribute to the understanding of spin structur<1. Curr0.nt results for the Ellis-Jaffe sum rules for th<· prnto11 and neutron from these c~xperim<\nts an~ shown iu Figures 1.5 and 1.6. TlH· \'iolat.ion of the Ellis-Jaffe sum rules sccu in this data have sparked nmch iut<•n·st iu what carries the spin of the nucleon. 1.8 Semi-Inclusive Physics The HERMES spectrometer is designed to mc~asurc semi-inclusive asymmetries concurrently with the inclusive mea.<;urements. (The spcct.rornder is described in Chapter 18 2.) Additional information about the spin distribution of the nucleon can be determined by measuring the asymmetries with the leading hadron detected in coincidence with the scattered lepton. For example, the K- meson (us) is an all sea object and should be sensitive to the spin of the strange quark sea b.s. Only a limited amount of hadron identification was av.ailable for the 1995 running period (see Section 2.Cerenkov) and these results will not be discussed further. The semi-inclusive physics at HERMES will be significantly extended for the 1996 to 1999 running period. HERMES is the only spin structure experiment which can measure semi-inclusive asymmetries with good particle identification. Th<'..'><~ me,umrements will become increasingly important as our knowledge of the im..:lm,ive measurements improves. 19 Chapter 2 2.1 Experimental Apparatus HERA The HERMES experiment is installed in the Em;t hall of the HERA collider ring at DESY (Figure 2.1). The HERA ring is a high <!nerg~', high current positron and proton colliding beam facility. The Lea.ms are stored in 6.3 km circumference rings with mwrgies of 27.5 GeV (positrons) and 820 Gr\! (protons). There are four intersection points for the beams at the North, South, Ea.'lt and West Halls. Two collider experiments, Hl and ZEUS, are installed in the North and South Halls and two fixed target experiments, HERMES and HERA-I3 (h quark production with the proton beam), are in the East an<l West Halls. HERA was designed to allow the storage of spin polarized positrons and provides longitudinally polarized positrons at the East Hall interaction point. At the East hall, the proton and positron beams have been horizontally separated by 72 cm. This allows HER ~.f ES to operate an internal target without affecting the proton beam conditions. . . HER \-B ' beam directmo ~~ ZEUS r transverse polarimeter c(/~ 'S+N ~-~!' -------+-----{)-o . ~-. . -·- • "· ~~ 0 . -.. _ _..+/'✓ longitudinal polarimeter J HERMES spin• mtatnr I Figure 2.1: Polarized Eh:trons in a Sturngl: Ring HI 20 HERA WITH SPIN ROTATORS 4-May-94 -._ 70 . - - - - - - - - - - - - - - - - - - - - - - - - - - - - -... ~ -60 ~ ~ 50 ~ 40 ....; ~ 30 Rise <f electron polarization at HERA ~ 20 Longitudinal polarization at HERMES JO + o~~~~~~~~~~~~~~~~~~~~~~~~~~...___,_~~_,, /3 /3.2 13.4 13.6 13.8 14 /4.2 /4.4 TIME(h) Figure 2.2: Polarize<! Electrom; iu t.h(' HER.A St.ornge Ring 2.2 The Polarized Positron Storage Ring The development of techniques to polarize the positron beam and measure the polarization were crucial for the approval of the HER.MES experiment and represent an euormonH technical achievement. The beam iH polarized by the Sokolov-Ternm· dfod. [21]. Positrons in a storage ring can become polarized parallel to tlH' magnetic gnide field because of a small difference in the spin flip synchrotron emis:-;iou rates. The spin flip represents only a very Hmall fraction of the synchrotron cmi:-;:-;iou proceHH Ho the polarization tends to build-up over a long time scale. [22] The polarization increases in time exponentially with (2.1) For an ideal ring, the time constant for the polari:r,atiou ris<~ is (2.2) with re. the dassical electron radius and p th<• bending radius of the magnetic field (707 m for HERA). At 27.5 GeV, 1 = E/me. = G4000 and the time constant Tp = 37 minutes. Figure 2.2 shows the rise of the beam polarization in the positron ring. Psr of 92.4% is the theoretical maximum for the equilibrium polarization with a 21 homogeneous magnetic field. In practice, the polarization must be optimized for the non-homogeneous fields of the ring. It is important to minimize any depolarization effe<:ts be<:ause of the slow build up time of the Sokolov-Ternov effect. Any out of plaiw bending in the beam optics will <:ause a reduction in the polarization achieved. A positron with a betatron orbit (an out of plane oscillation) will feel non-vertical fi<,l<ls in the quadrupoles which causes spin diffusion. The solution for a dosed betatron orbit is slig-htl:v 1uon~ complicated but the basic n~sult is the same as tlw polarization in a constant mag1wtic field. A discussion of tlw dosed orbit solution [23] adds au additional t<'rm to describe the spin precession around the axis of the magnetic field due to tll<' positrons gyromagnetic ratio. The frequency of the spin precession (11 = 1< 9; 2 >) ifi r<'f'c•rred to a:-. the spin tune. Resonant depolarization occurs when the perturbing fields add coh<~rently over orbits of the ring. Resonances are expc>cted to satisfy (2.3) k,l,m,11 are integers, 111i and 1111 arc the horizontal and vertical betatron tunes and 11., is the synchrotron tune. [24] Special tunes arc used to maximize the polarization of the positron beam. The tunes an~ 1~111pirically optimized to maximize th<• beam polarization. The polarization generated by the Sokolov-T<'rnov dfoct is transverse but a longitudinal polarization is needed for the asyuunet.r~· nw,umrements. Two spin rotators (Figur<~ 2.1) are used to first rotate tlw positron polarization to longitudinal before tlw HERMES interaction point and th<~n to rot at<! t.lw l><~,un polarization back to t.rausv1!rse. The rotators [25] arc designed t.o rot at(' t.lw spin direction by 90° without dia.ngiug th1\ beam positio11 or slope at the int 1•ract.ion point.. Switching the longitudinal lH\am polarization requires the moveuwnt and alignment of the spin rotator magnets. The beam polarization was not switdwd duriug the 1995 run because of the several day shutdown required for this realignment. 22 La~r and Polarizing Optics Coliffl.&l(lf'!'i Pt1!-itrn11 Beam Calorimeter ■ ■ Sweepini Magnet Figure 2.3: Schematic Diap;ram of the• Compton Polarimeter 2.2.1 Measurement of the Beam Polarization A Compton laser polarimeter [26) measures the polarization of the positron beam. The scattering cross section of circularly polarized photons on transversely polarized positrons is asymmetric with respect to the polarization axis of the positrons. The laser light is scattered almost head on with tlw positron beam and is boosted from 514 nm to high energies (E1 = 0 to 13.8 Gc~V). The scattered photons are collinear with the positron beam. The enerp;y and point of incidence is measured with a sampling calorimeter composed of lea.cl-tungsten a.ll<I scintillator sheets. Figure 2.3 shows the layout of the polarimeter in the storage ring. A calorimeter divided into four quadrants can measure the total energy and point of in<:i<lcnce from the energies ckpositcd in each quaclrant. Tlw polarization of the laser is switdwd at 90 Hz and the asymmetry in the c:aloriuwtc(r as a fund.ion of vertical (parallel to !warn polarization) position can be couvcrt<id to a beam polarization. [22] The polarization measured with the hcam polarimeter is calibrated with rise time measurements. Resonant depolarization can h<\ used to quickly depolarize the beam. A measurement of the buildup of th<~ polarization Y<irsus time can be used to determine PMAX for the beam. 23 Movable Collimollor I ---Thin Exit Window - - - - ----- - - - -- -- -- -- - - -- ----- --- --- --- --- - - -- - - - - ... - - - - - - -- - - - -- - - --- - - -~ Positron Bc.u11 ' Fix~ Collimator Stora~Cdl --------- Thin Walled Beam Pipe Figure 2.4: Polarized Posit.row; iu a Storage Ring I'c:ompton(t) = kPMAx(l - (' -(1-/~i)-,-'-' 1 AJAX). (2.4) The constant C cau be extracted from machi1w parameters and is independent of any depolarization mechanisms which may affoct the maximum polarization. The vahws of PMAX and k am cleterminecl from a fit to the polarization risetime and asymptotic value after depolarization. The 'k factor' is used to calibrate the beam polarimeter measurements. The uncertainty iu tlw beam polarization is dominated hy a 5% uncertainty in the 'k factor'. 2.2.2 Synchrotron Radiation Bends in the positron ring have been minirniz<•cl U<\ar the East Hall to reduce the amount of synchrotron radiation incident on t II<' (\Xpcrirnent. A double collimator system is used to absorb the rr.mainiug synchrotron radia.tiou before the target. A fixed collimator is located dose to tlw t.a.rµ;<•t all(! a s<~c<mcl movable collimator is located 2 m upstream of the targd. as showu iu Figm<' 2.4. After filling the ring, the movable collimator is dosed to 3.0 mm from the beam axis. The two collimators are designed to shield the target cell from radiation prod nc<\d in the magnets before the target and radiation which scatters from the first collimator. 24 2.3 The HERMES 3 He Target The development of highly polarized 3 He internal targets has been very important in the field of nuclear physics. \,Vith high intensity circularly polarized laser light it is possible to achieve atomic polarizations of up to 80% for 3 He in sealed cells by metastability exchange. [27] The HERMES experiment uses a slightly rnon~ complicated apparatus. The He atoms are polarized in a pumping cell and fiow into a storaµ;e cell where they cross the positron beam several tiuies before hcing pumped a,,.,ray. The polarizations attained in a flowing cell am lower than a sealed cell. In order to polarize the helium atoms, they arc first excited by a weak rf discharge (f ~ 200kHz) in the pumping cell to the 2:i S1 l<~vel. Circularity polarized laser light at 1083 um excites the 2a S 1 ---+ tJ P transition allCl the polarization is transmitted to the nuclei by hyperfine interactions. Finally, the polarization is transferred to the ground Ht.ate nudei by metastability exchange. {2.5) At HERMES the gas is polarized in a JH1111pi11g cdl and the polarized gas flows into the positron ring. A T-shaped target cell (Figure 2.G) is used to store the polarized gas in the positron ring. The target cell is elliptically shapc~<l and large enough that scattc~riug from the cell walls was negligible. Figure 2.G shows the closest approach of reconstructed tracks to the heam. The storage cell has no end caps so the beam interacts with a pure :i He target with no dilutio11 from other atoms. The storage cell inc:rea.-;es the target density 100-folcl over a gas .id all(! c:cu1 <:r<'ate target densities of the order of 10 15 atoms/c-m 2 for tlw :1Hc targc~t. The target thickness in the HERMES storage cell is ddermined to have little dfoc:t on the positrou lifetime in the ring. The lifoti111(~ of the beam for atomic lm~msstra.hlung from thP. target gas is [28] z ) _ T, 1 1 8.lxl0 2r.atoms/cm2 ( 0 Tgns 'n ln(,if7 Z(Z + l) 11 ' 3 ) {2.6) 25 H, D~ 'H~ I t I I e· I I e l A I p(z)~' z Figure 2.5: Schematic: of the T-Sha.pe<i Storage Cell ... /() ~ 8 ;.... 6 ----- 4 2 () --~: ·,,. -2 -4 ----- -6 -8 ' I -/0 -20 -/0 {) /0 20 x(mm) Figure 2.6: Vertex Distribution of Reconstructed Tracks in the Target 26 where T0 is the revolution time around the ring (21 /ts). The total lifetime for the beam with the target gas is 1 1 1 Ttotn.l Tfl"·' T/,cnm -=-+--. (2.7) For T/,cam of 10 hours we are allowed a lifetime due to bremsstrahlung in the internal target (T,1a.s) of 45 hours which corresponds to a target density of 10 15 nudeons / cm2 • The total lifetiuw in this cas<' is 8 hours so the operation of the other experiments is not significantly affoctcd. The ga.-; is stored in th<• target for a few milliseconds ( ~ 100 wall bounces) before leaving the storage cell and being pumped away. It is obviously important to limit the depolarization of the target during the time it is in the cell. A pair of large Helmholtz coils provide a uniform 10 G magnetic field in the target region with gradients of a fow mG/cm in the cell with a smalfor set of correction coils to cancel the residual gradient(~ 200 mG/cm) of the spectrometer magnet. Wakefield suppressors [22] connect the target to tlw beam pipe. These perforated pipes reelncc wake fields from the electron bundws awl allow the target gas to exit toward the pumps. The polarization obtainable iu a flowing cell is lower than that obtainable in a scaled cell because the polarization is dependent 011 the residence time of the atoms in the laser light. Thus, it is desirable to minimize~ the flow rate by cooling the target a.,; 11mch a.-; possible without depolarization. The storage cell is cryogenically cooled to lower its co11ductam:e. The conductance of tlw storage cell depcucls on temperature so the How rate) of the cell can be decreased if the) te\IU{Wrn.turc is lowered. Tlw d1!11sity of t,lw l.arv;ct is given by Fl F 2C ./T p=-<X- (2.8) where F is the flow rate: l is the length of the storage cell; C is the conductance and T the temperature). Th<> depolarization of the :i H<'. ehw to wall bounces is small at temperatures > 20 K [2a] due to helium's dosed electronic shell. A series of tests wen• performed at Caltech with a deuteron beam (i Fl e(d, p) 4 He) [30] to determine 27 3 He(d,ptHe FRONT 40.0 .\i=30.9+/-0.6 % T Eb=6.4+/--"1.0 meV 30.0 20.0 10.0 0.0 -10.0 1 10 100 T [Kl Figure 2.7: Temperature Dependence of :i He Depolarization from Tests at Caltech the temperature dependence of the polarization precisely. The results of analyzing pow<~r of this interaction (Ao) as a function of temperature are shown in Figure 2.7. The cun·e and parameters in the plot arc a model of depolarization due to sticking to the c<>ll walls (31 ]. It was determined that tlw taq~et could be cryogenically cooled to 2[; K with no significant, depolarization due to wall sticking. Tlw absence of entrance and exit windows 011 tlw storage cell has significant bendits for the experiment. The external radiativ<\ corrections and smearing (discussed in S<)ction 4.2.2), especially for the small :1: data, could IH\ limited by reducing the amount of material for heam interactions hdon! tlw target gas and interactions after scattering. 2.3.1 The Measurement of the Target Polarization Two polarimeters were used to measure the target polarization. A pumping cell polarimeter (PCP) provides precise measurement of the polarization of the gas in the 28 •••••• ,. (j() , ..... • ••••• • ••••• • • • • •• • ••••• • • • • •• Figure 2.8: Polarization Measurements in the TOM and Pumping Cell Polarimeter pumping cell. The PCP measures the circular polarization of 668 nm light emitted from the 3 1D 2 state. The nuclear polarization is mixed with the electronic polarization of this state by hyperfine interactions and the relation of circular polarization to nuclear polarization has been calibrated to within 5% with NMR measurements. [32] The target optical monitor (TOM) measures the optical excitation of the target atoms in the storage cell by the beam. The 4 D 1 excited state of helium has a long lifotime (37 ns) compared to the hyperfine mixinµ; (1.Gus). Thus, for this level the nuclear polarization is transferred to the circularly polarized photons emitted by this l< vel. Th<' polarization of the atoms in the storage cdl can be measured by analyzing 1 the circular polarization asymmetry of this line. [33] Figure 2.8 shows the polarizations measured by the TOM and PCP which suggest there~ is negligible loss of polarization between the pumping cell and the target. The PCP measurement has a higher statistical accuracy and is used in the asymmetry analysis. The TOM provides a useful cross check of the polarization of the 29 target and is also used for the polarization measurement during a short period when the PCP was not working. 2.4 The HERMES Spectrometer The HERMES spectrometer was designed for the measurements of inclusive and semiinclusive asymmetries. To accommodate this goal the spectrometer has a large acceptance: up to ± 170 mrad in the horizontal direction and ± 140 mrad in the vertical direction. The storage ring beam lines divide the the spectrometer into two symmetric halves above and below the plane of the beam lines. The front detectors are placed as close to the beam line as possible and the minimum angular acceptance of the spectrometer is 40 mrad. 2.4.1 A General Overview The HERMES spectrometer, which is shown in Figure 2.9, has been designed to provide a large acceptance for both inclusive and semi-inclusive physics. At the center of the spectrometer is a dipole magnet with a large acceptance both above and below the plane of the beam. The spectrometer is left-right symmetric for the simultaneous measurement of positive and negative charged leptons and hadrons. Tracking chambers in front and behind the magnet give a good momentum resolution over a large acceptance for both the scattered poi;itron and the hadronic final state. A particle identification package containing a Cerenkov detector, transition radiation <l<\tector, prcshowcr, and calorimeter arc used to S<\parate the positrons from the hadronie background an<l identify hadrons over a limited kinematic range. 2.4.2 Magnet The HER1IES experiment uses a single H-frarnc magnet to bend charged particles for momentum measurements. The magnet was designed to satisfy many constraints:[28] • an J B · dl = 1.3T · m with less than a 10% variation within the geometric acceptance. / FIELD CLAMPS '-... DRIIT CHAMBERS MAGNET I m --I I ·'H• l"L:~IPIXG . CELL _LI 0 0 STORAGE M CELL ·I '---._, I\.-,---- i i i II ~ :II II m I ~~/ I I I ~:::; -~' PROPORTIOK.\L CHAMBERS \ ' l':RTEX Cll.\~IBERS ~ ~ --~ ~--~I=== j ., DRIFT CHA~IBERS RIGGER l'RESHOl\'ER HODOSCOPE DETECTOR /'--., I I ••···-·"---· [f) = I,~~tg~J'Y ~ ~ ~ ~ ;11 ::i:: ::: ~ 0) ~ SEPTUM PLATE t -E TRO C•.\LORIMETER c--i ~ CERENKOV :::, -2 bO ~ 0 2 3 5 FIG. 1. 6 7 lTI 8 31 • small stray fields ( < .lT) near the drift chambers • minimal influence on the electron and proton beam optics • a large acceptance to match the detector acceptance • low power requirements ( 600 kW) A magnet with field damps in front and lwhind the magnet and an iron septum plate in the center plane meets all thcHe constraints. The field clamps minimize the stray fields outside the magnet region. The septum plate surrounds the beam pipes, shields them from the magnetic.: field, and divid<'s the sp<~ctrometer into two identical halves (top and bottom). 2.4.3 Tracking For the 1995 data, the tracking was performed ,Yith drift chambers in front (FC) and behind (BC) the spectrometer magnet. The v<'rtcx chambers (VC) were not used in the tracking becairne of efficiency and hot win' problems. Separate track segments were formed in frout and behind the magnet. These partial tracks were joined by requiring the front tracks segments to join tlH' hack segments at the plane in the center of the magnet bend. Figure 2.10 shows the front and back segments for an event with a high multiplicity. The .-w<~ragc multiplicity waR 1.5 tracks/event for <'V<\nts <·ontaining a DIS positron. The HERMES reconstruction program (HRC) HS<\S a pattern recognition algorithm [34] to look for gronpH of wire chamber hits whid1 are <:oHsistent with tracks through the front or back region of the detector. The al).!;orithm clivicles the detector in small subsections (bins) and replaces the position and rc•solnt.iou information of the chamber with a binary hit - 110 hit pattern. The pattern for tlH' <'V<~nt is compared to a database of all possible patt.erm; corresponding to tracks. _-\ tn~<• search [35] is used to improve the dficimu:y of this method. Rath<\r than check all patterns at a fine resolution, the bins an• ORed together to pro<l11cr a lower resolution detector. The search is initially performed on a very low resolution detector (2 bins 1wr plane). Figure 2.11 shows the start of 1-1 tree search for an event c.:ontaining two tracks. As the resolution is increased 32 PRE Cherenkov Ks-Decay l e + vc Target gas Magnet Drift chambers Drift chambers HI TRD CAL Figure 2.10: A High Track Multiplicity Evcut iu the HERMES Spectrometer onl,v the patterns (sous) which an~ link<'d t.o patt<~rns {fatlwrs) which were matched at the 1wxt. lowest resolution are checked. Because the magnetic field clamps contain most of the magnetic field to the magnet r<!gion, the tracks are essentially straight in tlw tracking regions. This limits the umnhcr of sous JH!r father so the number of patterns checked in the tree search is siguificantb· smaller than the number of patterns in the database at the final resolution. Some triggers still required au exorbitant amount of computational effort to att<•mpt to find tracks. These events have v<~ry high chaml><!r multiplicities and produce Iarg<~ 11111nb<~rs of possible tracks which must IH' 1n·o< '. <'SS<~d iu tlH~ tree search algorithm. This can I><~ understood iu terms of th<' w1111l)('r of pa.tt<)l'llS g<\uerated hy the extra 11ois<' hits. As the computer gcrwrates larµp 1111111lwrs of possible patterns containing tlw 110is<· at low resolution, the algorithu1 hccom<·s a seqncutial search of all patterns at <~ach level. (Dcll'Orzo and Ristori [3G] provide a good discussion of this and their simulation results are tabulated iu table 2.1 for a 4 hy 128 bin detector.) A maximum multiplicity cut was implement<~<! iu the back chambers to eliminate these triggers. Events with large multipliciti<~s <'.011s1mwd larg<~ amounts of processing 33 Noise(%) 0 1 2 3 4. 5 Patterns Checked per Track Found 54 82 135 212 315 446 Table 2.1: Mean number of pat.terns compared pert.rack a:,; a. fuuct.ion of noise (Monte Caxlo simulat,ion) for a. 4 by 128 bin detector time and did not have tracks reconstructing to th<> target. It was determined through careful study that these events were the ref-lnlt of stray 800 GeV /c protons starting showers in or behind the calorimeter which would fire the trigger and produce a large number of tracks behind the magnet. The parameter for the multiplicity cut was optimized by minimizing the time to reconstruct a series of runs with large proton background without reducing the number of tracks found. The drift chambers have vertical wir<)8 for x poi-;ition measurement and wires at ±30° to the x wirci-; (u and v) . Three tn~<• lin<• 8<)ar<:lwi-; are performed in the back region for, the u, v, and x directions. A tree lin<' is found if a valid pattern is matched at the final resolution of the tree search. All hits within a certain distance (called the road width in Table 2.2) of the found tree lim' are mwd to fit to the line in the u,v, or x plane. The tree li1wi-; found arc joined to form partial tracks. lu the front region the tree search is perform<·d in the n and v directions and the hits in the x region are matched to the x projection of the intersection of the u,v tree lines. This alteration of the tracking algorithm was dicta.tc<l hy the desire to include the VCs in the analysis. The VC x wires an! not rnplanar and cannot be used in the tree i-;carch. The ch,unbcrs hav<! some inefficiencies; iu fact. with t.h<~ large number of chamber plane8 in the HERMES spectrometer, it is lik<'l~· that at least one plane does not regii-;ter a hit for any given track. The i-;earch alµ;orithrn ii-; modified to accept tracks that match only partial patterns. The maximum number of planes without hits (called the missing hits per treeline) repre8ents tlw number of bins which can be missing in a partial pattern match. The nurnl><'r of required hits is the total number 34 l..cvd ' I I ' ;, , __ ' 12 bins per plane) ; ' ,I ' ,,, 2 I ' I4 bins per plane) ; '' I', ' ' (H hins llL"f plane) f I' ( H, him; per plane) : : : : : : :)•ii"' :::::: ; Figure 2.11: Track Finding with a Tn•e Search at. Increa~i11gly Higher Resolutions 35 Tree Search Parameter Ro::i.J Width Front Number of Tree Levels Final Resolution of Search Resolution of Chambers Number Missiug Hits Per 'free Liue Number Missing Hits Per Tree Scv;mcnt Road Width (X Tree Linc) Ila.ck Number of Tr<'(\ Lc\'('ls Final Resolution of Search Resolutiou of Ch,uuhers Number Missing Hits Per Tree Liue Nmnber Missin~ Hits Per Tn\(' Sc•µ;mcnt Maximum !\lnltiplicit.~· Value 1.3 bins 11 322 /Lill 3{){) /Llll 1 3 0.4 cm 12 4G9 /LUI 225 /Llll 3 9 22 Table 2.2: Tree S1•ard1 Parnumt<\rs of planes per direction (4 in the front region, 8 i11 the hack) minus the missing hits. An additional parameter (missing hits per tree seg11wnt.) can place a more restrictive track finding cut. This parameter represents the total number of missing hits allowed in the three treeline:-; (or two trnclines and x proj<!(:tiou in the front) which match to form a track se~ent. For the final 1995 tracking, t.hi:-; parameter did not represent a more re:-;trictive cut than the tree line cut. The standard tn!e search parameters for the 1995 analysis an! listed in Table 2.2. Any valid pattern identified at the maximmu wsolution of the tree search is used to dcfilw a. potential track segment. The position:-; and resolutions of the chambers along tlw segment arc used to find a linear best fit for the track. A x2 test is used to identify valid track segments. lf multiple track s<~µ;mcnts ns<\ tll<' sa111<· l1its. th<· s<~µ;nH\nt with the best x2 is considered the valid track Hcgment awl others an• n~j<!d<)d. The track segments found in the front and lia<"k an• rnatd1ed at the center of the magnet. This matching is referred to as 'bridp;inp;' . Tlw track segments are projected to the center of bend of the magnet awl required to match within a maximum distance in x aml y and slope in y. (The magnet prirna.ril_v h<~nds iu the x direction and the difference in the x slope is used to det<·rmine the moment1m1 of a track.) The bridging parameters are listed in Table 2.3. 36 -- Allowed Pattern (Cont.1incd in datuhase of valid pallems) Illegal Pattern (Not in d.,tahasc l Dat.thasc contains str:,itht lin.: rro.i<--ctions lhroui;h HXlr~, efficiency chamhcrs Figure 2.12: Pattern Matchiug Algorithm Ilridgiuµ; Parnuwter X match Y mat.ch y slope mat.ch Value f, Clll :; nn 0.050 (dy /dz) Table 2.3: Bridging Parameters 37 Track se{!ments match within bridi!ing parJmetcrs Standard Bridging Single Space Point in Front Projection of Back Track Segment to Center of Magnetic Bend Forced Bridging - ,- ' I . Figure 2.13: Improving the Momentum Mca:mrcmm1t. Through Forced Bridging The mom<\Htum of a track is calculat<\d h~r interpolating a lookup table in slope and difference of tlw front an<l hack slopes in the magnet. The uncertainty in the angle in front of tlw magnet greatly reduced the resolution of the spectrometer. Th<' wrtex chambers are not used in th<' 1990 analysis because problems with hot wir<'s ancl efficieuc~' limit<~d the track r<'cou:-;trnction with the vertex chambers. As a result the HER.MES tracking is sig11ifica11tly hdt<!r hd1ind the magnet than in front. Tlw four hack d1amhcrs can accuratd? ddiuc a position and slope of a track s<)gmcut. Tlw two front drnmlwrs ar<' dcsig1wd 1.o fuuctiou iu conjunction with the V<)rtcx d1amhers. They ar<' too dose together 1.o a.c<'.matdy ddiue a slope. (The BCs hav<) a lcv<~r arm of 175 cm while the FCs hav<) a kn)r arm of only 12 cm.) To improve the momentum measur<)mcut , tlw track information from the BCs was used to rccalculat<' the slope in the front rcgio11. This is referred to as forced bridging. Three points ar<> required to determi1w tlw mom<)ntum of a particle bent in the spectrometer magnetic fiel<l. The higlwr n\sol11tio11 projection to the center of the magnet from tlw back chambers is used to dc\fine On<) of the points. The front 38 i I i 100 l 'i 11¢RMES p~liminary 80 - . O.fi 0.65 0.7 Figure 2.14: Ks Mass Reconstruc.tion chambers are used to define a single space point which is forced to match to the projection of the BC track segment in the plane of the center of the magnet bend. This method is shown in Figure 2.13. A resolution of ~p /P of 1. 75% was observed for the sp<X:trometer. (Monte Carlo simulations suggest a resolution of ~Pf P of 0.5% can he obtained with the vertex chambers. [37]) Improvements of the vertex chambers should improve the tracking re~mlution for the HERMES data taken in 199G. The momentum resolution of the spectrometer can be seen in the reconstructed invariant mas:-; of JC decays shown in Figure 2.14. K -~➔ 7r + 7r - (2.9) The momentum rnsolution of tlw SJH\d.romet<~r wa.., <kduc<\d from the width of the J(~ peak. The invariant mass for the two pious is cakulat.<\d from their momenta and opening angle. (2.10) The resolution of the Ks peak can be expressed in terms of the momentum resolution of the reconstructed pions as: 39 (2.11) The observed Ks width of 1.2% is consistent with a momentum resolution of 1. 75% which was determined from Monte Carlo reconstruction without the VCs. 2.4.4 Alignment An initial survey was performed to align all detectors iu the spectrometer at installation. Two methods are used to monitor the alignment of the tracking chambers in the spectrometer. Partial tracks either in front or behind the magnet were initially used to determine the relative alignment of the front and back drift chambers and monitor any changes. The FCs and BCs were internally aligned by minimizing the residuals within each set of chambers for partial tracks. Data with the S})<\ctrometer magnet off was used to align the FCs and BCs with the target. Without the magnetic on, the tracks from the target can be reconstructed from the BCs through the FCs back to the target. The residuals for the chamber planes were again minimized for the full tracking system. The magnet-on residuals are checked throughout the experiment to check for relative movement of the chamber planes. A laser alignment system is d<>Bigned to monitor continuously the alignment of the tracking detectors. Two Fresnel zone plate:-; an~ 11101mted on each detector. The interference patterns from a laser incident on the zmw plates are recorded with a CCD nmwra. Shifts in the detector position can he ohs<)rvcd as shifts in the focal pattern at t.he <'Hill<'ra. Although the calorimeter frame is separate from the structural supports on th<' rest of the s1wctrometer, the alignment systems checks for any changes caused hy Yibrations due to the calorimeter movement. 2.4.5 Efficiency The efficiency of the tracking detectors was carefully monitored with a program (ACE) which uses the tracks found in HRC to calculate the efficiency for each plane of chambers and an overall efficiency for the front and back regions. The efficiency for 40 Tree Linc I Tree Lin< 2 ! ' ! .~: • 2' Tree Line J . • I • •",. ... ,..,' 1· I Tree Linc 4 (NOi Ro.:onsmw..1e<l) •.' • • •' • .:' • Figure 2.15: The Chamber Efficiency Algorithm a given plane is defined by: number of tracks which haV<~ a hit in the specified region of the detector plane f=----------------------------------number of trac:ks (2.12) HERMES does not have the luxury of auxiliary tracking detectors which can be ns<~d to define a sample of tracks. The hodosc:o1><~s provide only crude resolution in tll<' x direction and there is no information on tlw possihk track position in front of t lw magnet without the tracking chambers. Au at.tempt has been made to select. subsamples of tracks which do not introduce a hia:-- i11 the calculation of the efficiency. Track Subsamples Ead1 plaw~ of diamh<!rs has its own suhsarnpl<' of tracks used to calculate an dfici< nc_y. This sulisa.m pl<~ consists of all tracks for which the information in that 1 plan<' is r<\dnndant. That is, it is belicwd that th<• t.rnckiuµ; algorithm would have found tlw track whether this particular plane did or did not fire. For the front region this can b<~ simply dcfiucd; a 11,v,or x plane is redundant if tlwr<' is a hit within the road width for this track iu <'ach of the other three planes in the same direction. In Figure 2.15 the tracks containing tr<!<~ lines like 1 and 2 would 41 Typical Chamber Efficiency I 89% Front Back 93% Typical Total Partial Track Efficiency Front Back I 88% 99% Table 2.4: Typic,al ACE Efficiencies h<\ used to calculate the efficiency of plan<' :r. It is i111portant to exclude tree line 3 to avoi<l biasing the efficiency upward. Tree line 4 is rejected by the tree search so it cannot he considered in the efficiency calculations. The determination is slightly more c0111plicat<~d in the back region because certain combinations of planes such as three missing planes in BCl and 2 are forbidden. There is still an unambiguous determination of when a plane is redundant for a tree line. There may still be a bias from the definition of tr<\e lines. Using the information from the plane changes the track slop<~ and position at center of the magnet. One could consider biases caused by a larger fractiou of tll<' tracks with four hits per tree line successfully bri<lging than tracks with thn\c hits per tree line. Initial studies suggest that these biases arc small [38]. It would be computationally daunting to att.<•mpt to perform the tracking repeatedly Il<'glect.ing chambers. It would require :3G t.imes the CPU to perform the tracking 1wgl<\d.ing one plane at a tim<~- In order to n\dnce this time and <let.ermine tracking cfficicnd<~s on the burst level, only 01w pass of tlw tracking was performed and the dfidcncy analysis wa.-. perfornwd 011 tlw tracks fo1111d using the chambers. ACE sorts the hits for <\ad1 chamber that is n•quin·d and counts the tracks where the Ii it is rnquircd or not required . Tlw <·ffi<"i<·1wi<'s an· a crucial part of the determination of whether or not the data is suitable for as~'•mnctry analysis. The efficiencies determined are functions of the high voltage. t<•mpcrature, atmospheric pressure, chamber gas composition, and TDC thn~shold . The <)fficiencies varied considerably from fill to fill as is shown in Figure 2.lG. Each set of points represents one fill of the ring with positrons. Typical values for the effideucies are shown in Table 2.4. The 42 a: 0 t- o m -;: 0.95 u C Q) u :E w iii .c E o.9 1- l'IJ .c (J C I'll Q) :E: 0 .85 - 0.8 - I 8157.5 I 8160 I I 8162.5 8165 8167.5 time (Arbitrary Units) Figure 2.lG: Tiuw Depcudeucc of the Cluunher Efficiency for a Series of Fills ACE efficiencies were used to monitor any of thei-;e dfod.i-; V<\rnus time and ensure the dia.mhcrn were working correctly a.11d i-;tably durin~ tlw periods used in the asymmetry analysis. The efficiencies were not used to correct the event rate so small biases in the ca.lcula.t<\cl efficiencies are uot significant. 2.4.6 Particle Identification A s<~t of four detectors (preshow<~r, calorimeter, Cerenkov and TRD) were used for particle identificatiou at HER.MES. The particle i<l<\ntification methods, efficiencies, and contaminations will be discussed in chapter 4. The location of each detector in the :-;pectrometer and the physics involved i11 particle identification is described below. 43 2.4. 7 Hodoscopes The HERMES trigger hodoscopes were designed and built at Caltech. Their design and testing will be discussed in detail in App<indix A. Two hodoscope planes are installed in the spectrometer and provide fast signals for the first level trigger. Each hodoscope is composed of 84 vertical scintillator paddles ( 42 each top and bottom). The paddles overlap to cover completely the HERMES acceptance. The scintillator provides a large response (200 p.e.) for minimum ionizing particles so the paddles have a highly efficient respons<\ at thresholds wdl above the single photo c~lectron level with very little noise. The photonmltipli<\r tuh<>s (PMTs) (Thorn EMI 9954) were chosen to give a fast, linear respons<~ with a short recovery time. This allows a fast trigger response and good enerp,y reconstruct.ion even at high trigger ratei;;. The first plane comiists of two rows of staggc~red scintillator paddles measuring 9.3 X 91 X 1 cma (2% radiation length) of BC-412 scintillator. These 1 cm thick paddles minimize the electromagnetic interactions but provide a large signal to minimize the trigger background. This hodoHcope plane is desiRned to discriminate photons which will shower in the other trigger detectors (Sect.ion 2.4.13}. TlH' second plane is operated as a prcshower detector. A lead sheet ( 1. 1 cm = 2 radiation lengths) called the preshower starts electromagnetic showers before the preshower scintillator. Figure 2.17 shows the second hodoscope with the preshower as it "·as installed. The hadronic interaction lmtRth is much longer than the EM radiation length and the difference in enerJ.?;y deposit,~d iu the scintillator for hadrons and positrons (ronRhly proportional to the n11111lu~r of charged particles in the shower after two radiation lengths} can l>c used for hadron/positron separation. 2.4.8 Calorimeter A lead glass calorimeter is used to measure the energy of the positrons. The calorimeter ii-; composed of 840 9.0 x 9.0 x 50 cm:3 blocks of radiation resistant FlOl lead glass as shown in Figure 2.19. The lead glass was Cerium doped to improve its radiation hardness. This increases the attenuation of light iu the lead glass but will protect the 44 ''L ~h,iru•m11 • 1•llh ,. I'.!.:!:\ (,-i,h• ............ , ♦ 1... 11 .. •IMlrd- + ha ll lr.e•d) All llimeulli•u 1• ,;:m. Figure 2.17: Isometric View of the Hodoscope Density (g/cm;i) Xo (g/cm2 ) RM (cm) Ee (MeV) ,\ (g/cm2) 3.86 10.73 3.28 17.97 137.7 Table 2.5: Physical Properties of FlOl Lead Glass glass from attenuation length changes due to radiation damage. Each block is wrapped in a layer of reflective mylar surrounded by a layer of opaque tedlar which ensures light isolation between the blocks. The calorimeter measures the Cerenkov light from the shower of particles produced by the Bremsstrahlung of the high energy positron incident in the calorimeter. The energy deposition of electromagnetic and hadronic showers in the calorimeter can be described in terms of several parameters. The most significant of these are the radiation length (Xo), the Moliere radius (Pm), the critical energy (Ee), and the hadronic interaction length (.X). The depth required to contain a shower has a logarithmic dependence on the 45 incident energy and for a 27.5 GeV /c shower is given by: [39] £(98%) '.::'. 20X0 . (2.13) L(98%) is the length needed to absorb 98% of the energy of incident particle. The calorimeter is thick enough (18 radiation lengths) to stop the scattered positrons after the showers begin in the preshower (2 radiation lengths). Au energy measurement is made from the Cerenkov lip;ht emitted by tll<' shower of particles emitted through Bremsstrahlung and pair production a.-; the positron stops. Er is the energ-y at which ionization <~1wrp;y loss <~qnal the loss from Bremsstrahlung. Low energy particles (E '.::'. E,:) arc quickly stopped by ionization losses. The critical energy can be considered to be the end of show<~r development. At energies above the critical energy, a tree of progressively lower erwrp;y particles develops in the calorimeter. Showering particles below the ionization energy arc quickly stopped. The total track length of the showering particles in the calorimeter is estimated to be proportional to E/ Er.. Lead gfa.'-ls has a high index of refraction (n=l.65) and electrons and positrons prodnc<\ Cerenkov radiation over tlwir <·ntin\ track length. The number of Cen\nkov photons is therefore proportional to track l<\ngth and also the incident <~nergy. It is 1wcessary to :-,elect a region of blocks large enough to contain the transverse distribution of the shower. The transverse clistrilmtion is dominated by multiple scattering for the lower <\nergy particles. The Molim·e radius (Pm) describes the average lateral deflection of low <mergy el<~ctrous in mw radiation length. The lateral del><'Hdenc<~ of tlw high erwrgy show<\r is given l,y t l1<· typical angle for brerrrnstrahlung <~missio11 (8 1,rr,m., = ·m/ E). Tlw transverse distri 1>11 t iou cau be described a.<; a central <"Or<' from brems:-;trahlnng with a halo d1w to nmltipk scatt.<•riug. For the purposes of <'llPfJ,W rrwasnrcuwnt, the show<\I' occurs within a <"yliudcr of radius 2 Pm· For tlw HERMES calorimeter, 2 Pm is 6.5 c111. To ensure the selected cluster contained the full energy of an electromagnetic shower, three by three clusters of blo<:ks W<\rn chosen. Even if a track enters the calorimeter ur.ar the boundary between two blodrn, the full energy shonl<l be contained in a dust<~r centered on either of the 46 blocks. The resolution of calorimeters is described with two terms; a term due to photon statistics and an intrinsic resolution mostly due to shower leakage and miscalibration. The HERMES calorimeter clusters have a resolution [40] of J o-(E)/ E[%] = (5.1 ± 1.1)/ E[G<'l'] + (1.5 ± 0.5). (2.14) Hadrouic show<~rs have a more complicakd distrilmtiou because they combine small ionization losses with large energy depositions due to hadronic interactions. These hadronic interactions produce large muuhers of pion and nucleon secondaries (including many 1r0 's which decay electromagnetically). Similar to the radiation length, the hadronic interaction length (A) d<!S<TilH~s a characteristic scale for hadronic interactions. The calorimeter's length wa~ miuimized to wduce the probability of hadronic interactions. Hadronic showers are also mw:h wider than electromagnetic showers. The secondaries in a hadronic show<!r have significant < PT > and produce a wider deposition of energy. As a. mc;;ult, a significant portion of the incident energy of hadrons can he carried out of the calorimeter by nucleons and charged pions or deposited outside the Hhowcr cluster. Figure 2.18 shows a GEANT 3.12 [41] l\fonte Carlo spectra for three types of particles showering iu the calorirrwter. The ratio of e1wrgy deposited to momentum is normalized to 1 for the electrons. Tlw ,,. JH'ak is the miergy deposition due to ionization for a particle traversing the calorim!'t,er. The 1r distribution contains a broad peak due to hadronic showers with a miuinrnw iouiziug peak due to 1r's which do uot have a large hadrouic intcra.<:tiou iu t,)l(' <·alorimd<\L The difference in the fraction of energy contained in a thre<~ h:v thrP<' <"lnst<)r of blocks for the two shower t~11ws is us<)d to distinguish posit.row-; from hadrons. Tlw calorimeter is mounted on a 1110Yahk platform. It ll!OV<\S 50 cm away from the beam to protect against radiation damage duriuµ; dump and injection. To monitor possible~ radiation damage, four additional l<\ad g;lass counters were mounted near the proton and electron beam pipes. The::;e blocks wc\r<) made of a much more radiation sensitive material than the calorimeter aud then~ was no evidence of radiation damage 47 !l = = 0 U 2000 1500 5000 µ 1000 500 .... 10000 1T 2000 e 1.2 E/p Fi~urc 2.18: Mont.(' Carlo Calorimeter R<•spo11s1• for r, G1iV /c Particles 48 ··-... _) ' 20 cm ···· 9x9x50 cm .I 90cm ( /0 cells) 48 cm 90cm ( /0 cells) 371'1 m1 (42 cell.,') Fig1m• 2.1!): Isometric View of t.lw Caloriuwt.er 4!) exit window 1.•nu-,u\1:1.• winduv.• 111it'1"11fS IIOOmm Figure 2.20: HERl\lES Ccrcukov Dl't<•ctor in these~ blocks during 1995. Because the HERMES spectrometer has au open design, radiative photons from the tarp;d vcrt<~x arc' oh:-;erv,~d in the spectrometer. This photon distribution peaks a.loop; the mouwutm11 wet.or of the emitting positron. If the momentum is above about 10 GeV these photons arc not rc.'-iolwd, but smn11ied iu tlw energy of the calorimeter. This c:a11 result in au upward hias iu th,, E/p ratio ll<'nrnse the spectrometer does not Iwud t.lw hip;h moment nm positron c\11011gh to r<!solv<' the two dusters. 2.4.9 Cerenkov Detector A tlm\shol<l Cereuk(n- d,~tector was used to distinp;nish part.ides which have a velocity ahov<\ t.h<! local vd<wity of light iu the rn<·dimu. Tlw o~reukov dfect is well described i11 llllllWl"OUS texts [42]. Tlw HERMES Cen•nkov <letector (Figure 2.20) w11sist:-; of two identical threshold <letectorn, above and below the beam line. Tlw radiator in 19!)5 was nitrogen gas at atmospheric pressure and room temperatun!. The c,~rcnkov light is collected in each count<)r hy a set. of 20 mirrors and photomnltipli<~rs arranged iu two rows of ten in each det<!dor a,'> 8hown in Figure 2.20. The entrance and exit windows are made of 50 Particle Mass (GeV /c) electron pion kaon proton 0.0005 0.139 0.493 0.938 Momentum Threshold (GeV /c) Nitrogen C4Fio 0.02 0.01 5.72 2.76 20.23 9.78 38.42 18.61 Table 2.6: Momentum Threshold of Cerenkov Detector tedlar/mylar. Gas filled Cerenkov detect.om an~ esp<~ciall~- us,~ful in high energy experiments because their low index of refraction allows tlw separation of particles with high {3. For nitrogen gas at one atmosphere pressure, this gav<) au index of refraction, n, of 1.000298 at 589 um [43). Iu 1995, the C<'n~nkov was used primarily for electron/hadron separation and this was the primar~· motivation for the use of nitrogen gas. The detector must have large, thin entrance and exit windows to cover the acceptance behind the magnet and minimize the scattered particle's interactions before traversing the i,econd set of hack drift chamlwrs. I3ec:ausc of these windows, the Cerenkov cannot support a large pressure diffonmtial with tlw Em;t Hall and must be near the local atmoi,pheric prc&<.;Ur<). The difforential prcssun· with the atmosphere was slightly positive) to protect tlw purity of till' nitrogen gas from contamination by room air. Till' momentum threi,holds for Cc•n•nkov light c·mission is determined by the equation. '/ II, I', = --;:::== J11?· - 1 (2.15) Tlw C<•nmkov thn)sholds for various partic:lc~s iu uitrogc~n ga.<.; at one atmosphere are listed in tahlc 2.G. The Cc)rcnkov d<•tc•C'tor was usc•d to irnprow the hadron rejection for particles with a momentum lwlow (i Gc•V /c. [klow this momentum, hadrons do not produce significant Cerenkov radiat.iou i11 11itrogeu ga.<.; at atmospheric pressure. Other ga.'ies can he 1rned for differeut purpm,cis. Tlw Cerenkov was filled with C 4 F10 (n=l.001270) [43] to perform II identification owr a larger momentum range in 1996. The second maiu issue for the performaH<:<) of ;t Cer<!nkov detector is the number of photoelectrons detected in th<~ photoumltiplic\r tul><!s. The number of Cerenkov 51 photons is proportional to the length of the radiator so a large radiator is required to produce a large signal. The HERMES Cerenkov faced serious problems because the area behind the magnet is extremely crowded and scattered particles enter the Cerenkov at many different angles. The length of the radiator for the HERMES Cerenkov is 90 cm. The average number of photoelectrons for a /3 = l particle ( n;,:) wa:-. 3.0. The response for heavier part.ides is given h~·: (2.16) Tlw largest component of the hadron background is expected to be pions and the < nP" > versus momentum is shown is Figure 2.21. The mean response as a function of monwntum shows the correct threshold hehm·ior although the observed number of photoelectrons is lower than would be expected for pious alone. This is not surprising since the hadron sample is composed of both pious and heavier hadrons which will not emit Cerenkov radiation. Tlw no1t-:wro mean signal for hadrous hdow the C<~renkov threshold for pions is caused by scintillation in the Cerenkov gas and knock on electrons. The single photo electron peak due to these procC8ses cau he se<\ll in Figure 2.22. A seri<~s of LEDs were used to calibrate t.lw C<~renkov. A separate calibration trigger fin\d the LEDs at 1 Hz and recorded th<· gain at the single photoelectron peak for each tube. 2.4.10 Transition Radiation Detector Transition radiation (TR) is produced when a n·la.t.ivistic particle crosses the bounda.r~· h<~tw<'<'n two uwdia with diffor<\llt di<~kct.ri(' constants. This phenomena can be understood classically from Maxwell's <~quations much like Cerenkov radiation (44]. The <~mission of transition radiation (TR) from a. single surface is linear in the Lorentz factor (, = E / m). Ideally, a TR radiator consists of a series of foils at a regular spacing to ensure constructive interference of the generated TR at each houn<lar~· followed hy an X-ray detector. It ,wmld be impossible to maintain the 52 ui 3 ~------- - - -- - - - - - - - - - - - - e;, .,,a, C 8. .,,a, • 0 C 0 "' 0 0 0 a: "C Meas!ffed Hadron Response Expected Pion Response (Theory} 0 0 2 J: • • • • • 0 C :g :;; 0 • • 0 • 0 • • • • . ,. 5 10 15 Momentum (GeV/c) Figure 2.21: Cerenkov Response for Hadrons . c:, 0 0 10 - ·1 2 , Cerenkov Signal (P.E.) Figure 2.22: Cerenkov Response of Hadrons Below tlw Cerenkov Threshold 53 Momentum (GeV /c) 5 25 Lorentz factor (-y) Positron P ion 9785 36 48923 180 Table 2. 7: Lorentz Factor for Positrons and Pions spacing for a large TRD such as the one at HER :11ES. Instead, a random matrix of fibers is used to provide a large number of intcrfan~s. 111 this case, the TR is viewed as forming in a "formation zone." The effects of intcrfornuce cause the energy flux to saturate\ after the formation zone. Various configurations wc!re tested to find a fiber matrix with a good yield of TR. Only high energy electrons and positrons haw a high enough 'Y to produce significant TR (see Table 2.7). Hadrons produce au mergy deposition consistent with a minimum ionizing particle crossing the proportional chamber. The HERMES TR.D consists of six identical modules above and below the plane of the beam. Each module contains a radiator followc>d hy a Xe/CH4 filled proportional c:hambc'r as shown in Figure 2.23. A 6.5cm thick random matrix of (10-30 µm radius) polypropylene fibers is used as a radiator. Th<' tram;ition radiation produced by partidc•s with high energies i:;; typically in the X-rn.,· rep;iou. The8e X-rays are detected in 2.5-l c:m thick proportional counters with 12.7 m111 wire spadng. Xe/CH4 (90:10) "·as chosen a.-; a ga.-; mixture for the TRD lwca118c Xe ha.-; a very high X-ray absorption cro88 Hc•d.ion (i.c~., high Z). A significant backbrround for the TR.D is 6 - ray production in the proportional chamhc'rs. The 6 - rays are prefc~rentially emitted perp(~ndic:ula.r to the particle. How('n'r. thC' <) - rays which arc emitted nearly parall<'l to a wire can be trapped by the "·in;s <•b:tric field aud deposit a large amount of 1•1wrp;y iu a single module. A trun- rntc•d 11wa11 of the six modules was used in tlw anal~·sis 011 tlw TR.D signals to improve the r<'jection of hadrons which emit 6 - ray. Y:,f=, T RD; - '/f/,(1,'.I:(T RD;) Truncated Mean = - - - - - - - -- -. 5 (2.17) The truncated mean is less sensitive than the snm of the modules to a large energy 54 cr---i .lt 75µm j Radiator .1 12.7mm ·1 63.5 mm ---11 25 4 mm 11• - - - - - 10.16 6.35 mm cm - - - - 1 Figure 2.23: TR.D .Mo<iul<) deposition in a single module and can provide 100:1 hadron rejection at positron efficiencies > 98%. 2.4. 11 Luminosity Monitor The luminosity monitor detects the Bhahha scatt<\ring of the positron beam from the electrons in the target atoms [45]. Two calorimeters w~ar the beam pipe detect scattered leptons at angles expected for syunnetrie Bhal>ha scattering. The luminosity is the rate of coincidences with energies greater than 8 GeV in each calorimeter. Tlw calorimeters arc made from 12 (22 hy 22 h~· 200) rnm:i NaBi(W0 4 h crystals. ~aBi(\V0 4 ):L was chosen for its high n~sistaHc<' to radiation damage. Tlw calorimeters an) placed dm;e (30 111m) to tll<' IH'alll pip<\ to look for Bhabha scat.t<·rcd pi>sitrous and electrons with enerµ;ic•s lwl.w<~<~n 8 and 20 GcV /c (Figure 2.25). Them is also a significant singles rat.P with a lm-ge energy deposition in a single caloriuwtcr. Coincidence rates vary between 40 and '.200 Hz at a nominal target density of 10 15 nucleons/cm 2 and beam currents between 10 and 35 mA. Precise knowledge of the luminosity is Hot nen~ssary for the asymmetry measurements. Only the ratio of the luminositi<~s for th<• two spin states is necessary. Cal- 55 io.&s G.5&511 :t 0.1111£-m ± ,g "::, i ~ =~ "ii 0.6 C ~ • ~::, ~ . --.-· • • • • • • a: ?:o.ss i _,::, .., ---~----'------~ ,. •• 10 lumi vs curr 25 :JO Current (mA) Figure 2.24: Current Dep<•udeuc<' of t.lw Lumiuosity cnla.tions of the absolute luminosity arc c:omplicat.<~d lw<:anse many Bhabha scattered l<\ptons travel through the thin wallc><l h<'am pip<~ and s<~ptum plate. The energy degradation in these media is significant and vm·~· s<~nsitiv<~ to scattering angle. The luminosity monitor has very small backgrounds. There is no rate is the lumiuosity monitor when the beams are dn:ulating the rings but there is no gas in the target. Figure 2.24 shows that the lumiuosit~· rate is very well described as pro- portional to the product of the current and target density. A term proportional to (current times target density) 2 would l><• expected for random coincidences in the luminosity monitor. The random coirn:id<·nccs n•pn~s<·nt l<~ss t.hau 1% of the rate in th<• lmninosity monitor and varies slowb· 011 tlH' ti1tic seal<· of the target polarization flip. 2.4.12 Gain Monitoring System Lw,cr gPncrnted light signals monitor tlw gains of t.ll<' pr<'shower, calorimeter, and luminosity monitor. A 500 um dye la.c.;er is ns<'d as a light source for the gain monitoring syst<~m. Fiber optic cables are used to cm-r~- the light to the second hodoscope, calorimeter, and luminosity monitor. A rotatiug filt<)r wheel attenuates the laser 56 ------- ... C.ahMlmch.'1' ( ',11, trillk.'h:r ,, 11,in w.iUcd ~ tlc.un Pirc 120mm '1011m Fif!,llre 2.25: Lumiuo:-;itY .\l011itor 57 0 C c( G) ~3000 0 0 .c 0. 2000 - .f 1000 1000 0 2000 Hodoscope ADC Fig1m~ 2.26: Gaiu Monitoring Data for One Run pulses and provides light pulses of six different amplitudes to the detectors as well a.-; triggers with 110 light. The gain is measured rdativ<~ to a group of photodiodes. Photodiocles were chosen for their long tnm gain stability. Th<' la.<;er pulses at ~ 1 Hz. Tlw gain moui tor data for a single hodoscope paddle aud run are shown iu Figure 2.26. 2.4.13 Trigger The ma.iu HERMES physics trigger is a c:oiuci<l<·11n~ or th<~ Imuch crossing and a series of detc~:tors which indicate a pot.<'utial DIS positron in the spectrometer. Trigyer [(Hltov n H2top n CALt 011 ) U (Hl1w1 n H2 1m,. n CAL1.,ot)] n HG The components in the trigger are: (2.18) 58 • HC = the bunch crossing time provided by the accelerator RF system ('HERA Clock') • HI = a signal above 1/2 the expected signal for a minimum ionizing particle in the first hodoscope • H2 = a signal above 1/2 the expected signal for a minimum ionizing particle in the second hodoscope • CAL = A signal above 3.5 GcV in a 'two column sum' in the calorimeter The 'two column sum' is an analog OR of :20 calorimeter blocks in two adjacent columns. There are 41 column sums for each half of the calorimeter (42 columns). The column sums a.re staggered so every pair of adjacent columns is included in the trigger. The details of the calorimetry were discussed in Section 2.4.8. The columns should contain most of the energy of an EM shower regardless of the position where the positron hits the face of the blocks. Scattered positrcms with less than 4 GeV /c monwntum cannot be used in the asymmetry a.nal.vsis lwcause of large radiative correctior1s (Section 4.2.2). Thus, the trigger threshold was chosen to select showers which deposit mon• than 3.5 GeV in tll<' calorinwter. This calorimeter threshold provid<~s a factor of 10 hadron rejection a,ll(l acc<~pts tlw positrons in the interesting energy range for the experiment. The arrival times of beam hunches at the HERMES interaction point are measured hy the HERA Clock and thiH signal ii-; delayed to lw the final element in the fourfold trigger coincidence. Background Then· were two major d<~nients to th<~ Imckgro1111d Ill t.lw HERMES spectromet.<ir. Charged hadroni-; can fin• tlw t.rigµ;<'r if a sig-r1itica11t <~11crgy is deposited in the calorimeter. The hodoscope elements r<~quin~ a d1a.rg<~d particle to traverse the spectrometer (the firnt hodoscope rejects photoni-;). An <~ncrµ;y deposition of more than 3.5 G<N from a hadronic shower or a high energy photon in coincidence with the hadron can tire the trigger. The trigger rate from hadrons with > 4 GeV /c momentum is 59 HI H2CAL I l◄ ERAOud, I Protons Tim..: Figure 2.27: Trigµ;cr Timiug suppn~ssed by a factor of ~ 10 by the calorimct<•r threshold. Hadrons in coincidence with a high energy photon also provide a significant trigger rate. There is a second background from the proton hcam. The proton and positron beams arrive at the interaction points simultaneously in the HERA ring. This means there is a time difference of 42 us (2 x 7 m) hetw<~cu their interactions with the calorimeter relative to the HERA clock. This diff<•n~uc<! is exploited to veto the proton events with the clock :-;ignal. Effectively, the caJoriuwt.er and hodoscope signals are early relative to the HERA dock for protons. Figure 2.27 :-;hows the timing for the standard proton and positron bunches. The coirn:idcucc timing is set so protons showering through the spectrometer will not fin· tlw trigg<~r. The protons can also have stable orbits outsid<• of the standard orbits defined by the RF, thus showers from protons outside tlw RF l,uudws which interact upstream of the calorimet<~r can fire the trigger. This background varied dramatically from fill to fill and <•veu within fills. Triggers a.'-isociated with this lm.ckgrouml do not contain tracks which reconstruct to tlw tarp;<~t and ha.v<' a clisti1wtive high multiplicity in the back dct<~d.ors due to the 800G<N /c proton showers tr;m~rsiug the BO,. This background c;u1 contrilmte significantly to the dead time in the data acquisition system because they occa."iionally have a high rate and the t,rigpprs have a large size due to high umltiplieitics in the chambers <wuts. 1 In g<~neral, the dead time was very small for most of the data taking. With a current of 30 mA and a targd <lensity of 10 15 nncleons/cu1'\ tlw expected DIS rate is 4.4 Hz [22]. Typically the trigger rate is 65 Hz and the liwtime is 95%. Approximately 30 Hz 60 of this rate is due to hadrons which deposit enough energy to trigger the calorimeter and the remainder ~ 30 Hz contain no tracks. (These are probably due to photon conversion before the first hodoscope.) The trigger rate did reach 200 Hz when the proton background was very bad. 61 Chapter 3 3 .1 Particle Identification Particle Identification A dean and efficient idc•ntificatiou of the scatten~d positrons is crucial for inclusive nwasuremcnts in the HER.l\IES experiment. Furthcrmort\ it is desirable for semiindusive physics that hadrons be identified ov1!r a large kinematic range. The HERMES experiment uses four particle identificatiou d1~t.ect.ors: a lead glass calorimeter, a pn~shower detector, a Cerenkov detector and a. transition radiation detector. In concert, these detectors provide clear separation of hadrons and positrons. The goal of the particle identification \\'a!-i to use this informatiou to extract an optimal sample of positrons with a high efficiency over all monwnta with low hadron contamination. The detect.on, were discussed in Chapter 2. This chapter shall focus on the identification of positrons and hadrons m;ing these detectors. As an introduction to this discussion. tlu~ n~spo11s1\ of the detectors to hadrons and positrons is shown in Figure 3.1. The samples of particles ,wrc selected hy placing strict cuts on the other particle identification detectors and th<~e cuts an~ a convc~nicnt starting point for the particle identification dis<:ussiou. 3.2 Particle Identification Cuts A simple part.id<~ idc\ntificatiou sd1cm1) would IH' a sC't, of cuts on the spectra in th1• PID detectors. This 1·om1110nl>1 used method is very convenient because the positro11 l'fficiern:y and hadron rejectiou fa.c:tor cau be) uwa.sured for each detector iud<•1umdc\ntly. The hadron r<>jection factor for the calorimeter is low because most of tlw calorimeter's hadron rejection is at the trigger level. For example, most hadrons with 5 GeV /c momentum deposit less thau 3.5 GcV/c in the calorimeter. (This is effectively a first levd trigger cut at 0.7 iu Figure 2.18.) Efficiencies and hadron rejection factors for a series of cuts is provided in Table 62 0.02 Preshower Calorimeter 0.1 0.015 0.075 Hodrons 0.01 llodcons 0.05 •. ✓- ; ✓ \ ~ I' 0.025 ♦ ♦ . • ,/· __c,!!!(IJ...,_.,-i ' - - . 1 . . - . , ~ : . . . _ i_ .$P 0.01. 0 Energy (GevJ 0.5 1.5 1 2 Energy/Momentum TRD Hadrons - ♦ ♦ 0.005 0 0 0.001 0.08 ~ / Positrons - Positrons P < 6 GeV/c 0.06 -1 10 0.04 -2 10 0.02 0 0 20 10 _;30 40 ~o Energy (keVJ 0 2.5 5 7.5 10 Photo Electrons Fip;mc 3.1: Particle lclcntification Detector Spectra for All Tracks in the DIS Acceptance Dd.ec:tor Calorinwt(•r Pre.<ihowcr TRD CerenkoY All Four (P < GGeV/c) Cal/Pre/TR.D (P > GGel'/c) Cut E/v > 0.8 E > 0.0lGcV E > 17.5kcV S'i_ynal > 0.25P.E. P11:-;it.rnn Effici1111cy ().!)!) 1 0.!)G9 0.975 0.!)38 0.88G 0.945 Table 3.1: Efficiency and Rejection Factors for PID Cuts Hadron Rejectiou 0.752 0.914 0.930 0.956 0.999 0.998 G3 3.1. This set of cuts provides very good hadron rejection both in the momentum range where the Cerenkov is useful for PID and at higher momenta. 3.3 Likelihood Method Rather than using cuts on the individual detectors, tlw information from the particle identification detectors has h<~eu combined into a likelihood function which describes the probability that a particle is a lepton or hadron. This more complicated particle identification scheme has been chosen to ad1icwe a hip;her positron efficiency while retaining a large hadron rejection factor. The likelihood functions arc derived from tlw measured spectra of hadrons and leptons within a momentum and angle nmge. The likelihood of a certain type of particle is given by the probability of a lepton at the designated momentum and angle producing tlw given signal dividc\d h~, tlw probability of a hadron giving the signal. The likelihoods arc based on a Bayesian probability cak:ulation. {3.1) Iu this equation the following variables an\ m,cd: JI is the momentum of the particle, .f (c 4 Iv) is the ft ux of posi trous with mouw11tm11 p, Si=l ,1 are the calibrated signals of the particle iclcntification detectors, and P(AIB) is the prohahilit:v of A µ;iwu 13. The probability cldi11<•d iu t,hi:-, way \\·as not nscd for the particle identification hc~ca.nsc of ambiguities in t.lw <lcfiuitiou of t ll<' fl11xc~s. Tlw fluxes depend on the choice of physics (e.g., inclusive or only c\Y<'nts with multiple tracks) and the particle identification variables (PID) were c:hoseu so tlw cuts would be independent of these fluxes. A likelihood ratio was defined for use in tlw pmt.ide identification: 64 Particle Identification cut PI D3 + 0.31T RD(keV) > 5.48 PI D2 + 0.5 IT RD(keV) > 9.00 PID3 > 0 Fraction of Data 82% 15% 3% Average Contamination 0.9% 1.7% 1.6% Average Efficiency 99% 99% 99% Table 3.2: Average Contamination and Efficiencies for the PID Methods Used +I P(Si= l ,4 je+IJ,) R(c J>, si=I,4) = I'( S·1= 1,411/, +1J>, ) (3.2) The likelihood ratio is either very Hmall or wr~' larg;•~ for most tracks. This distribntion cau be viewed more <~ru.ily by diHplaying; the log; of the likelihood ratio. The PID variable (3.3) will be used throughout this analysis. 3.3.1 The Likelihood Functions Three difforent particle identification fuuctiouH ,wn~ defiued for use in the final data analysis. Two log likelihood ratio variableH wen~ nHe•l, PID3 and PID2. PID3 is the log of the likelihood ratio for the calorimeter, preshower and Cerenkov. PID2 is the log of the likelihood ratio for the calorimeter and pn~hower. PID3 and PID2 were used in conjunction with the '<lowu-Hhifting' scheme. Downshifting is the selection of a valid PID Hdection ha.-.;ed 011 checks of the detector resporn-;cs. The cletails of the down-shifting an~ provided iu Sc!ction 4.1.5. The standard PID was PID3+TRD (a cut in tlw PID:1-TRD plmw), lmt additional data was indndcd where either the C<m~ukov (PID2+ TRD) or TR~ (PID3) were not functioning correctly. No data was nsed when there W<~re prohkms with the preshower or calorimeter because these elements arc rcxp1ired hy the HERMES DIS trigger. The shapes of the PID3 and PID3+TRD clistrihutious an! shown in Figure 3.2. Positrons are concentrated in the peak at positive Yahws whik hadrons form the broad distribution at negative values. 65 Cl) C ::::s 0 (JIOOOO 5000 0 -20 -10 0 PID3 Cl) c 8000 ::J 0 0 6000 4000 2000 0 -20 -10 0 10 20 PID3 + 0.31 * TRD/keV Figur<' 3.2: Part.id<! Id Varial,lc Distrihutious 66 i: bin 1 2 3 4 5, 6 7 8 9 PID3 Contamination Efficiency 5.5 ± 0.6% 97.2% 5.0±0.4% 97.8% 2.5 ±0.2% 98.5% u; ±0.1% 98.8% 0.5 ±0.1% 99.2 1¼1 0.2 ±0.1% 99.4% 0.1 ± 0.1% 99.5% 0.0 ±0.1% 99.5% 0.0 ±0.1% 99.5% Table 3.3: Contamination l\,foa~uw11w11t. from TRD 3.3.2 Hadron Rejection and Efficiency M,~asuring the hadron rejection and efficiency of a :-;ingle PID detector is straightforward. Very strong cuts placed on the other thn\c detectors provides a very pure (although, low efficiency) positron or hadron :,;ample. Bccau:-;e the signals in the four detectors are mostly independent it is possible to id<\ntify an unbiased spectra for the detect.ors. (There is a weak, negative <:orrdation between the calorimeter and preshower.) The hadron rcj<-•ctiou and efficicuc:~' of a cut can easily be calculated with the:-;c pure :-;ample:,;. It is more difficult to estimat<\ the contamiuation and efficiency for the likelihood method because of tlw lack of iwlependcut detectors to place cuts 011. A very strong cut on the TRD (energy deposited > 30 keV fore+ or < 12.5 keV for hadrons) can he used to identifv sample.-; for PJD3. The distributions for positive hadrons a.ud positrous art> shown iu Figure :3.3. Tlw PID3-TRD plane is shown in Figure 3.4. The dean separation of hadrous awl positrons can be easily seen in this picture. The PID3 di:-;trihutiou for hadrons and positrons is shown in Figure 3.2. From thcs<\ distributions, the hadron rcjediou awl co11tallliuatio11 can be calculated for a cut 011 PID3. Table 3.3 shows the uwasmed hadro11 co11ta.rnination and positron efficiency for a cut on PID3. The :1; bins used in t.lw analy:-;i:-; are defined in Section 4.1.17. (The lower bin numbers correspond to low :r:. ) These contaminations and effidendcs for PID3 are useful for periods when the TRD is not used in the PID. The other PID methods (PID3+ TRD and PID2+ TRD) 67 are not amenable to a direct calculation of efficiency and hadron rejection. The Cerenkov does not provide a clean sample of hadrons at any momentum nor a clean sample of positrons above 6 GeV /c. For the PID3+TRD cut, there is no independent particle identification information to use to calculate the efficiency and contamination. 3.4 Positron and Hadron Fluxes for the Inclusive Measurements To det<~rminc the hadron contamination as a function of :r:, it is necessary to measure tlw relative fluxes of positrons and hadrons v<~rsns mom<mtum for each x bin. The large runnbcr of hadrons at low momenta results in a larger contamination at low x. Some of this effect is mitigated by the Cerenkov clet.c<:tor which increases the hadron rejection at low momenta. The momentum and :r: distributions of positive hadrons and positrons (Figure 3.5) shows tlw range where positron identification is critical. For scattered positrons with monwnta above lG GcV /c which corresponds to hiµ;h :1:, the hadron contamination is ncµ;li~ihl<! as the positive hadron to positron ratio dccwa.ses rapidly with energy. 3.5 Monte C arlo Compa risons A Monte Carlo :--imulation of tlw HERMES dd<'dors wa,s; developed to calculate dfici<\ncics and contaminations of the various part.id<! identification methods. In principle, thc:--e comparisons could h<! done with a sa111pl0. of the full HERJ\IES Monte Carlo (l-H\IC). Th<• simulation of particle:-- ill tlw PID detectors was not done in HMC IH~cansc of the CPl" iut<!n:,in~ nature of simnlat.io11s 011 EM showers. A boot strap Mo11tc Carlo was ,kwlopcd iu parallel with H}.1(' to sirrmlat<) the PID detectors. A samplP of tracks i11 each d<\t<!d.or are used to ge1wrat.<! input spectra for the Monte Carlo. A comparison with the measured contarninat.iou awl dficiency for PID3 and straight TRD cuts suggest the simulation produ<:<!S n·asouable results. The contaminations from the Monte Carlo and measured with cuts on tlw TRD are shown in Figure 3.6. 68 - - - - - - - - - - - - - - - - - - - - - - - · - - · - - - - - -- - - - - ~ Solid Line = Positive Charged Tracks Dashed Line = Positrons Dotted Line = Positive Hadrons 10 .-..' .-·''',_, -20 -10 0 10 PID3 Figure 3.3: PID3: Solid Line All Part.iclrn, Da:,ll<'d Liuc Posit.rou8, Dotted Line Positive Hadrons 69 :'. ...•·······.:::::::::·.: .· •••••···· ··• .. . .· ··- .. . •- .. 300 250 200 ::< >/ 50 .·· 0 Fi~urc 3.4: PID3 vs TRD Plam• 70 e 0~ ~ 10 3 ......... o°<b ~ n,___ 7...l • 10 2 Positrons Positive Hadrons O . . . ._ . . . . . . . . . .. ......... ~ • 0 Cbo • 0¢, Q,. 10 0 . 20 30 Momentum (GeV/c) 10 4 10 3 ••• . • 0 0 0 • • .. • 0 10 2 0 9 10 0.2 0.4 0.6 X Figure 3.5: Momentum and .r Di:,t.ributiow, for Hadrons and Positrons for a Sample of Data 71 ... . 0 .• 0 Mo,,t• Carlo • 6 ~ • u ~ ~ Hadron Contamination vs x Figure 3.6: Hadron Contamiuatiou for the HERMES x Binning It is not possible to mca.'mre the contamination for PID2 + TRD and PID3 + TRD clirectl:v. The efficiencies and contaminations for these methods were measured from t.lw l\1onte Carlo, and the rnsults from Monk Carlo agree with contaminations and dfic:ie1wics calculated by extrapolating the tails of the PID distributions [46]. The hadron contamination must be known to correct the contribution of misidentified hadrons to a8ymmetry measurement. The efficiencies arc measured to gauge the effectiveness of the particle identification system. The HERMES experiment is statistics limited. Every attempt is made to idcntif~, the positrons as efficiently as possible~ while maintaining minimal hadron c:ontamiuatio11. 72 X bin 1 2 3 4 5 6 7 8 9 PID3 Hadron Contamination 5.4% 4.3% 2.3% 1.4% 0.6% 0.2% (J.1% 0.0% 0.0% Efficiency 98.3% 98.6% !)8.7% 98.8% !)8.9% 98.9% 98.9% 98.9% 99.0% Table 3.4: Monte Carlo Contamination m1<l Positron Efficiency for PID3 :r. hiu 1 2 3 4 f, G 7 8 9 PID3-TRD Ha.drou Contamination 3.0% 2.1% 1.3% 0.8% 0.3% 0.1'¼ 0.1% (1.0'¼ 0.0% Efficiency !)9.3% 99.3% !)9.3% 99.3% 9!).3% 99.3% 99.3% 99.3% !)9.0% PID2-TRD Hadro11 Couta.minat.ion G.8% 4.1% 2.4% 1.4% Cl.G% 0.1% 0.1% (J.0% 0.0%, Efficiency 99.3% 99.3% 99.3% 99.3% 99.3% 99.3% 99.3% 99.3% 99.0% Tahle 3.5: Monte Carlo Coutamination aud Posit.mu Efficiency for PID3-TRD and PID2-TRD 73 Chapter 4 4.1 Data Analysis 1995 HERMES Data Analysis The 1995 HERMES experiment started iu May 19%. Aftn several months of commissioning the spectrometer and target, HERMES started recording asymmetry data in August 1995. From the start of polarized data taking to the 1995 HERA winter shutdown, 150 fills of data were recorded in the HERMES spectrometer. Each fill began with the successful injection of~ 50mA of 820GeV /c protons and ~ 30 mA of 27.5 GeV /c positrons. The beams would orbit in the storage rings for the next 8 to 12 hours and the positron current would d<~cay to lOmA before the beams were dumped. Some fills ended prematurely but the majority of the HERMES data were recorded during complete fills. The fills are ns<!d a.s tlw starting point for the HERMES data analysis. 4.1.1 An Overview of the Data Analysis To keep the data files a rea.sona.bl<! HiZ<\ <)a.ch fill was subdivided into a series of runs of approximately six to ten minut<!s. The nms contain approximately 1GB of raw data and represented about 1% of a fill. This divi<bl the data into pieces which could lw easily handled by the data analysis cha.in. Au initial nm sel<)d.ion was performed t.o select the runs of interest for the inclusive a.-;ymmetry analysis. Runs without a polariZ<!d targd, aud runs used to test various compolH~nts of the detector W<'r<~ rnmoved at t.his staµp. Each nm is divided into a series of scaler 'bursts'. Each burst corresponds to a set of scaler and slow control information that wc~re rc,ul every ten seconds. The events from tlw HERMES spectrometer w<~rn synchronized to the correct bursts to ensure that the correct slow control information and scalers (such as the luminosity scaler) were included. The burst is the smallest time 1111it which is used in the HERMES 74 analysis. The data were analyzed burst by burst and only bursts which satisfied strict data quality controls were used in the analysis. Additional cuts were placed on the runs and fills to ensure the data used was from stable data taking periods. The top and bot.tom hah-es of the detector are analyzed independently although some of the inputs and data quality cuts an~ identical (luminosity, beam polarization, target polarization). 4.1.2 The Analysis Chain Data were taken at the HERA East Hall and stored locally 011 8mm tapes and a series of local disks. At the end of a fill, the data were transferred to the computing center at the DESY main site. The data stored at the uiain site wa.-. used for the analysis chain and the original data storage tapes an~ used as a hackup of the data. At the start of tlw data analysis, the HERMES decoder (HOC) converted the digiti:1.ed time (TDC) and integrated char1?;c (ADC) :-;ignals to positions and energic:-; a.'i:-.ociated with track:-; through the :-;pectrometer. Tlw reconstruction program (HR.C) 11:-;ed this i11formation to reconstruct tracks through the spectrometer. The files (hrc.evcnts) containing all tracks with 110 1>art.ide id<\ntification selection are substantially smaller than the raw data and arc :-;tored for further analysis. Several it<!nttions were performed on this stage of the analysis to correct the calibration and alignment information used iu the analysis a.ud to optimi:w the tracking parameters. The fifth vcrnio11 (version E) of the reconst.rndiou was used i11 the final analysis. This tracking i11fonnatiuu is then merged with the slow control information to produce a. data smmw1r~- tap<• 'DST' whi('h n111 IH' 11scd for the a.c;;ymmetry analysis. The DSTs iudnde t.11<' DIS rnndidate events. Figun~ 4.1 shows the flow of information in the aualy:-;is cha.in. Several iterations were 1wrformed on the cxtnu:tiou of the DSTs to check the event synchrouizatiou codrs and information extraction. Tlw data sd has been thoroughly checked and the final aual~·sis is based on vcrsio11 £;:; of the glDST. 75 Event Files Tape Archives Trigggcrs and Scaler Reads Decoder Reconstruction Calibration and Geometry Servers Beam Polarimeter Tracks Synchronization Data Summary Tapes Asymmetry Analysis Figure 4.1: Off Li1w Analysis Chaiu 7G Detector Calorimeter Hodoscope 2 # of allowed bad channels Top Bottom 3 1 4 1 Table 4.1: GMS Gain Cuts 4.1.3 Initial Run Selection Of tlw 3238 runs, 2811 were acceptable for the a:-;)·mmetry analysis. Runs which were obYiously not appropriate for the asymmetry analysis wen\ rejected. These included rnus with 110 target gas, hydrogen or deuterium ga.-; iu the target, detector studies at non-standard voltages, tracking studies with tlw s1wct.rometer magnet off, and unpolarized 3 He runs. 4.1.4 Particle ID Criteria Information from the particle identification detect.on; wa:-; used to reject runs without c11oug-l1 hadron rejection for the asymmetry analysis. Many of the checks of the particle i<lentification det<~ctors (such a.-; efficiency a.nd µ;ain uwa.-;11rements) required more statistics than are in a burst. Thus, the part.id<' idc!ntification checks are performed 011 a nm ha.sis. Gain Monitoring System Tlw GMS wa.<; used to monitor th<' gain stability of the preshower, calorimeter and luminosity monitor during the experiment. Tlw information for the preshower a.11(1 calorimeter was used to chc~ck the gain of i11divid11al photomultiplier tubes to dd.('nniH<' if the cfot.cct.or was functioning <·01-redl) A li1war fit. of detector response 1• vs GMS photo diode response-\ was perfi:mned for ca.ch nm. If the slope of the fit diff<•n•d hy more than 15% from nominal , th(' d<'t<\d,or was considered bad for that rnn . Tlw cuts placed 011 this information for tlH' dctc\ctors arc shown in Table 4.1. The calorimeter rnts rliffer because a single calorimder block in the bottom of the dd,P<'tor waH off for the entire rlata takiup; period. Detector Efficiencies The (~fficiencies of nominal cuts for the four particle ID detectors (Cerenkov, TRD, 77 Detector Calorimeter (E/P) Preshower (GeV) Cerenkov (P.E.) TR.D (keV) Nominal Cnt 0.8 0.010 0.25 17.5 Good Cut 0.9 0.020 0.50 25.0 Table 4.2: Cuts Used in Efficiency Studies PID method used PID3 + TRD PID3 PID2 + TR.D Frac-t iou of R1111s 82% 3% 15% Table 4.3: Fraction of Data Involvl'd in Down-shifting preshower, and calorimeter) were determined hy the following formula, e.g.: N ((cer) nom (T RD) · f/OOd (1,r<')• f/mxl (ml) · ' ' good ) fccr = N ( (T RD}_qo(J(l (pre)gmxl (r:al)gmxl) (4.1) wl1<~re N is the number of positrons which satisf\ tlw chosen cuts, nom indicates the nominal cut for the d<itedor, and _qood indicatc•s a strict cut on the detector which gives a dean positron sample. 4.1.5 Down-shifting The efficiency of the Cerenkov detector wa:-; wqnin!d to h<~ above 92.5% for the run to be used in the analysis. (The nominal efficienc~' for the C<~renkov was 95%.) The efficiency for the TRD was required to lw ahm·e 92.5 for a cut of 17.5 kcV. (The nominal dficiency of this cut Wci.'i 97%.} The dfi<:iencies of the PIO ddectors mouiton·d tlw performance of the detectors a.ud sd<1cted the method of PID used iu tlw ,urnl~·sis. For <:<~rtaiu periods in the data, <!it.her tlw Cerenkov or the TRD was uot fuuctiouiug correctly. If both the Cerenkov and the TRD , or either of the Hodoscopes or caloriuwt<!r, W<\r<) not functioning, the run wa.'i thrown out of the analysis. If one of the Cen•nkov or TRD were not functioning, a PID 'down-shifting' scheme was used. Basid_Y. th<~ information from the disabled detector was ignored. The experiment could still function with three PID detectors 78 Selection Criteria Runs Remaining Top Bottom full data set log book beam polarization target polarization particle id 4011 3046 2326 2180 2006 4011 3046 2326 2180 2130 Table 4.4: Run Qualitr Sunuuarr because of the large n~dundancy in the HERi\IES spPct.romd.er. This scheme could not be used with the hodoscopes or calorimet<\r. If <•itlwr wen~ uot functioning nominally, preliminary analysis showed that events wew not <ldccted by the first level trigger and the detected events wen~ therefore unusable. 4.1.6 Burst Quality Criteria 2180 runs (2006 Top and 2130 Bottom) rmnairn•d after the initial run quality selec- tions. These rnm; (Table 4.4) satisfied the prdiminary data quality checks and are considered to be of suitable quality to us<~ iu tlw 1wxt stage of the asymmetry data selection., The bursts within the selected runs were d1<•cked for problems on a shorter time scale. The burst selection is based on tlw followiuµ; nit<~ria: • Beam polarization • Target polarization • Luminosity and live titn<• • Chamber efficiencies (high voltag<\ trip dd<•<tiou) • Scalar Ratei:; Each of these criteria will be discussed in turn. These criteria were applied to the upper and lower halves of the detect.or separat<·l~- (when appropriate). A burst was determined to he "good" for inclusive physics if at least one half of the detector passed all the criteria listed above. 79 4.1. 7 Beam Polarization The beam polarization was required to be abov<> 40%. The luminosity tunes for the storage ring include an optimization for positron polarization and easily satisfy this criteria. Establishing the luminosity tune would take approximately 45 minutes after the positron beam was ramped to its final energy. Tlw Sokolov-Temov effect polarizes the beam in about 30 minutes so the polarization reaches its asymptotic limit before the data taking bep;ins. The data n'mowd h_v tll<' polarization cut fall into two other categories. 1) There are several periods where no polarization measurement was available because of problems with the beam polarimeter. 2) It is necessary to depolarize occasionally t.lw h,~am in order to measure the rise time for calibration purposes (sec Section 2.2.1). Tlw rise times calculated from these fills dominate the systematic error of th<' lwam polarimeter [22]. An attempt was made to balance the demands of the polarimeter for quality rise time measurements and the need for rlata with stable beam polarizatio11. The polarization nwasurements arc ma.cle 011 a ow\ minute time scale. The raw bl\cllll polarization is fit to a cubic spline and tlw spline values are used in the analysis. The average beam polarization was 55% with a fractional systematic uncertainty of 5.4%. The uncertainty was dominated by tlw calibration e1-ror from the rise time nwasurements. A resonant depolarization and subsequent ris<~ time is shown in Figure 4.2. 4.1.8 Target Polarization Two polarimeters (Section 2.3.1) wen~ nscd to provid<~ a n~dundant measurement of tlu~ tarµ;d polarization. A pmnpiuµ; cdl polminwtcr (PCP) wa.<; the primary polarirrwt<!I' and rrwa.~ure,l t.lw absolute polarization of tlw t.arµ;et gas to a high statistical precision. A target optical monitor (TO:!\I) was also HS<!d which measured the polarization relative to the PCP. The TOI\I was calilirnt<~d rdative to the PCP at the start of the experiment arnl the polarimeters 1wY<\r significantly disagreed during the 1995 running period. The polarization value from the PCP was used for most of the data 80 '#c 60 - .......... .....••••••••.• .2 1ii N ·;:: .!!! . 0 • • • • a. E al m 50 • •••••• - .... • • 40 • • • 30 - • I 8157.75 I 8157.8 I 8157.85 Time (Arbitrary Units) Fip;ure 4.2: BPam Polarization \"1·nms Tim<! Dmiup; a Risd.imc~ Measurement 81 set. For a small time period, the PCP was broken and the TOM was used to measure the polarization. Because of the lower statistical accuracy of the TOM, only one polarization value per fill could be determined. This value agreed with the average polarization value of the PCP during fills when both polarimeters were working and no time dependence within a fill (other than spin Hipping) was observed. Th<' target spin direction was flipped every ten miunt<>s and it took approximately 30 seconds for tlw spin to precess from 01w <lin~<:tiou to the other. Data acquired while the spin wa."i flipping were> not used in tlu~ a."iymmetry analysis and the bursts where tlw spin wa."i starting to flip and finishinv; the flip WPW also eliminated from the data sd. The absolute value of the polarization as tlw spin flips is shown in Figure 4.3. The target polarization measurement wa."i required to be in a reasonable range for analysis. It wa."i not possible to get polarizations ahov1i GO% in the flowing cell and data with a polarization below 30% wa."i not used because of its low statistical significance. Thus the following cuts wcrn placed 011 the t.arv;d. information: • Targ;et polarization parallel or anti-parallel to lwam • PCP polarization: 30% < P,. < GO'Xi • TOM polarization: 30% < Pt(fill av1irage) < GO% Tlw average target polarization was 46% for th1· aual~·zcd data with a fractional systematic ,~rror of 5%. 4.1. 9 Luminosity For 1!ad1 burst t.11<• rat<~ in the luminosity 111ouit.or was n•1p1iw<l to be between 40 and 210 H;,;. 13ecausc th<~ beam l'.lllTCnt varies 011 a time seal<' co11sistent with the target spiu flip, nu accurat<' luminosity nwa.<;urenwnt for tll<' t ,,·o spin states is crucial for the HERMES mea.<surcments. Typically the HERA e+ beam was filled to ~ 30mA and ,hnnpPd at approximate!~, 10 mA. This corresponds to a 13habha scattering rate in the luminosity monitor of 17j Hz at tlw hq.1;i1111inµ; of a fill and 60 Hz at the end of a fill wit.h the standard target density (10 1''nndPons/nn 2 ). The luminosity from the luminosity monitor is cross-checked with the beam cur- 82 -c so - C 0 •••••• • • ; as • • • • • • • • • • 0 N ·;:: ••••• • • ••••••• □ as 0 -... a. G) C) as I- 40 - 30 - 0 Parallel to Beam i.'? Spin Flipping 0 Antiparallel to Beam ■ Solid Symbols Good Bursts I I I I 12990 13000 13010 13020 Burst Number Figure· 4.3: Target Polarization V1\rsU8 Ti11w NP,U' a Spin Flip 83 rent and target density measurements as shown iu Figure 4.4. It is possible to use the beam current and target density to calculate the total luminosity. However, the target density depends on the temperature of the gas in tlw target which is not well measured. The nozzle temperature is measured but tlw uncertainty in gas temperature is still too large to make a better measurement than tlw Bhabha scattering. The following cuts were imposed: 40 < luminosity rate < 210/i,:; (4.2) luminosity rate 5.0 · 10- 15 < - - - - - - - - - - - < 7.2 · 10- 1r.Hz/mA/(nucleon/cm 2 ) beam current * target thickrwss (4.3) \Vithin a fill, the ratio of luminosity monitor rate to beam current and target thickness was constant but it varied from fill to fill. The asymmetry analysis was performed on a fill by fill basis to avoid any problems due to fill to fill luminosity normalizations. Tlw 1% time dependence of th<' luminosity within a fill is small and was discussed in S<'ction 2.4.11. 4.1.10 Live Time Tlw Ii ve time was required to be at least 60%. Tlw raks in th<' HERMES spectrometer am low and the livetime is usually greater than 90%. The proton background can greatly iucrea."ie the event rate in the spectrom<~ter. Whcu the proton background is larµ;<', tlw livetime can noticeably decrease. Th<• structure seeu at small live tiuw S<\<\B in Fiµ;ure 4.fJ(a.) is the result of a period at th<· start of each nm when tlw trip;ger is w-initia.lized . The first three bursts (30 s<~con<ls of 10 minutes) arc not used h<~<:ause of this prohl<\m. The livetime for each burst iu a run is shown in Figure 4.5(b). Varying the live time cut between 50 and 80% had little effect on the result. The results of systematic variations of cuts an~ summarized in Section 4.6.1. 84 -N 200 :c a, co 150 a: > ~ ,n 0 100 C E :::i ..J 50 0 17000 18000 19000 20000 21000 Time (Arb. Units) -,n 0.7 C ::::, ... .0 - 0.65 <( 0 :;::::; . .. . .. 0.6 co a: E 0.55 ;: : .. ··- ........... : . . . ...- . .. . .. ..... ... ... ...... ... ... . . .. ... .....-. ...... . . .. .--···... . .. ........ . .. . . .... • •• •• ••· · ••• ••0••• • •••• ·D· •• D••• •• ■■ • • ••••••••• tt~it~i~W.liinirri:rn!titmmtiiit~~i~tmmmmt~!1tm1m:m~; ·: ··: ~~?t.;:::::;!;~:~;=:::?·=~·:·:=:~~;~/)j?'::;:::=--: ·::j:· :·.:~·= :::i ..J 0.5 17000 18000 19000 20000 21000 Time (Arb. Units) Figurn 4.4: Luminosity Versus Time aucl Lm11i11osit~-/Cmre11t/Target Density for a Fill 85 (/) ~ 103 ::::I Ill 0.2 0 0.4 0.6 0.8 1 Livetime Cl) E 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .0 .:; dJ Cl) > ::::i 0.75 0 Bursts Excluded at Start and End of Run • Bursts Used in Middle of Run 0.5 0.25 0 12180 12200 12220 12240 Burst Number Figure 4.5: (a) Live Time DiHtribution for a Subset of Dat,1 a11d (h) Livetime per Burst for One Run 86 4.1.11 Chamber High Voltage Trip Detection The ACE program (Section 2.4.5) was used to calculate burst by burst efficiencies for all drift chamber planes and total track finding efficiencies for the front and back regions of the top and bottom of the spectrometer. A detailed discussion of ACE was included in Section 2.3.4. The total tracking efficiency is created by smnminp; the product of efficiencies over c~ach possible combination of chambers that would prodrn:e a. n~constructed track. An efficieuc.;y cut wa:, used on these front and hack cffic:imu:ics that. was varied from 80% to 97.5% to study the systematic variations. The standard cuts were 80.0% front and 95% back. The bac.;k region tracking effkieucy is higher than the front because of the higher chamber redundancy in the back region (Sc\ction 2.4.3). Bac.;kgronnd due to hadronic showers from the c:ollimators and synchrotron radiation cau produce high currents in the drift chambers. The high voltage of the drift chambers would often 'trip' (rapidly turn off) d1w to tlwse high currents to protect the chambers. When a trip wa.'i detected, the tripped half of the HERMES detector (top or bottom) was not analyzed until the efficiency had risen above the threshold (voltage had ramped back to its nominal value). The burst before the trip was also removed. (The rapid onset of trips often meant the hnrst hcfore a trip contained a fow seconds of good data followed by a period with no n~coustructed tracks. The hmst will then have a rea.<mnablc tracking effici<•tu-~• calculated from the tracks at the start of the burst but the total number and time distribution of the tracks indicate a track rcconstrudion problem.) The effidency of any Iila1w was defined to be zero if 110 tracks <!Xistcd to ca.lculate au effidcncy for that d1amlwr. \\'lwu the high voltage~ trips off the yidd of tracks rapidly goes to '.l,ero. Figure 4.6 shows the tracking efficiency (which is a. strong fund.ion o( cliamhc!r voltage) and total tracks pc-~r burst.. It is dear that the data with lmY tracking <!fficiency is unusable. A c:ut is placc~d to <!rnmre the data ha.-; a high c\fficic•ucy hut no correction is made for the tracking efficiency. The d1amber efficiencies <lo uot fully correct the difference in cn~nt rate whc\n the chambers are run at difforc!nt voltages or thresholds. The corrections within a fill are small ( < 1% variations iu t.h<\ efficiency for good data 87 within a fill) so they were neglected because of the problem normalizing periods with large efficiency differences. 4.1.12 Scalers The scaler rates were used to determine if the first hodm,cope was working. The rates are very background sensitive but requiring th<' snl.l<•rs be non-zero for each burst removed several periods where several d1ann<•ls had tripped. (The PMTs like the drift chambers will trip to protect thcmsdv<~s if t ll<'ir <:nrrent is too large.) Requiring the scaler rates in ea<'.h paddle to be uon-:wro 1n·oyidcs little information on the gain of each paddle but is sensitive to trips which turn the paddles off. The first hodoscope is required in the trigger, and including data during hodoscope trips can introduce helicity correlated false asymmetries due to tlH' d1aug<)S in tlw trigger efficiency. 4.1.13 Synchronization and Run Initialization A trigger initialization procedure wa.'> J><)rformc•d at the start of each run. During this procedure tlw digital signal proc<~ssors wen• n•loadcd with the trigger logic. As a result , the first three bursts of each nm had ver~· larg<~ d<\ad times and were not used iu tlw analysis. The last burst of <~ch run was eliminated to msnrc correct synchronization . The end of nm signal from the electroni<:s was uot s~·11d1ronir,cd with the burst reads so th<~re ar<) ambiguitic.'> in the amount of time cv<~uts m'r<) recorded during the last burst of <),u:h run. 4.1.14 Summary of Burst Cuts Siug;l<) bursts were removed from the data. set if tlw~· fail1 •d mw of the following criteria: 1) 0.6 :s; livetime :s; 1.0 2) 40 Hz :s; luminosity rate :s; 210 Hz 3) Burst length < 9 seconds or > 11 s<•1·onds 4) Previous burst wa.'> iu a <lifforent t.arg<'t spin state 5) Efficiency Cuts (80% front , 95% lia('k ) 88 ----- - - - - - - - - >- 0 C cu -0 0.8 ;;:: w • 0.6 0 Good Bursts u.. 0.4 • Bad Bursts C 0 ... • 0.2 0 17800 17820 Burst Number -"...' :::I 80 0 m ... cu a. 60 "' ooo 0 0 Oo 0 0 0 Oo 0 0 0 0 0 0 • 0 .)(. 0 oO 0 0 ...ca 40 • ~ 20 • 0 17800 17820 Burst Number Fi~1m' 4.6: Efficiency awl Reconstructed Tracks pm- Durst Near a Detected Trip m the Front Chamber 89 Selection Criteria initial set run stability fill length Top Runs Fills 2006 88 Bottom Runs Fills 2130 88 1517 1441 1609 1556 72 55 73 61 Table 4.5: Secondary Run Quality Summary G) The first three bursts and last burst from c~ach run were removed to eliminate ambiguities from the event synchronization and rnn initialization problems. 4.1.15 Secondary Run and Fill Selection The firnt level data quality checks reduce tlw HERMES data set to 2180 runs for asymmetry analysis. The burst cuts remm·e bursts throughout these runs. An attempt has been made to ba!->c tlw analysis on 1><•riods of st.able data taking. Thus, several other periods were removed from the data sampl<~ to select only periods where the data ta.king was stable. Runs where large p<'riods fail the burst cuts were not used in the analysis and fills with only a small amount of data after these run cuts wen~ also not used. Any nm where more than 30% of the burst:-; W<'r<~ n~mow\d because of trips or any other problems was considered to he unstahlc. This 'swiss cheese' cut was used to remove periods where tlwre may he instabilities iu t.Iw sp<d,rometer. The runs which remained after this cut wen• s11muwd by fill. If a fill had fowcr than 200 good bursts in eitlwr target spin state, the fill wa.<; rejected. Only a small number of fills were removed hy this cut awl most of tlw data W<)l'<' from fills with long periods of stable data ta.king. This ,lc•fiued the HERt\IES data for t.lw a.s~·mmctr~· analysis. G4 fills contained lou!J; I><)riods of stable data taking which WPr<~ co11sidPrPd to he s11itable for asymmetry analysii.;. Table 4_.5 s11rnmarizes the final data s<'i<•ctiou . A total of 1642 (1441 Top and 1556 I3ottom) runs arc included in the inclusive physic:.; analysis. 90 4.1.16 Event Selection The DIS positrons are extracted from the bursts which have been selected for the analysis. To be selected as a positron candidate, a track must pass a series of cuts to determine that it was a deep inelastic positron from the :i He target. The cuts placed on the data are listed here. • y < 0.85 (y = 7// Ebearn) excludes the rngion with large radiative corrections. • ()'2 > l.0[GeV/c]i) ensures the data can lH\ int<\rprct,\d in t<)rms of a quark-parton modd. • lV 2 > 4.0[GeV/c]2 excludes the resonance r<\gion hy demanding a large invariant mass. • -30 < Z Vertex < 30 cm (z position at drn,<'st approach to the beam axis) and • T Vertex < 2.0 cm ( transverse distanc<\ from tlw heam axis at closest approach) select the He target region. • abs(0 11 ) > 0.04 <!nsur<·\S the track is fully inside the HERMES spectrometer. • PIO cuts were discussed in Chapter 4. The positron candidates are binned in :1:, y , target spin state, and detector half for t.11<' a.-.;yumwtry analysis. 4.1.17 Y Binning Tit<' cl<\polarization factor, D, was introdm:<•cl iu Chapt<\r 1 iu the discussion of the <'Xtra<:tion of A 1 from the rnca.'mr<~d a.sy11m1<'tr_Y. Tll<' dq>olarization factor weighs the 11H•,umrcd a.-;ymmetry and represents th<· polarizatiou of tlw virtual photon exchanged by the positron and nud<!US. The HERMES spectrometer ha..c:.; a wide kiu<~rnatic acceptance and the depolarization factor varies by up to a factor of three for <·n·uts with low x. The data is also bi1mcd iu // y= E (4.4) 91 to reduce the variation of the depolarization within a bin. The boundaries of the nine .-r by three y bins are shown in Table 4.6. Table 4. 7 shows the variation of the mean depolarization for the chosen boundaries. The boundaries (Yiow, y 1 _ 2 , y 2 _ 3 , and Yhiyh) of the three y bins provide roughly equal statistics for each bin. :r. bin 1 2 3 4 5 6 7 8 9 X/ow XJ,.i!lh 1/tnw J/t-2 1/2-:{ J/hi!Jh 0.023 0.04 0.055 0.075 0.1() 0.14 0.2 0.3 0.4 0.04 0.055 (l.00 0.00 (l.00 (l.00 0.()() 0.00 0.00 (1.00 (1.00 0.68 O.i:i3 0.-!:2 0 .3-1 0.:27 0.22 0.17 0.1-1 0.15 0.78 0.67 0.58 0.49 0.42 0.34 0.2G 0.23 0.22 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85 o.on; 0.01 0.14 0.2 0.3 0.4 O.G Table 4.6: :1: and y Din Boundaries Us< <l in the Analysis 0 By binning the data in y a!-i W<\ll a.c;; :1:, the variatiou of the depolarization factor for a p;iven :r: bin can be reduced. The a.c:;ymmetries ,m' calculated for each x and y bin and averaged OV<!r the y bins for quantities whieh arc a function of x. A (:r:) D A (:,:, y) D(y) -11- = < ~11 - - > (4.5) c:ombine8 the data with different statistical si1,!;Bifica.m:e in a natural fashion. Oill 5 0.1920 0.3083 0.5G49 ;J; y Din 1 2 =~ 1 0.5981 0.7404 0.8339 2 0.4308 0.5825 0.7700 3 0.3194 0.4669 0.706G 4 0.2472 0.3776 O.G328 (i 0.1Gl8 0.2502 0.4813 7 0.1163 0.1938 0.3920 8 0.1049 0.1690 0.3501 9 0.1234 0.1771 0.3281 Table 4. 7: i\foau Depola.rizatio11 for tlw :r,JJ Oi11s 4.1.18 Corrections from the Transverse Asymmetries Bccaus<! the momentum of the virtual photon is uot parallel to the momentum of the positron, th,~ measured asymmetry, A 11 / D, coutaius contributions from both A~He 3 and A/le. 92 X < Q2 > A] 0.035 0.050 0.078 0.124 0.175 0.248. 0.344 0.466 1.06 1.27 1.87 2.69 3.40 4.00 4.46 5.52 -0.080±0.241 -0.007±0.lGG -0.0lG±0.138 -0.210±0.156 -0.313±0.204 -0.013±0.241 0.219±0.424 -0.945±0.787 ,.JR 0.58 0.54 0.5G 0.53 0.47 0.43 0.39 0.33 Ta.hie 4.8: A1 '.\foa.'ime11H•11tH from El42 (46] (4.6) A measurement of the transverse a.'iynunetr:v was dcforrcd to maximize the statis- tics in the measurement of the longitudinal as~rmuwt.ry. Using the positivity bound on A 2 (./R) would introduce a significant systematic mu:crtainty in this measurement. Previous measurements of A?c suggest that it is consistent with 0, and Table 4.8 shows the values of A 2 = F;uePnA~ll c/ F2i uw,umred hy tlw El42 collaboration [47]. It has heen assumed that A 2(.1:) is Z<\ro and a systematic error equal to the statistical <\rror of prcviom; mcasuremmts has h,•c11 assiµ;ucd to this quantity. For the two highest :r: hius, the positivity limit ( .JR) is us,~d IH~Crl.llHC the statistical errors in the measurement are not a strong<'r constraint 011 the asymmetry than the positivity limit. Because it has hccn as:mmcd that th<' t.rnu:-;vcrsc contribution to the measured asymmetry is zero, the trnnsvcrs<• t<•nu:-; will IH' H<!glcctcd in the following analysis formul.w until the discussion of syst<·matic ,~rrors is coutinucd in Section 4.6. 4.2 Calculating A~He \.\Tith tlw event selection complete. tlw as~'lllllH'tr_v could he extracted from the data sununary tap0.s. The raw asymrnetr~· for scaUPriuµ; from aH e, A11, is extracted for (\ach fill via N-L+ -N+ L All(-7:. !I)= N- Lt, + N+ L,. (4.7) 93 where the following quantities are sums of all good bursts in a fill: • N is the number of positrons in a x,y bin, • L is the obr-.erve<l luminosity (sum of the luminosity monitor scaler), • and Lp is the total polarization weighted luminosity ('J:,LPtPb), The signs refer to parallel (+) and anti parallel (-) spin alignment of the beam and target. A11 is used for systematic studies of the data (sec Section 4.4.1) and the asymmetry is averaged over y bins to calculate A11(:1:)/ D (see Section 4.1.17). Further corrections an) required before the physics asymmetries discussed in Chapter 1 can be extracted from the data. These include background, nuclear, and radiative corrections. Background correctious modify the desired DIS scattering asymmetry due to misidentified hadrons and positrons from charge syuuuetric processes. These backgrounds can dilute the desired asymmetry and introduce additional a.symmetries which must be treated a.'> corrections. The a.'>y1mnetries from tlw hackground processes are measnrcd along with the DIS positron a.<;ymmetrics to correct the measured asymmetry and extract Af / D, the asymmetry from DIS positrons. Radiative corrections arc necessary to extract the single photon exchange asymmetry (Born asymmetry) from the observed asymmetry which is the sum of the first order process and higher order electro-weak processes. N udcar corrections relate the ;u;_vmmetry for the :i H <'. nucleus to the neutron asymmc\try. 4.2.1 Backgrounds There an~ two compoucnt.s i11 the• hackgrouwl for the i11dt1sivc\ positron measurement: contamination of misidentified positive hadrons awl positrons from non-DIS charge symmetric processe:-.. (4.8) e+ is the number of events from DIS scat.tere.d positrons. 94 e+ e- 1,,+ 1,.- 1 266323 2 304438 3 356959 4 355833 5 420981 6 -423038 7 395999 8 167323 75803 9 18305 9234 5545 2755 1171 305 90 17 G 955883 670453 503592 2833Hi 145011 44118 10352 1480 454 771548 508733 367422 200337 100516 28965 5617 541 12G x bin Table 4.9: Tot.al Events iu Full Run List (Nomiual Cuts) c- i:-; tlw number of events from charge symmetric processes. 1,,+ is the number of ,~vents from misidentified hadrons. All these quantities are measured simultaneously iu tlw HERMES spectrometer. With a. kuowledgc of the fraction of event:-; of each t~ f><) and the asymmetries of the 1 background processe:.;, one can calculate the a.s;_vnunetry from DIS scattering from the a He nuclei. Table 4.9 display:.; the total event sample for each particle type in the spectrometc)r. The details of the particle i<lcntification arc inducbl in Chapter 3 and the two backgrou~1d corrections will now b<) discussed. Hadron Contamination The correction for tlw misidentific)cl positive· hadron:-; is relatively simple. Studies of tlw hadron contamination (Chaptc)r 3) suggest that a small fraction of the hadrons an) misidcntifie<l. The asymmetry for tlw idcntific)d hadrons (Af() is shown in Figure 4. 7. Tlw correction to the measured a.s;y11mwtry i:-; small rnmpared to the statistical llll<'.crtainty in tlw raw a.s;yrnmetry. Tlw hadrou cont.amiuatiou C++Z~+1i+) and hadron a.:-;_vmmet.ry are iud11dc•d in Table 4.2.1. Charge Symmetric Contamination Positrcms from decay processes as wdl as DIS positrons can satisfy the kinematic cuts placed on the data. These extrarwous events are exp<~cted to be charge symmetric, and it is c:onYentional to make a corn)<:tiou to tlw positron rate based on the oh:-;erved electron rate. The charge symmetric: contamination is slightly more complicated than the contamination from positive hadrons lwcause the electron rate is 95 <t.- 0.1 • 0 0.05 I .. .' Top Bottom . .'''' ~ 0 ◄• ' ' ' -0.05 , --'--''-- - - - -l - - - ' - - --'---0.1 ' - - ---'--- -'-'_ _,_,_ _,_,_,.____,_ ·1 10 -'----'------'L___J . 0.05 - ■ Top + Bottom t -0.05 I -0.1 10 -1 Fi~ure 4. 7: Pm,itive Hadrou As:vmuwtry A(( :r. hiu 1 2 3 4 iJ G 7 8 !) Hadrou Co11t.a111inatio11 0.03G 0.025 (l.015 0.009 0.004 (l.001 (l.001 0.000 0.000 41, + · ' II -(l.010] ± 0.0290 -0.()183 ± 0.0407 -0 .0457 ± 0.0523 -0.1158 ± 0.0742 -0.1398 ± 0.1132 -O.OG77 ± 0.2192 0.3293 ± 0.4075 L.3108 ± 0.9312 -0 .00G!J ± l.Gl29 Table 4.10: Corrections for Misidentih◄ \d Positive Hadrons 96 x bin e-J(e+ + e- + h+) 1 2 3 4 5 4.5% 1.3% 0.6% 0.2% 0.1% 0.0% (1.0% 6 , 7 8 {l.0% 9 ().{)% Ac·11 -0.0101 ± 0.0290 -0.0183 ± 0.0407 -0.0457 ± 0.0523 -0.1Ui8 ± 0.0742 -0.1398 ± 0.1132 -0.()677 ± 0.2192 0.3293 ± 0.4075 1.3108 ± 0.9312 -0.00G!J ± 1.6129 Table 4.11 : Charge Syuuu,~tric Ilackp;round Correction significantly smaller than the negative hadron rate. As a r<\sult, a significant number of the <~vents identified as electrons are in fad. misid<\utific<l negative hadrons (~ 30% in the lowest .7: bin and the count rate is consist.cut with the expected misidentified hadrons rate in the upper :r: bins) . A correctiou for the hadron contamination is indnd<~d to avoid double counting the hadron liackp;rournl. (4.9) wh<~n~ ,,++:=+h+ r<\l)f<'.'>ents the corrected contamination; Nr.- is the raw number of el<~d.rons and Ch-(:1:) is the negative hadron coutamination. The asymmetry measured for the <~led.ron cawlidat.es is shown in Fignre 4.8. As a comparison, the asymmetry for the negative hadrons is shown in Figun~ 4.9. The t.wo asymmetries are similar awl are hoth slightly negative at. small :r: when\ the dmrp;e symmetric correction is significant.. No correction is ma<le to the electron asymmetry for the negative hadron contamination. The correct.ion is very small lwcanse the nwa.<;ured asymmetries are similar and tlw statistical 1111cert.ai11t.y iu t.lw diarp;e syuunetric corrections does not contribute significantly to the tot.al mcasnrcuwut. The <'OlT<~ctions for diarge syumwt.ric pro<:<~sses an~ aJ!;ain small compared to the ohscrv<~d asymmetries. Table 4.11 :-;hows the size of the corn~ction factors for charge synunet.ric background. 97 < ~ 0.4 r f- 0 l.i.. 0.2 r' 0 i.. L -0.2 + f f - - , --------- - ~ 0 t 0 -0.4 I 10 ·1 Figure 4.8: El<!ctron As~·mmP-try 98 < 0.1 -0.05 - I -0.1 10 1 < o. 0.05 ~ ■ -1 l Top+ Bottom T I -00: ~----■ -- ------------- -,---+ ---- -- ---,;-----,.------ ----- --0.1 I 10 -1 Figure 4.9: Negative Hadro11 Asymmdry 99 4.2.2 Radiative Corrections The formulae used in the discussion of DIS measurements refer to the lowest order diagrams which contribute to the scattering amplitude (Born approximation). Higher order diagrams also contribute to the scattering cross section:-, and asymmetry. These contributions are referred to as' radiative coned.ions. Ela.borate and powerful schemes have been developed to calculate the radiative' rnrn~d.ious in DIS scattering. (48] Tlw radiative corrections are traditionall~· divi<l<-<l iuto two categories, internal and <~xterual. Internal radiative corrections occur at tll(' primary scatt,c!ring vertex. Many different proc<~..,ses are iududed in the internal radiatin~ cmT<~d.ions such as the following: • Initial (Final) State Bremsstrahlung • Vertex Corrections • Vacuum Polarization • Two Photon Exchange • Hadron Current Corrections Fe:vnman diagrams for these processes ar<' shown iu Fip;ure 4.10 . .Just as the first-order Boru process has au as,vnundry, the radiative corrections an• uot symmetric for the two lepton-uucbm spiu combiuations. The formalism for p;enerating the radiative corrections to spin dependent DIS has been developed 1>n~vio11sly. The radiativ<~ corrections are ca.lc:ulat<•d with t.lw POLRAD code (49] which has IH~<'ll adapted for the HERMES ac<:<\pt.a11<'<' awl ki1w111a.tics (50]. The code uses a paranwteriiation of the Schaefor mo<ld for A'{(:r) [;il] t.o modd the asymmetry. tlRC is ('alrnlated by radiating the model of A~•. Tlw rndiatiw <:OIT<~ctions are iterative and tlw uwdd 's parameters are varied until tlw radiated a...,ymmetry fits the asymmetry caknlated from the data. The values awl 1111n·1tainti<~~ of tlw radiative corrections are talmlat<~d in Table 4.12. The formula for appl~ i11g the radiative corrections is: 1 (4.10) 100 T Initial State Bremsslrahlung ~ rinal State Bn."lnsstrnhlun!! Venex Corrcclion Vacuum Polarization Two Photon Exchange Hadron Current Correction Figure 4.10: Diagrams Which Coutrilmtc to tl11• l11t.< •rnal Ra.diativ<1 Corrections 101 \\Tith D.RC = Aradiated - (4.11) A8orn · Studies [52] have estimated the contributiou of the radiative corrections to the systematic error. The dominant uncertainties an• due to different parameterizations of A'i'" which descrilw tlw data. <x> 0.035 0.04!) 0.066 0.088 0.119 0.168 0.244 0.342 0.464 Radiativ<· C:orn•ct.io11 0.0059 0.0051 0.0048 0.0044 0.0042 0.0040 0.0040 (l.0040 0.()()39 ,5 HaclCorr 0.002!) 0.0015 0.0007 0.0005 0.0007 0.0010 0.0013 0.0015 0.0019 Table 4.12: Radiative Correct.ions for A';'"' External ra<liativ<) corrections arc tlw intcra.d,ion of the positrons with material lwfon• aud after the scattering nudci. The HEIUvlES target is very thin and interactions before the scattering can l><' 1wglcct<)d when calmlating the asymmetry Af. Int<•ractions after the scattering vertex change t.11<' <~1wrg~' and direction of outgoing tracks. This can shift the binning; of tlw <)vents a11d ':-;i11c•ar' tlw a.,;;ymmetry by averagiug different kinematic regions. Tlu~ HERMES sp<•c:tromder is very 'thin', that is, the scatt<•rcd particles only encounter ~ 7% of a radiation lm1gth before the hodoscopes. So, tlwre is very little multiple scattering and l\lo11tc• Carlo studies suggest that the <'ffoct of smearing cau I><~ neglect<)<!. (53] 4.2.3 The Measured Asymmetry A';"'' Tlw values for A/ic from tlw top awl bottom spc•dromct-.<·r were averaged together for die calculation of AI' and 9;1- The results for the two sp<~ctrometers can be seen iu Figure 4.11. The difference of the two spectrometers is 2 a for the two lowest x points, hut the x2 / <~{ is 1.2 for the nine points which has a confidence level of 20%. 102 a> :c M 0.1 • <( 0 0.05 Top half of Spectrometer 0 • + -0.05 I -0.1 10 ! Bottom half of Spectrometer . •~ I I i ; 0 I I C) 0 • I I I I • I I ¢ (!) I ♦ -2 10 • I I I I I I I ·1 X cu :c M 0.1 ■ <( Top and Bottom 0.05 • ' • • ••• • • 0 ' -0.05 -0.1 10 ·2 ' ' 10 ' • ·1 X Figure 4.11 : A'; 11 ,. \'1•rs11s :1: 103 Figure 4.12: Primary Part of :i H, • \\'ave Fnuctiou Partial Wave s S' D L 0 0 2 s I',; I',-; I',; I',-; 1/2 1/2 3/2 1 2/3 1/3 () 1 4/3 2/3 1 2/3 4/ 3 1/3 2/3 % 88.6 1.54 8.37 Table 4.13: Partial Wave Decomposition of :i He 4.3 Extracting A 1 It is not feasible to use a free neutron target for DIS experiments. Unlike the proton Rtructurc functions, neutron structure fnnctio11s an• 11wmmred with a multi-nucleon mu.:leus. Experiments using polarized Dor :i H<'. can IH~ used to extract Af since simple models rdatc the spin of the nudcus to tlw spi11s of tlw nucleon constituents. These unclear l'ffccts must be taken into account in tlw calculation of neutron structure functious. In 1995 a polarized :iHc target was O}H'ntl<'d iu the spectrometer, and this discussion will focus 011 extracting A;•· from A::"". Tlw ohservatiou that the spin of the nentrou dominat<~s tlw spin of the 3 He nucleus has motiYatcd the us<~ of polarized :i He tarp;ets to uwas11n· neutron spin structure functions. In the simplest model of :i He, tlw 1111d<•o11s aw in a. spatially symmetric S state• allCl tlie Pauli principle constrains the protons to lw paired autisymmetrically in a, spin singlet. Figure 4.3 shows this coutrilmtio11 . :\ mon• n~alistic model [54] suggests that this is the domiuant portion of the wa.w function with small contributions from S' and D states. Table 4.13 shows t.he contrih11tio11s of the S, D and S' state which has a mixed spin and isospin symmetry. A best tit to the results from many different moclc-ls of nucleon - nucleon interac- 104 tions [55} [56} suggests that the polarized 3 He can be described as a slightly depolarized neutron with a small component of proton polarization opposite the direction of the nuclei's spin. 1'11 Pn = 0.86 ± 0.()2 (4.12) = -0.028 ± 0.004 (4.13) and tll<' asymmetry of the helium nucleus can lw written [56]: ~lie(, ) - A, .r, - Ff(:r;) n(, ·) FJ'(:1:) P( ) F:i'(:r,) + 2Ff (:1:)PnA1 .l, + FJ'(:1:) + 2Ff(:1;)ppA1 X (4.14) where Af is the virtual photon spin asymm<'tr.v for tlw proton and F 2 is the spin independent structure function. Values for F2 an' obtained from fits to experimental <lata [57} and At from the previous E143 uwa.-.;un•meut [5). 4.3.1 The Measured Asymmetry A~1 The Yirtna.l photon m,ymmetry AiL can now be <~xtrad.,~l from the data using Equation 4.14. The results for tlw top and bot.tom sped,romd.er have been averaged and a total a~ymmetr:v for th<~ experiment wa.<; calculated. Tlw results for A;1 are shown in Figure 4.13 and talmlat<~d in Table 4.14. The E142 [4] n·s1ilts with statistical errors arc shown in Figun~ 4.13 for comparison. <x> 0.035 0.049 0.0GG 0.088 0.119 0. IG8 0.244 0.342 0.4G4 A verap;<~ A; 11 '' ±Htat. -(),()245 ± 0.0111 -0.02G5 ± 0.0121 -0.0180 ± 0.0129 -0.0311 ± 0.0148 -0.0240 ± 0.0158 -0.0391 ± 0.0187 -0.0208 ± 0.023G +0.0239 ± 0.0408 -0.0391 ± 0.0G04 Aj'±Ht.at. -0.1045 ± 0.0411 -0. l 098 ± 0.0450 -0.07.';8 ± 0.0483 -0.1232 ± 0.05GG -0.0%3 ± 0.0G31 -0.15G3 ± 0.0785 -0.0748 ± 0.1057 +0.1478 ± 0.1981 -0.15G0 ± 0.3270 " 1(': Top aud Dot.tom Averaged Table 4.14: Aj' and A/ 105 c .... 0.4 <( e HERMES 0 0.2 E142 0 0 -0.2 N' ·~ C>( )0 \.>C Q'.. ~ - -0.4 IV -0.6 10 -2 10 )0 ~ -1 Figure 4.13: A~' Versus x With Systematic Errors (Solid Band) 106 4.4 Systematic Studies of the Asymmetry 4.4.1 Time Stability of the Asymmetry The g~1 analysis wa.'i performed on a fill by fill basis. Within fills the luminosity was stable and an average of the fill based asymmetries wa.'i used to calculate the physics asymmetries. The time dependence between fillfi and within fills was used to check the stability of the analysis. The asymmetry (A11) over the entire :i: range (from 0.023 to 0.6) is used for these studies. The statistical errors on the measun~ment,:,; of Au for positrons and positive hadrons arc similar, and the error for negative hadrons is slightly larger. Within fills, the m;yrnmetry is calculated for groups of five nms which represents about fifty minutes of data and averaged to calculate au as~·mmctry per fill. The x2 for the asymmetries with a fill ani used to calculate a rnnfidcncc level that the data are statistically distribukd within each fill, and the asyunnctrics per fill are fit to a constant to observe the time stahility for th<\ foll cxp<~rimcnt. Groups of five mus were chosen to indud<~ at l<-ast two sets of data in each spin st.at<' so thr statistics in each spin state woul<l lH' roughly balanced. There were not enough statistics to calculate a meaningful time dependence for the electrons while the positrons and hadrons provide good statistical accunu:y for groups of five run and fills. The tot.al asymmetries per fill aud the co11ficlcun~ levels with the fills are shown in Figun~s 4.14 to 4.19. The top of <~ach plot shows the measured asymmetry versus fill 1111111b<~r, and the bottom plots show tlw con(id<·uc<~ l<~vds of the groups of runs within a. fill. Tlw coufid<~ncc l<\vels an~ shown wrsus fill 11umher to show fills with low c011fi<kw:e levels aud histogramed to show 1.h<· t ota.l confidence level distribution which should have a uniform density. The p<~r fill confidence lew~l suggest that then~ arc 110 large non-statistical effects within a till. The distributions of confidence l<\vds should IH\ flat. The time stability for the total fills is slightly worse. The asymm<'tr>· should lw constant versus time, hut the x1 per degree of freedom for this hypotlwsis arc souwwhat higher than would be expected. None of the value of x2 p<~r <legr<~<~ of freedom is below a 1% confidence 107 level, but three of six confidence levels are under 10%. 4.4.2 The Determination of the Statistical Errors Although there is no large time dependence in the HERMES analysis, additional studies were performed on the yield distributions to check that the data was statistically distributed. Th<> yidds cannot lw compared directly lwcause there arc large (~ 10%) variations in th<' ~-idd from fill to fill as shown in Figure 4.20. Tlw variations in yield can have many canses including variations in the tracking chamh<~r efficiency effecting the count rat<~ and variations in the gain or position of the lnminosity monitor. It should be noted that between fills the detector is completely turned off and the luminosity monitor aud calorimeter arc moved away from the h<~am pipe. In addition, the time betw<~en fills can be from hours to days. Sine<~ the efficiencies of the top and bottom chambers are highly correlated, either of these effects could produce the top-bottom correlations evident iu Figure 4.20. Figure 4.21 shows the yield of every good run compared to the mean yield for that fill normalized by the statistical nncertainty of the mu. The expected width of this distribution is 1.0. The observed distribntions suggest that the fluctuations are slightl~· larger thau expected. The statistical 1mcerta.inty in the yield is ~ 4% per nm, and the observed widths suggest there is an additional fluctuation on the order of 11¼, per nm in the yield. This may be due to tlH' 1% raw a."iymmetry (Au) or the 1% variation in the yield observed a."i a function of <:111Tent although the effect is slightly larg<~r t ha.n would he expect,~d for these effects. Additional studies h~· the European analysis group [G8] suggested that this effect may IH' due to additional statistical fluctuations larger than expected from the number of ohs<'rvcd positrons. The results of these stll(lics arc cqniYocal as th<! stability of the as~·mmetry p<~r fill suggests there is a small additional effect while the studies of short<'r time• scalc\s show either no effect (asyrnmctri<\S for groups of five runs) or a small dfect ( the yield per nm). For further clisrnssiou sc<~ Appendix B. 108 <t..- 0.2 0.1 x2/ndt 70.39 AO -0.1033E-01 ± I 54 0.3494E--02 - 0 -0.1 - -0.2 ,_ - - - --'---------~ 100 50 150 Fill Number Top A 3He e+ 6 4 2 10 -3 ~-"--'----"--'-----'---'----'-----' 75.5 150 Fill Number 0 0 0.5 1 Confidence Level Figure 4.14: Time Dcpm1dc11c!i Plots for Positrons ill t.lw Top Dct<'ct.or: The a.<;ymmetry per fill versus till number, the contideucc levd of sets of nms within each till, and the distribution of the confidence levels 10!) <t..- 0.2 0.1 x7/ndf 75.54 AO -0.3827E-02 ± / 60 0.3299E-02 - 0 -0.1 -0.2 50 100 150 Fill Number Bottom A3 He e+ ca.... C) a, C a, 0 10 ·1 6 C Cl) "C ;;: C 0 0 10 ·2 2 D 10 -3 ~~-~--~~-~~~ 75.5 150 Fill Number 0 0 0.5 1 Confidence Level Fiµ;ure 4.15: Positron Time Dependence Ilot.t.om Dd.c!dor a.-; Dc\fine<l in Figure 4.14 110 <t.- 0.2 58.79 / 54 -0.6286E-02 :.J: ~ - - - ~ - - - ~ - - - - . . _ __ -0.2 0.3674E-02 ____J _ _ _ __,_____ _ __, 50 100 150 Fill Number 3 Top A He h+ •..,.,. • • (0 II,.. tJ) Cl) C Cl) 0 10 -1 C Cl) :;:: C 0 \ •• "C 0 .• •••-• • 10 ·2 I - - - - - - - -8 6 4 • 2 10 .3 ~ ~ ~ - ~ -- - ~ - . . _ _~ 75.5 150 Fill Number 0 0 0.5 1 Confidence Level Figure 4.lG: Posit.iv<' Hadron Time Dependence Top Det.<dor as Defined in Figure 4.14 111 = 0.2 <C 58.99 / 60 -0.6226E-02 :L 0.3339E-o2 I 0.1 0 -0.1 -0.2 c _ __ _ _ _ , __ _ _~ - - -- - ' - - - - -~ -- 50 - -"----~ 100 150 Fill Number Bottom A3He h+ as 11., 0) Q) C Q) 0 10 -1 7.5 C Q) "C 5 ;;:: C 0 0 - -2 10 □ 2.5 10 ·3 L__~-~~~-~~-~~ 75.5 150 Fill Number 0 0 0.5 1 Confidence Level Figme 4.17: Posit.iw Hadron Tim<• Dep<'ndcuce Bot.tom D<>t<•d.or as Defined in Figure 4.14 112 <t.- 0.2 //ndf 61.36 / 54 -0 .7890E 02 I: AO 0.1 0.4215E-02 - .I . 0 II -0.1 -0.2 50 ....... . ,"••. ,. • • 100 Top A 3He h- ...m 10 0) Cl) . . . . .! C a, 0 10 -1 C Cl) • •• • • "C ..:: C 0 0 150 Fill Number 7.5 •• -2 10 5 ·- 2.5 • -3 10 75.5 150 Fill Number 0 0 0.5 1 Confidence Level Figure 4.18: Negative Hadron Time Dependence Top Dd.e<:t.or a.-; Defined in Figure 4.14 113 <t.- -·---- 0.2 //ndf 58.04 AO -0.11 OSE-01 ± I 60 0.38 4E-02 - 0.1 I. II II 0 I I -0.1 -0.2 100 50 150 Fill Number Bottom A aHe h- ...cu - 1 - ~□ EifPci C) Q) D C Q) 0 □ [I] -1 10 fj C IC!@ ~ OIItJo D c51 15 C\§1 □ □ □ □~ 10 Q) "C ;;:: C 0 (.) 10 lrJ ·2 5 B q I -3 10 1 75.5 150 Fill Number 0 0 0.5 1 Confidence Level Figure 4.19: Negativ<~ Hadron Time Depe11de11<:<' Ilot.t.om Detect.or a.<; Defined in Figure 4. 14 114 0.2 ·'···'·•• I . ....· .......,,.•·.·.·· .. -- ' ·u,• ' • 100 150 0.15 0.1 - 0.05 0 0 50 Positron Yield per Fill (Top) 0.2 .... - • • .· ·I I ... ,, 0.15 0.1 0.05 0 0 50 100 150 Positron Yield per Fill (Bottom) Figure 4.20: Positron Yield Versus Fill for the Top aud Bottom Detectors 115 //ndf 10 2 -4 -2 0 63.89 / 61 66.19 0.1562E-01 1.032 2 4 (Run Yield - Fill Mean)/(Error in Yield) for the Top x2/ndf 10 72.39 / 65 68.78 0.1693E-01 1.043 · -4 ·2 0 2 4 (Run Yield - Fill Mean)/(Error in Yield) for Bottom Figun• 4.21: Fluct11at.iom, iu Pm,it.rou Yidd: Top aml Dot.tom JOO ·Dashed Ta,gt!t Spin Anti.Parallel Beam ·Dotted r,rget Spin Panlllel Beam :~ :· 200 100 o.a O.B5 O.IS 0.1 1 Front Chamber Efficiency tor Six Fills Fi6'1lre 4.22: -Efficiency Distribution Used in False Asymmetry Checks 4.4.3 False Asymmetries The rapid flipping (every ten minute:-;) of the tarp;et should average over any false asymmetri<!H. Any properties of the experiment which chanp;e on a time scale longer than the spin flip should not contribut<~ to any false a.symmetry. Numerous tests did not observe correlations with the spin flip of the t.arp;«!t which could produce a false a.<;ymmetry. All quantities such as the chamber dficiencies, particle identification response and luminosity monitor rate as a function of current were studied carefully and W<\r<~ found to be independent of the spi11 state. One of the chamber efficiency distributions a.'> a function of ta.rg<'t spin is showu iu Figure 4.22. 4.5 Extracting gi'' The relation of gi' to A;1 was discuss<~d iu Chapter 1. The structure function 91 can now he cakulated from Equation 1.41 (assmninµ; A1 = 0): c.n _ 91 - p,11 1 A"11 2:r:(1 + R) D 117 The unpolarized structure function F2 and the ratio of longitudinal to transverse virtual photon cross sections (R) are required to calculate Af and Yi• Neither quantity is measured in the present experiment but fits to previous data exist for both F2 [57) and R [59]. The value of F~i is determined by (4.15) The rci-;ults at the measured Q2 arc\ di:,;played in Figure~ 4.23. 4.5.1 Evolving the Structure Function g\,. to Constant Q2 The measured structure function is evolved to constant Q2 to compare with theoretical predictions which are made at constant Q2 • No Q2 dependence of Ai has been observed over the Q 2 range which is n~levant for HERMES [60]. As a result, the structure function g;1 is evolved by assuming A;' is not a fundion of Q2 and evolving with Ff(:c, Q2 ) and R(.r,, Q 2 ). The re.<mlts are evolved to a constant Q2 of 2.5 [Gcv/cf" and plotted in Figure 4.24 and tabulated in Table\ 4.15. < :1: > (l.035 0.049 0.06G (l.088 0.119 0.1G8 0.244 0.342 0.4G4 = R(Q 2 2.5) 0.3115 0.3036 0.2924 0.2775 0.2585 0.23G3 0.21G8 0.2050 0.198-1 F2n(Qi = 2.5) 0.332G 0.3259 0.3180 0.3079 0.293G 0.2708 0.2326 0.1792 0.1175 !li'±stat.±syst. -!U895±0.1490±0.059 -0.2810±0.1148±0.032 -0.140G±0.0901 ±0.015 -0. 1G7G±(l.0776±0.019 -0.0922±0.0G 19±0.011 -0.1005±0.0512±0.012 -0.0281 ±0.0414±0.006 +0.0331±0.0431±0.005 -( ).( l1(j!J±0.0345±0.003 Table 4.l!J: !li'(x,(J 2 = 2.5(GcFJ,:]2) 4.5.2 Measured Integral of g;tr:, Q2 = 2.5(GeV/c) 2 ) The integral of the rwutron spin structure function, J y]'(:1:. Q2 )d.r,, is of fundamental inten~st since it appears iu t<'sts of the Bjorken and Ellis-.laffo sum rules. We evaluate the integral at a fixed Q2 = 2.5(GeV/c)2. The integral in the measured region is: 118 c ..... 0) 0.2 0 -0.2 -0.4 \liiiii i i -0.6 -0.8 10 -2 10 -1 Figure 4.23: gt' vs x at Measured (J'1- Wit.Ii Systrn11at.ic Errors (Solid Band) ll!J c,- 0.2 C) 0 -0.2 -0.4 f ~ -0.6 I L I ~ -0.8 I 10 -2 10 -1 1 Xbj Figure 4.24: y;• VR :r. at ConRtant Q2 With Systematic Errors (Solid Band) 120 /0.8 lo gf(x) dx = L gr 6.x = -0.034 ± 0.012, (4.16) bins 0.023 where the sum is over the nine data points and the 6.x are the bin widths. The statistical errors are added in quadrature since they are uncorrelated from one bin to the next. 4.6 Dominant Systematic Errors The systematic errors for g\ 1 are much smaller than the statistical errors due to poor beam delivery in 1995. It is still important to investigate the contributions of the quantities that dominate the systematic errors iu A;'· aud _q11 • The total systematic errors and contributions of the components to each error arc summarized here. There arc other coutributions to the systematic error such as the uncertainties in Af and F~' but these contributions are significantly small<~r thau the errors which are tabulated. Tab}<\ 4.16 cont.aim, the systematic errors for A~'- which arc dominated by the uncertainties in A2. Ta.hie 4.17, the systematic errors for .'l~'(Measured Q 2 ), and Table 4.18 for _qj'(Evolved Q"l. = 2.5{Gdl/c)"2)) arc domiuatc<l by the uucertainties in A2 and the radiative corrections. The uncertainty in A 2 is not as significant for g1 because the ( -./ff - 1/ )A2 term is significantly smaller than the 17A~ term in Al'. Both these terms should b<~ reduced in the future. Radiative corn\<:tions can be reduced by constraining the shape of the A't model with hetter statistics. The uncertainty due to A2 nm he constrained with the soon to he published E154 data [61]. Source Pi, P, RJUlCorr A":l n. ])11 v,, Total Ilin 1 0.005 0.005 0.011 0.007 0.005 0.003 0.001 0.016 2 0.005 0.005 0.006 (l.008 0.006 0.003 0.001 0.014 3 0.003 0.003 0.003 0.011 0.003 0.001 0.001 0.012 4 0.007 0.006 0.002 0.016 0.007 0.003 0.002 0.020 r, G o.oo:i o.oo:i (l.009 0.008 0.004 0.040 0 .009 0.004 0.004 0.043 0.003 0.028 0.()()3 0.001 0.003 0.029 7 0.007 0.006 0.006 0.064 0.005 0.002 0.006 0.065 8 0.008 0.007 0.007 0.114 0.006 0.004 0.008 0.115 Table 4.16: Systematic Errors 011 Aj'(x) at th(~ Measured Q 2 9 0.012 0.011 0.010 0.114 0.007 0.004 0.011 0.117 121 Source P1, P, Rad.Con- A!i' R Pu JJ,, Total Cont.rib. To int. (%) Bin 1 0.01G 0.015 0.033 0.028 0.014 0.008 0.002 0.051 0.086 2 0.012 O.Qll 0.013 0.015 0.007 0.006 0.002 (1.02G 0.040 3 0.005 0.005 0.005 0.010 0.002 0.002 0.002 0.014 0.027 4 0.009 0.008 0.003 0.009 0.002 0.004 0.003 0.016 0.039 5 0.003 0.003 0.003 0.009 0.000 0.001 0.003 0.011 0.042 G 0.005 0.005 0.003 O.OOG (1.000 0.002 0.003 (1.011 0.065 7 0.002 0.002 0.002 0.004 (l.000 0.001 0.002 0.006 O.OG3 8 0.002 0.002 0.002 0.003 0.000 (l.001 0.002 0.005 0.047 9 0.001 0.001 0.001 0.002 0.000 0.000 0.001 0.003 0.050 Integral 0.002 0.002 0.002 0.003 0.001 0.001 0.001 0.005 (abs) Tahle 4.17: Syst.emat.ic Errors 011 y;1 (:.1:) at the Measnre<l Q2 Source P1, P, RrulCorr All:l R JJ11 ]!1, Tot.al Cont.rib. To int. (%) Bi11 1 0.020 0.()18 0.039 0.033 0.014 0.009 0.003 0.059 0.101 2 0.013 0.012 (l.014 0.016 0.007 0.006 0.003 0.029 0.044 3 0.005 0.005 0.005 0.011 0.002 0.003 0.003 0.015 0.029 4 ().()09 0.008 0.003 0.009 0.002 0.004 0.003 0.016 0.040 5 0.003 0.003 0.003 0.009 0.000 0.001 0.003 0.011 0.043 G 7 0.005 0.005 0.003 O.OOG 0.0(1() 0.002 0.002 (1.(111 0.064 0.002 0.002 0.002 0.004 (l.000 (l.001 0.002 0.006 0.062 8 0.002 0.002 0.002 0.003 0.001 0.001 0.002 0.005 0.048 9 0.001 0.001 0.001 0.002 0.000 0.000 0.001 0.003 0.057 Integral 0.002 0.002 0.002 0.003 0.001 0.001 0.001 0.005 (abs) Table 4.18: Systematic Errors 011 y 1'(x) at (J 2 = 2.5GeV 2 4.6.1 Cut Dependence of the Measured Integral of gi'(x) The many cuts detailed in the analysis select the data which is used for the analysis and , thus, the measured asymmetry. The effect. of these cuts was studied by varying th<' cuts over a range where the time dependence was r<'asonahle. That is, the x1 / r{f for the asymmetry per fill wa.-; approximately tl1<1 same a.-; that for the standard cuts. \~'ithin this rea.-;onahle range, varying tlw cuts had littl<' effect on the measured a~rmnwt.ry or the iut<igraJ .1;:'..~~:i.lJ\'(:1:)tl:1:. Tlw Yaria1.io11 iu cakulatcd asymmetries from these studies is small<ir than the systematic errors from the inputs to the calculation of _q\1 • As a nis11lt, no additional systmnatic error has been assigned for the cut d<>pendeucc. The integral had the strongest dependence on the front chamber total effic:icu c~· cut and the results for variations of this cut am shown in Table 4.19. 122 Efficiency 10% 40% 80% , 85% e+ Ji+ 2 x /df 2 x /df 0.97 1.24 0.85 1.24 0.81 1.G4 0.61 1.28 1.44 1.01 1.5G 0.98 1.71 1.12 1.Gl 0.95 1,.- X2 /df 1.54 1.37 1.41 1.43 l.G2 1.48 1.40 1.23 C'·b n . 0.0:B 91 -0.033 ± 0.010 -0.031 ± 0.010 -0.032 ± 0.010 -0.028 ± 0.llll Ta.hie 4.19: Front Chamber Tot.al Tracking Efficimu:y Cut Dependence 4. 7 Comparison to Theory In order to compare the results of the experiment to theoretical predictions, it is necessary to extrapolate g;• into the unmeasured regions of :c between O and 0.023 and O.G and 1.0. These extrapolations will be cliscus.<.;cd next. 4. 7 .1 Low :r: Extrapolation The integral in the 1mmeasured region, 0 < :r. < 0.023, is estimated by assuming a R.egge-like behavior [G2] [G3] [G4], g 1 (x- > 0) = :r:-n, where the Regge intercept a nu1 var~' from -0.5 < n < 0. In this region H<~a and gluon contributions dominate the nud<•ou structure, and it is generally assumed that no difference should exist between proton and 1wutron behavior. (4.17) Using tlw leading logarithmir intercc!pt value of n = 0 and fitting the data in the two low<~st :r: hini-;, W<! obtain an integral of r-1,0-1,3 /o .<Jitr:) d:r; = -0.00G ± 0.005. (4.18) A 100 % uncertainty has been a.<.;Hmrwd in this <\Xtrapolation. R.,~cm1t work [65] indicates that an NLO treat11w11t of the low x region could yield different, significantly more negative rei-;ults for the low x extrapolation. An NLO 123 treatment of the extrapolation has not been performed and the Regge-like extrapolation is consistent with previous extrapolations [4). 4. 7 .2 High x Extrapolation To determine the integral at high x (> 0.6), we estimate Aji and the contribution to the integral. There are theoretical reasons to believ<' that Aj1 goes to 1 as x approaches 1 (66]. The high :r: contribution to gr' is theu determined hy a:-;:-mming that Af is positive. A constant value of A~' = 0.5 ± 0.5 i:;; used for :r > O.G in the extrapolation. The x dependence of F]' is obtained from the paramcteri~atiou of the NMC proton and deuteron data [57). This produces a total high x extrapolation of /1 9r (:r:) d:r: = 0.003 ± 0.003. 1 lo.6 4. 7.3 (4.19) Total Integral of gf(x, Q'2 = 2.5(Gf'll/('.)'2 Combining all of tlw previous rcsult.8, W<\ find (4.20) where the <~rrors are statistical, systematic, awl extrapolation. This result at nmstant (J'l ca.n now be compared to the CJ'l (\VOIV<!d vahws of the structure function :-;11111 rulc\s. 4.7.4 The Ellis - Jaffe Sum Rule The Ellis - .Jam-~sum rule (Section 1.5) pr<'<licts (4.21) At < ct· > of (2.GGeV/c)'l the QCD conc\ctious t.a.kc the values 124 (4.22) (4.23) and the sum rule has the theoretical value 1 r;' = - 12 (F + D)Cns + ;G (3F - D)Cns + i(3F - D)C., = -0.013 ± 0.005. (4.24) This falls two sigma outside of the present me,umrement. 4 . 7 .5 T he Bjorken Sum Rule Using the E143 proton result of [5] rnQ 2 = 2.5(GcV/c)2) = 0.130 ± 0.011. {4.25) The value obtained for the Bjorken sum rule is f 1i'(Q 2 = 2.G{GeV/c)2) - f't'(Q 2 = 2.G{Gcl ·t('.)2) = 0.lGG ± 0.016. (4.26) The tlwon~tical expectation is (Sect.ion LG) 0.165 ± 0.005. Tims, tlw HERMES data combined with tlw r<~sults of E143 i:-. in excellent agreenwut with the tlwordical prediction of tll<' Iljork<~H sum ml<!. This confirm:,; pwvio1rn re:,;nlts :,;ngge:,;ting that the Ellis~.Jaffo :-.um rules are violated whil<· tlw Bjorken Hlllll rule iH satisfied. The vahlPS of r~'· aud the :,;piu contribution of the quarks. n· <:all be used to extract 125 ~ Blorken Sµm Rule 0.1 8 HERMES Neutron b;] E142 Neutron rJ E143 Proton 0.05 0 -0.1 -0.05 0.05 0 0.1 Neutron Integral Fi~urc 4.25: The Agreement Bet.ween Data From Various Expniuumt:-: and the Iljorken Sum Rule 4.7.6 Quark Contributions to the Spin of the Nucleon Using tlw mea.•mred values for tlw inte~rnl r;• as w<·ll as th<~ values of I~ I and F /D from hy1wro11 <lecay, OW\ extracts the systern of <•q1111tio11s [G7] [68] rnI - 1 l (Au - Ad)C,,, + : G(~u + !::.d - 2As)Cn.~ + 12 3 1 9(!::.'11, +Ad+ !::..c;)C.- (4.27) 1.<JA I= 1.257 .<Jv (4.28) 126 3F - D = .l:::,.u + .l:::,.d - 2/:::,.s = 0.579. (4.29) Solving for SE = .l:::,.u + .l:::,.d + .l:::,.s we obtain .!:::,.E = 38 ± 11%. (4.30) This can be compared to the Ellis-.laffo assumption (.!:::,.H = 0): .!:::,.E = .l:::,.u, + .l:::,.d = 3F - D = 57.9%. (4.31) Now, the spin decomposition can be performed, yielding 86±6% (4.32) -41 ±6% (4.33) -6.6 ±3.7% (4.34) (4.35) which can he interpreted to mean that the <tnarks carry a fraction of the nucleon spin and that the strange sea is negatively polarized. 127 Chapter 5 Summary and Conclusion The neutron spin structure function g;1 has lwen measured with a polarized 3 He target. The results are in agreement with those of the SLAC E-142 experiment, but have been determined by an entirely 1ww tedmiquc - a windowless polarized internal target with pure atomic species in a positrou stonige ring. This measurement was made during the commissioning year for the HERJvIES spectrometer. This indicates the many exciting possibilities of the HER11ES spin program, especially with the numerous upgrades to the spectrometer. The repair of the vertex chambers and insertion of au additional set of drift chambers near the target will greatly increase the tracking resolution and efficiency. The substitution of C4 Frn gas in the Cerenkov cl<)t<•ctor will allow 1r identification over a much larger momentum range and the propos<•d upgrade to a RICH (ring imaging Cerenkov) will extend this to 7r and K identification owr the full momentum range of tlw spectrometer. Semi-inclusive asymmetries will benefit from both of these upgrades. The higher tracking efficiency will increase the rate of multiple trnck events and the better hadron idm1tification will allow the identification of th<• l<~a<ling hadron. This will allow the decomposition of the asymmetries for diffon•ut ttavors of struck quark and separate valm1c<\ and sea contributions. A program of spin physici-; rrwa."iurmwnts has h<~gun at HERMES. The 1996 and 1997 proton data will begin the program of s<·mi-indusiv<~ measurements and should produce definitive measurements of the smni-iudusive 1f asymmetries. HERMES is part of a second p;eneratiou of spin physics <~xperiments and will benefit from the high statistics measurmnents of ElG4 [69] and E155 [70] at SLAC and upcoming measur<>ments of the hi~h x dqwndcnc<\ of A~'- at CEBAF [71]. 128 Appendix A Design and Testing of the Hodoscopes A .I T h e HERMES Hodoscopes A. 1.1 Introduction The HERMES hodoscopes were rlesigned and built hy Caltech. Details of the construction and performance arc discuss,\d h<~low. Two planes of scintillator are used as hodoscopes and provide fast signals for the first l<\Vd trigger. The second hodoscope is operated as a pre:.;hower detector to improv<~ tlie partick~ identification of the spectrometer. A 1. 1 cm :.;beet of lead initiates electro-magnetic showers before the second hodoscop<~ and the calorimeter. A. 1.2 Components and Assembly The paddle:.; arc made from BC-412, a fast :.;cintillator with a large attenuation length (300 - 400 cm). The scintillators arc coupled to 5.2 c111 diameter Thorn EMI 9954 photomultiplier tube:.; with fiHhtail light guide:.;. A:.;s<\lllhlies of scintillator, light guide aud PMT were glued together with optical C<\lll<'llt awl irn,talled as single units in the hodoscopcs. Thc:.;e units were designed for eai.;y iustalla.tion iu the hodoscope frames and stahili:i:cd the PMT lightgui<l<> joint against mcdianical vibrations. The frame was cl,~signed for easy installation all(l removal of tlws<~ 1111its. A sketch of the top of au a."iscmhl,\d ho<loscopc is shown in Figun~ A. l. Tlw paddles am wrapp<~d in on<' la~-<~r of higlil:v rdfoctiw aluminum foil and a layer of opaque te<llar (0.005 .. t.hi<:kness). Au ah11ui111nn cud cap was installed over the <\IHls of the foil-wrapped :.;ciutillator to <~nstm\ dcctrical contact between the foil wrappinp; and the ho<loscope framC' and to prod11<:<) a 11uiforrn mechanical alignment for placement in the frames. Th<> <'nd caps W<\r<) 1.0 cm high and fit into a series of 0.G cm deep grooves cut iu the base of the hodoscope frames; the top of the end caps _. ] Screw 130 I.J cmr '"cmI·"I 1.0 Lc"'1 0.3cm H ScinliJ1'111,r I l I I Figure A.2: Hodoscope Pa.cldJi, Arrangement wa.<; taped to the tedlar to ensure a light tight \\Tapping of <)ach paddle. The tedlar <)xtcnded near the end of the lightguidc>,s and tap<' was used to ensure the continuity of the light tight surface over the edge of th<~ P:\IT. The modules an\ staggered in two overlapping rows to provide coverage of the entire region within the acceptance with no gaps het.w<'<~n paddles. The rows overlapped 3 mm (Figure A.2) to completely cover the actin~ ar<)a of the spectrometer with the minimum number of paddles. Thi:,; arrauµ;cBwHt provide:,; only a crude position measurement ru:; the drift chambers provide much lH'tt<~r resolution than the 9 cm wide po:-;ition re:-;olution of the hodoscopes. The rows of overlapping paddles are arranged so that the first paddle (furthest to the left wll<'n looking along the beam direction) is in the front row (dose:,;t to magnet) for Hl awl tlw hack row for H2. Each PMT wa."i housed inside a 0.5 mm thick c~·liuclrical ,,, - metal shield which provided additional magnetic shielding in addition to a11 integral shield in the PMTs. Tlw paddles ar<) held by an ah11Bin11111 fra111<· which gripped the paddles on the light.guide and at the end of the sciutillator. Tll<' franl<' was de:-;igned to have a small awa ucar the heam pip<~ and avoid the HERl\IES ,IC<:<!ptanc<~ while supporting the l<)ad pr<!shower without sagging nH>r<! than 1 11u11 iu t,lw middle. Each hodoscope p,ulcll<~ had an almuimnn end cap 011 tlw <'11<1 of th<· sciutillator. The aluminum end caps eusnr<!d correct alignment i11 the hott 0111 plat<' of tlw hodoscope frame. In the bot.torn frame, spacers were also mounted 1war th<· liµ;htguides. The end caps and spa<:<!l'S secured the hodoscopes in rdatiw posit iou awl pwvented shifting during the <!XJwrirrwnt. A lead sheet is used to initiate the EM shmYNs hd'orc tlw second hodoscope. To protect the lead from creeping and ensure rnc!diauical stability during installation, 131 two stainless steel sheets are glued to the faces of the lead sheet. Each preshower module has 8 lead sheets attached to the front of the frame. The edges of the lead are beveled as shown in Figure A.2 to prevent any gaps parallel to the path of the particles. Figure 2.17 shows the front view of a hodoscope plane with the lead sheets installed. A.1.3 PMT Testing The PtvIT's exhibited a single P.E. response that was used to calibrate the gain wrsns voltage for each tube and evaluate the noise~ l<'V<)ls in the tube. The tubes were operated iu a light tight box for one hour to stahiliz:e the dark rate aud gain. An attenuated light source was used to provide light in the 'blue' range. The response to single photoelectrons was recorded. If the~ sing-le P.E. peak could not be clearly resolved from the pedestal (Peak to valley ratio of 1.5), the tubes were rejected. The voltage dependence of the gain was fitted to an exponential and used to select appropriate voltages for operation at DESY. The noise a.t the single photoelectron lc\wl is not r<)levant for the operation of the c\xperiment. Several hundred photoelectrons W<'r<) obserwd for a minimum ionizing particle traveling through the scintillator, aml tlH' trigger threshold was set at half of the signal height for minimum ionizing pa.rt.ides. Tlw clark noise from the tubes is small at this threshold if the single photoelectron peak can IH\ resolved. A.1.4 Attenuation The padcllc)s wew required to have an dfoc'.tiv<) at.k1matio11 lm1gth of at least 250 cm to he\ IIS<)d in the HERMES SJH!dronwtc)r. This limited the variation in signals due to attc•111iatio11 to 30% from top to hot.tom of a paddle witliiu the acceptance. Tll<' <·ffoctiw a.ttcuuatiou length was rn<·asm<'d for each paddle at Caltech. Two pairs of finger scintillators were placed above• and below two hodoscope paddles (FigHrf> A.4) to identify a sample of cosmic rays through the paddles. The spectra of minimum ionizing particles were recorded fr>r two positions near the ends of each scintillator paddle. An effective attenuation length was calculated from the most likely energy deposition from a fit to a Landau distribution [72]. The effective at.ten- 132 Light Tight Box Light Source (He Vapor Lamp) Attenuators Figure A.3: PMT Gaiu :\l1•as11r<!IIH!uts 133 Front View TF2 TF I D D Paddle l (Top) I =:t I 76cm Paddle 2 (Bottom) 7cm D c I D TF4 TF3 J:-1 7cm 1cm I :::::==S=i_d_e-=--=-V-=-i-e_w-=..-=..-i--::?,__ _ _ _ _ _ _ .J 9cm 9cm I I 15cm Figure A.4: Hodoscope Pa.ddlc At.t.enuat.ion Tests nation length a.sstmws an exponential dependen<'<' for 1.lw attenuation in the paddles. This length was used to quantify tlw attemmtiou of each paddle and the measured effective attf!Ht1ation lengths were between 250 a11<I 450 cu1. This effective attenuation is au oven~tima.tc of the actual attmma.tion lcnJ?;th l><!GlllS<! of the reflection from the rdi< d.ive a.lnmiunm a.t tlw end of the paddle. Th<• a.dual position dependence of the 1 att<·1matio11 is mor<\ complicated than a simpl<~ <·x1><m<·utia.l <l<~cay as discussed next. A. 1.5 Detailed Attenuation Studies An additional s<~ries of attenuation tests were p<•rformcd to ddermine the attenuation as a fnuction of position along the paddle. Reflections from the end of the scintillator mitigate the attenuation near the end of the paddk a.ud acceptance effects near the light guide also alter the distribution. The resultiuµ; distribution differs by up to 134 10% from an exponential dependence. This dependence was parameterized to correct the position dependence of the signals in the spectrometer. Figure A.5 shows a parameterization of the attenuation distribution for a paddle with a relatively good effective attenuation (412 cm) as an example. TIH' data wa.'-i parameterized via E Ecorr = (1 + A(Acff )1/2)<'-!I/B(>..,,ff) (A. 1) where >..eff is the measured atteuuatiou l<·nµ;th; A and B are functions of the attenuation leugth and have typical values of l.lxl0- 1 <:'111,-2 for A and 96 cm for B for Aeff of 300 cm. A.1.6 Final Gain Tests After the :;;cintillator assemblies were glued tov;<•tlwr, a final te:;;t was performed with the cosmic ray attenuation measurement apparatus. This provided the total gain for the assembly at a selected voltage and checked the attenuation measurement. The gain of the a.'-isemblieB was up to a fact.or of two higher with a glued PMT lightguide joint compared to a coupling with optical v;rca.'-i<'. The gain mea.<:.ured in this test was used with the gain curve measured for the PJ\IT to select an appropriate voltage for the assembly. The paddles with longer attenuation lengths W<'r<' used iu th<~ H2 detector to make the attenuation corrections smaller. Paddles "·ith shorter attenuation lengths were installed on the outside where there is little rat<•. Tlw paddl<~s in the H2 had effective att<'lluation lengths bet.ween 450 cm in the middl<• and 300 cm at the edges. This kept tll<' attenuation corrections to under 2!:;'¼) in th<• 1n·<·show<)r dd<~dor. The attenuation l<'ngths w<~re hetwc<-!11 300 cm in the middl<• awl 2S0 cm at the edges for the Hl. Tlw first hodoscopc has only photon pa.rt.id<· id,•ntiticat.iou ability where the tag for a photon is essentially no pulse height, so gain (·orrcd.ions arc not as important.. A. 1. 7 Y P osit ion D ep endence The attenuation measurements are used to corn'et the y position dependence of the data ill the off-line analysis. 135 -u, C :::, ... .c ct ( ti C C, en 1 · Attenuation of Light in Paddle (1...,, = 412 cm) - 0.9 .... . . . . . . . . . . 0.8 0.7 0 .6 0 20 40 60 80 Distance From Lightguide (cm) Figure A.5: Light At.teuuat.iou iu Hodoscop(~ Paddles 136 After a correction is made for the attenuation in the paddle, there is less than a 1% systematic dependence of reconstructed energy on position along the paddles. Figure A.1. 7 shows the most probable energy deposition of minimum ionizing particles as a function of position in the second hodoscope. ~lonte Carlo simulations suggest that a gain shift of this size will have no appreciable Pffect on the particle identification in the HERMES spectrometer. The variations of the height of the minimum ionizing signal observed on an oscilloscope are much smaller (a few%) than the variations in the total integrated charge. This is a result of reflections from the en<l of tll<' paddle. For signals near the lightguide, two peaks a.re resolved by the phototnh<•. A large peak from light traveling toward the tube followed by a smaller reflection peak up to ten ns later. The signal from near the end cap has a smaller total charge, but the two peaks (direct and reflected) arc not resolved. This significantly reduces the effoct of attenuation on the trigger. A.1.8 X Position Dependence Calibrations of the HERMES hodoscopes wen' performed in two ways. The GMS system used a series of laser pulses to calihrat<' tlw gain relative to a photodiode (Sect.ion 2.4.12) and the minimum ionizing partid<~s were used to provide a fill to fill calihrntiou of the hodoscope paddles. The gains nwasurecl this way are used both to track any significant changes in the hocloscop<• gaius and to c:orrcct the gains during a second pass of the off-line analysis. The gain variations in the paddles was wr~· small ancl agreed for the two methods. Tlw average gain per fill for most paddles diang<·d onb' a fow percent over the course of tlw entire year. The accuracy of the rni11in111m iouiiing measurement depended strongly on the position of the paddle. TlH' n·ntral paddl<\S had very high rates, but the event rate falls quickly away from the central n\giou. The gain could be measured to within 1% for all but the four paddles at <'ach <•dg<~ of tlw sc\cond hodoscope and six paclclles at each edge of the fin;t hodoscope withi11 a nm. The gain variation of eight H2 paddles for the first month of data an\ shown in Figure A. 7. The outer paddles mentioned above detect particles which arc h<'llt a large amount in the magnet, that 137 >(1) C, ·2 x'/nc.Jf 12.56 AO 0.2037E--02 / 8 -X10 en -- C 0.22 0 "O ca :I: 0 >, C) (1) C w 0.2 (1) .c ca .c ...0 0.. en 0 2 0.18 20 40 60 80 100 Distance from Plane of Beam (cm) Figure A.6: Hodoscope Y Depeudcm·p .-Ht<\r Off-liue Correct.ions 138 is, particles with very low momentum. The DIS positrons are all incident on the well calibrated paddles. A.1.9 Particle Identification The H2 counter provides discrimination betwc~cn positrons and hadrons. A radiator initiates electromagnetic Rhowers that are detcdc•d in the H2 scintillator. The 1.1 cm lead sheet represent 2 rndiatiou l<\ngths and high energy positrons passing through the sheet will begin clectromagn<'tic showers. The energy deposition distribution of positrons in the scintillator is wry broad because the deposition is very sensitive to the depth of the lea<l where the :,;hower begins. The mean energy deposition in the :,;cintillator is near 40 Me V. The nuclear interaction length is 10 cm for lead and most of the hadrons pass through tlw lead sheet without interacting. These non-interacting hadrons deposit significantly le:,;s energy in the scintillator than positrons with equivalent momentum. The width of the lead preshower was dtOS<\n to maximize the hadron separation of both the calorimetc~r and pre.shower together. Increa.'ling the width of the lead aids the hadron separation of the preshower but hurt:,; the energy resolution and therefore the hadron separation of the calorimeter. The particle identification abilities of the preshower and calorimeter were test<\d at CERN. A.2 CERN Test Beam Au initial test of the preshower was performc~d at tlw Xl tc\st beam at CERN from Octohm- 11 to 21, 1994, in coujunctiou with tlw \\·AsD colla.hora.tion. Additional data were• ta.ken to rnea.<.;1m~ the <~ncrgy resolution and li1warity of tlw calorimeter with the pre:,;how<\f installed and to te:,;t tlw pa.rtick id<•ut ificatio11 ability of the detectors at au <\nergy range relevant to HERMES. A.2.1 Experimental Setup Particles were identified by two threshold Cerenkov detectors and three finger scintillators. The first Cerenkov contained He gas and the second, N 2 . The pressure in the 139 Hodoscope Gains vs Fill 0.003 0.003 ( 0.002 0.002 0.001 0 f~ .....,.....,.... ·~ 0.001 20 0 H2 Upper 14 Gains 0.003 0.002 0.001 0.003 0.002 0.001 20 r-::-· ~--•.•■-•~--■- 0 H2 Upper 16 Gains 0.003 0.002 0.001 20 0.003 0.002 0.001 fr-••···· r 0.001 0.002 I ~--~- .-...·........ , 0 H2 Upper 19 Gains •~ 20 H2 Upper 20 Gains '~ 20 I 0.003 ~ N•,~ 0 20 c- H2 Upper 18 Gains 0.003 .~ H2 Upper 17 Gains r-•:··· .-·.••■-•,----·~ 0 20 H2 Upper 15 Gains t-·.--·· 0■■--■,■■■N1■H■, ~ 0 .. 0.002 0.001 l t-~ ~--·.· -,·--· '" 0 20 H2 Upper 21 Gains Figure A.7: Ga.in Va.riat.iou Durillp; tlw First 25 Fills 140 Beam Momentum (GeV /c) 5 10 15 20 25 , 3 X 3 Cluster Resolution \Vithout Preshower With Preshower 3.9 % 6.8 3.2 % 5.0 2.7 % 4.3 2.7 % 3.6 2.5 % 3.1 Table A. l: Calorimeter Resolution With and Without Lead Preshower two Cerenkov detectors wa.'> varied so that tlw dd.<\dors could be used for electron 7f separation at various momenta. The tri~ger wa!-i a coiucidence of the beam burst with the S1 and S2 finger scintillators. Au array of 60 calorimeter blocks (G X 10) wa..., mounted on a movable platform at the Xl test area. Of these 60 blocks, 3G could he centered on the beam. A test preshower was placed 10 cm in front of tlw fac<' of the calorimeter blocks. The test preshower was a hodoscope scintillator paddl<- with a small (9.3 by 9.3 by 1.1cm) lead and stainless steel sandwich mounted 5 cm iu frout of a hodoscope scintillator paddh~. The sandwich had an identical profile as tit<~ pre:-,hower sheets used in the s1>ectromcter. A.2.2 Shower Distributions The euercy leakage from 3 X 3 dusters of calorinwter blocks wa.<, measured versus the position of the beam 011 the <niter hlock of tlI<' duster. The analysis suggests that 3 X 3 dusters contain the majority of the <\Iwrg_v of the shower regardless of the iucidcut position and these clusters c;m I><' ns<\d to tll(~a•..,uw the energy deposited by <'lectromaguetic showers in tlw calorimet<•r. Tlw n•solutiou of these dusters versus <'kctrou h<\am energy is shown in Tahl<· A.l. A.2.3 The Linearity of the Calorimeter The absolute energy calibration of the 3 X 3 matrices of lead glass counters is shown i11 Figure A.8. From an energy of 5 GeV to 30 G<>\.', tlw <lat.a is reproduced to within 1% b:v a linear fit. With the inclusion of DESY test h<~am results, this linearity can be extended down to 1 Ge V. 141 ...G>>C) C LU -... "C G> ..· 0 - ,, , :::, ~ .· .· 20 ,, - 0 0 G> a: ;··/ , 10 . • :>' :-• .· ~ · ;-;>-' -;, ,, .-··,, ,, 0 0 10 20 Beam Energy (GeV) Figure A.8: Calorimetc•r Liuearity 142 Momentum Cut (ADC) 100 200 300 400 500 600 700 10 GeV/c 1r rejection 0. 725 ± 0.005 0.895 ± 0.004 0.921 ± 0.003 0.933 ± 0.003 0.939 ± 0,003 0.943 ± 0.003 0.946 ± 0.003 e- efficiency 0.998 ± 0.001 0.996 ± 0.001 0.990 ± 0.002 0.983 ± 0.002 0.969 ± 0.003 0.952 ± 0.003 0.933 ± 0.004 15 GeV /c 1r rejection 0. 706 ± 0.004 0.880 ± 0.003 0.912 ± 0.003 0.923 ± 0.002 0.929 ± 0.002 0.933 ± 0.002 0.937 ± 0.002 e- efficiency 0.998 ± 0.001 0.997 ± 0.001 0.995 ± 0.001 0.988 ± 0.002 0.979 ± 0.003 0.970 ± 0.003 0.959 ± 0.004 Table A.2: Haclrou Rejection and Electron ld<~nt.ificatiou of the Preshower A.2.4 The Hodoscope Response The response of the hodoscope to hadrons and positrons ha!-i been shown in Figure 3.1. The CERN tests provided the first mea.•mremeuts of the pre.shower response to high energy particles. The mean energy deposition of <>le<:trons in the scintillator is shown a!-l a function of beam energy in Figure A.9. A.2.5 Particle Identification The main goal of the CERN tests was th<\ measurement of the particle identification c:apahilitics of the combined prcshower and calorimeter. The hadron distribution for HEB:'.\IES is exp<~cted to be a i,;trong function of 111om<\ntum with the majority of the hadrons at low mouwutnm. For the identification of d<)<!p indastic positrons, it is important to have µ;ood pion rejection between ;j and 15 Ge\' / c. Data with the pion and <>lcdron beams was taken at 10 and 15 GeV /c. Tlw pion rate was too low to tak<• a rnasouable data sample at momenta helow 10 GcV /c in the available time. Data samples of G381 7f - and 4030 ,,- wen• ta.ken at 10 G<N /c and 11086 7rand :294G e - at l;j GeV /c. The mcasun\d dfici<~nci<~s and hadron rejections for the 1n·<•showcr and calorimeter an\ talmlatcd in Tahl<•s A.2 all(l A.:3. The hadron rejection and <'l<~ctron efficiency for the preshower ,H<\ also plott<)d iu Figures A.10 and A.11. 143 hodo energy . . 0 0 0 0 ~ .N . . 0 0 v-J ~ 0 0 (Jl 0) 0 -.....J 0 \ \ \ \ (Jl ~ \ \ \ \ ~ 0 0- \ \ (D 0 \ 3 ~ (D ~ (Jl ::::J \ egg_ \ (D 7 \ LO \ '< N 0 ~ \ \ N (Jl \ ~ \ \ \ v-J 0 Figure A.9: Mean Electron Energy vs Momentum for the Preshower: Both Scales in GeV 144 Momentum Cut (E/P) 0.7 0.8 0.9 10 GeV /c e- efficiency rejection 0.047 ± 0.003 0.987 ± 0.002 0.028 ± 0.002 0.984 ± 0.002 0.009 ± 0.001 0.974±0.003 1r 15 GeV /c e- efficiency rejection 0.035 ± 0.002 0.997 ± 0.001 0.020 ± 0.001 0.991 ± 0.002 0.012 ± 0.001 0.976 ± 0.003 1r Table A.3: Hadron Reject.ion and Elect.rou Identification of the Calorimeter > 0 C .!!! 0 ;;:: w 1 C 0 - -• ~ ... ~ llo. 0 -9! ... • Q• ~ w ~ 2 • • 0 ... ... 0 0 • • - 0.9 0 • • 0.8 0.7 0 • SGeV A 10 GeV A 25 GeV I I I I 200 400 600 800 Preshower ADC cut Figure A.10: Electron Effici<•uc\· of Preshowcr 145 C 0.5 0 .:: 0 Q) ·ar a: C 0 a: 0.4 c---- 0.3 ~ • 10GeV ■ 15 GeV ■ • 0.2 ' ■ • 0.1 I 0 0 I I ■ ••• ■ ■ ■ • I I ■ • ■ • I I I I 250 500 750 1000 ADC cut on Preshower Figure A.11: Piou Rc:jectiou iu PrcslimV<'r 146 Appendix B Merging Independent Results Two groups independently analyzed the 1995 HERl\IES data. The NAPA (North American Physics Analysis) results have bec>n prc!sentcd in <letail in this thesis while the EURO (European Physics Analysis) results an' preseute<l elsewhere. [58] Since the time dependences and results for the two analyses were very similar, it was not dear which analysis should be selected for publication. It. wa.c.; decided that an average of the two results would be created for the ofiicial HERMES 1995 A~He_ <x> NAPA A/fr±stat. 0.035 0.049 0.066 0.088 0.119 0.168 0.244 0.342 0.464 -0.0246 ± 0.0113 -0.0250 ± 0.0122 -0.0137 ± 0.0130 -0.0317 ± 0.0149 -0.0153 ± 0.0159 -0.0395 ± 0.0l!JO -0.0251 ± 0.0241 +0.0292 ± 0.0416 -0.0394 ± 0.0610 EURO A';11 •·±st.at.. - 0.0244 ± 0.(ll09 -0.0280 ± 0.0121 -0.0222 ± 0.0128 -(J.0305 ± 0.0147 -0.0327 ± 0.0156 -0.0387 ± 0.0184 -0.01G6 ± 0.0232 +0.0187 ± 0.0401 -0.0388 ± 0.0597 Average - 0.0245 ± 0.0111 -0.0265 ± 0.0121 -0.0180 ± 0.0129 -0.0311 ± 0.0148 -0.0240 ± 0.0158 -0.0391 ± 0.0187 -0.0208 ± 0.0236 +0.0239 ± 0.0408 -0.0391 ± 0.0604 Tahle B.l: Avera~<~l Mea:mrrn111•11t. of A';u.- <:r. > 0.035 0.049 0.066 0.088 0.119 0.168 0.244 0.342 0.464 Average A; 11 e ±st.at. -0.0245 ± 0.0111 -0.0265 ± 0.0121 -0.0180 ± 0.0129 -(J.0311 ± 0.0148 -(1.0240 ± 0.11158 -0.0391 ± 0.0187 -0.0208 ± 0.0236 +0.0239 ± 0.0408 -0.0391 ± 0.0604 .4.j'±st.at.. !li'±st.at. -0.1045 ± 0.0411 -0.1098 ± 0.0450 -0.0758 ± 0.0483 -0.12:32 ± 0.05G6 -0.0%:l ± 11.0G.JI -0.156:l ± 0.078:, -0.0748 ± 0.1057 +0.1478 ± O.l!JRl -0.1560 ± o.:l270 -0.3203 ± 0.1260 -0.2498 ± 0.1024 -0.1316 ± 0.0839 -0.1630 ± 0.0750 -0.0!)28 ± 0.0614 -0.1029 ± 0.0517 -0.0296 ± 0.0419 +0.0317 ± 0.0425 -0.0146 ± 0.0305 ., Table B.2: A~'· aud !It' From tlw Avera.~e A/1r There is little statistical motivation for av<~raµ;iuµ; two alternative measurements with the same data, hut the differences iu the r<!!mlts arc small. The values of gf (Table B.2) calc11late<l from the average A?" vahws ar<' consistent with both the EURO and 147 NAPA gi' values. The integral of gf over the measured region is -0.034 ± 0.012, the average of -0.035 ± 0.012 for the European analysis and -0.033 ± 0.012 for the American analysis. The difference between the analyses is of the same order as the cut dependence studies and no additional systematic error has been assigned for the difference between the alternate analyses. <x> 0.035 0.049 0.066 0.088 0.119 0.168 0.244 0.342 0.464 NAPA gj'±stat. - 0.3214 ± 0.1283 -0.2371 ± 0.1032 -0.1037 ± 0.0846 -0.1660 ± 0.0755 -0.0589 ± 0.0618 -0.1040 ± 0.0525 -0.0373 ± 0.0427 +0.0373 ± 0.0434 -0.0147 ± 0.0308 EURO !1; 1 ±stat. - 0.318 ± 0.0-18 -0.265 ± 0.029 -0.161 ± 0.023 -0.167 ± 0.021 -0.131 ± 0.016 -0.103 ± 0.(l17 -0.024 ± O.CllO +0.025 ± 0.013 -0.0ll ± 0.011 Average - 0.3197 ± 0.1267 -0.2510 ± 0.1041 -0.1323 ± 0.0858 -0.1665 ± 0.0767 -0.0949 ± 0.0619 -0.1035 ± 0.0522 -0.0307 ± 0.0424 0.0312 ± 0.0427 -0.0128 ± 0.0304 Table Il.3: Averaged Measurement. of !Ii' at. Measured Q 2 To <·ompensate for this effect, the statistical <'rror ha.rs of the published data have hcen <·\Xpanded by 10% to account for these fluctuations. 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