SLAC-R-697 UC-414

Measurement of the Spin Structure Function of the Neutron G1(N) from Deep Inelastic Scattering of Polarized Electrons from Polarized Neutrons in He-3 *

James A. Dunne

Stanford Linear Accelerator Center Stanford University Stanford, CA 94309

SLAC-Report-697 1995

Prepared for the Department of Energy under contract number DE-AC03-76SF00515

Printed in the United States of America. Available from the National Technical Information Service, U.S. Department of Commerce, 5285 Port Royal Road, Springfield, VA 22161.

* Ph.D. thesis, American University, Washington DC, 20016

MEASUREMENT OF THE SPIN STRUCTURE FUNCTION OF THE NEUTRON g,"

FROM DEFf INELASTIC SCATTERING OF POLARIZED ELECTRONS FROM .,?

POLARIZED NEUTRONS IN 'He

by

4ames A Dunne

submitted to the Faculty of the College of.Arts and Sciences

of the American University

in Partial Fulfillment of

the Requirements for the Degree

of

Doctor of Philosophy

Date

in

Physics

Signatures of Committ

Chair

I995 The American University Wahington, D <' 200 16

7 7 w

,

1

MEASUREMENT OF THE SPIN STRVCTURE FUNCTION OF THE NEUTRON g,"

FROM DEEP INELASTIC SCATTERP~G OF POLARIZED ELECTRONS FROM * _

, ?

P O L Y ' E D MUTRONS IN 'He -

FROM DEEP INELASTIC SCATTERP~G OF POLARIZED ELECTRONS FROM * _

, ?

P O L Y ' E D MUTRONS IN 'He -

by . c

JarnesA Dunne

Q ABSTRACT

Polarized electrons of energies 19 42, 22 67, and 25 5 GeV were scattered off a

polarized 'He target at SLAC's End Station A to measure the spin asymmetry of the'neutron t

From this asymmetry, the spin dependent structure hnction g,"(x) was d e t e k n e d over, a

range in x from 0 03 to 0 6 with an average @ of 2 (GeVIC)' The value of the integral of

g,* over x is Jg,"(x)& = -0 036 * 0 009 The results were interpreted in the frame work

of the Quark Parton Model (QPM) and used to test the Ellis-JaiXe and Bjorken sum rules

1

0

The value of the integral is 2 6 standard deviations fiom the Ellis-JaRe prediction wtule the

Bjorken sum rule was found to be in agreement with ths datq and proton data fiom SMC and

E- 143

F

ACKNOWLEDGMENTS . \

I would lige to thank ail the members of the E-t42 collaboration and the SLAC d . -

technicians fo'r making thts experiment possible' They are a talented group of people I

would especially like to thank Zein-Eddine Meziani Charlie Young, Jim Johnson,. Henry

Band, and Emlyn Hughes for taking the time to answer questions, give guid;mce, and for just

,

/ being there to talk It was also a pleasure workmg with my fellow graduate students, Michael

Spenios, David Kawall, Yves Roblin, James Xu, and Hunter Middleton 5. ,

A great deal of credit is due to my advisors, Ray Amold, Peter Bosted, Steve Rock, a t .

and Zen Szalata fiom the American University I learned a tremendous amount fiom each of

them They answered all of my many questions during my tenure at SLAC I t d y benefitted 4

fiom the collaborative analysis mektings we had They hold a seemingly limitless knowledge

of physics and computers I believe 1 now possess a sound background in physics and that

is attributed pnmanly to them

I would like to extend my thanks to the profess& at the American University for

teachng me the fbndamentals of physics and math I genubely etjoyid my time back at AU

Special thanks is owed to Dr Segnan, Dr Reiss, Dr day, Dr Schot, Dr Casey, and Dr

Bruce Flanders Looking back on my first year, I guess 1 have come a long way since my first

a .

exam in Intro to Quantum

I have made a lot of lasting friendships during the last few y e a p My social sanity is

. . . I l l

I. .

I

due to people like Jim Talamonti, Mervyn Naidoo, Jeff Ffllbaum, Thia Keppel, Bany

Hellman, Rolf Ent, Rad Antonov, Dave Reyna, and Robih Erbacher But most of all t o

Michael and Effie Spengos They are great people and great neighbors I am indebted for

/

life to Effie and her cooking (especially her fish) They made life in Califomia truly enjoyable

I worked very closely with Michael and I have tremendous respect for him, his family and his * physics Thanks for everything

%

c

A huge amount of thanks is due to my family for the support given during my many

years as a student But the most gratitude is due to my wife who had to put up with-me

during the writing of this document She has helped me in countless ways and probably now

knows (against her will) more about spin physics than most We have spent some very long

days'and nights trying to produce this final document and that alone deems her worthy of all

my gratitude But it goes beyond that, she is my best friend, she is my life And for those

reasons, I dedicate this thesis to her, Demi b

9

iv

1

,

i

TAEiiE OF CONTENTS

* ABSTRACT 11

ACKNOWLEDGMENTS 111

LIST OF TABLES X

a'

LIST OF ILLUSTRATIONS a xiii

CHAPTER 1 INTRODUCTION 1

Structure Functions

Unpolarized Structure fimctions

Polarized Structure Functions

Asymmetries

Lepton-Nucleon Asymmetry

3 Virtual Photon-Nucleon Asymmetry

Quark Parton Model

Sum Rules

Bjorken Sum Rule

The Ellis-Jaffe Sum Rules

The Burithart-Cottingham Sum Rule

Motivation

3 &

2

7

1 1

1 1

12

17

17

19

20

21

r-.

V

". ,

,

v * CHAPTER 2 EXPERIMENTAL SETUP

Beam transport and monitoring

a

I The Polarized Target

Spectrometers

Detectors.

Cerenkov

Shower Counter

Hodoscope

Trigger Electronics

Shower Signals

Cerenkov Signals

Hodoscope Signals

Lucite Signals

Main Trigger

Eficiency Triggers

Trigger OR

Hodogate

Beam Gate

Data Acquisition

The Run Plan

25 .

25 f

". 36

41

. h 41 '-

44

45

48

52

53

55

56

56

57

58

60

61 4

61

62

64

vi

CHAPTER 3 . DATA ANALYSIS 6 5

Shower Analysis 65 \

Clustering Algorithm

Shower Calibration

65 1

66

.a Shower Cuts 70 \ .

Ghost Cut ' @ 7 0 '

71

71 \ . Dead Block Cut

Overlap cut *I

Neural Network Cut : 72

Efficiency Dm 73

7 6.

76

Beam Analysis Lv

Beam cuts <

Beam Polarization Cuts 77

Beam Polarization measurement 79

Tracking h s i y s i s

Tracking Algorithm

81

81

Efficiency 83

Cerenkov Analysis 85

Target Polarization 86

E+ent Selection t

Main Cut Definition

87

88

Binning , 88 I

1

Pion Analysis

t ,

88

'- 4

92 I -. Positron Aqalys~s

Dead-time Cdmection c

95

Radiative Corrections 99

Internal corrections c I O 0

I a: \ i

* - / *

External Radiative Corrections ~ 104

Models- ' I07

1 / r

Dilution Factor 110

Method 1

od II "i

fi Term

1 1 1

113

115

Resolution Correction 116

119 CHAPTER 4 RESULTS AND CONCLUSIONS

Systematic Uncertainties I19

False Asymmetries 124

Raw Asymmetries I26

Electron-nucleon asymmetries A,, and A , 127

The longitudinal and transverse electron-nucleon asymmetries of the neutron 1 34

The virtual ph~ ton-~He asymmetries A I "lC and Az3'" 140

The virtual photon-neutron asymmetries A," and A,"

The g," structure hnction 153

I43

I47 dependence of A," and ,q,/F,

... VI11

Extrapolations 159 I

. .

Low x extrapolation

High x extrapolation

Summary ofg,” Results -

Implications

’ 159

1 6 f

I64

164 . Bjorken sum rule coinpanson with E-I43 A b

Bjorken sum rule comparison with SMC 168 ’

167 * ,

Conclusion

APPENDIX A

Introduction

‘ 1 69

171

171

New Analysis . 172 - 1

New Corrections and Factors 175

Comparison of kallY4 and @rick Analysis 181

Low x point

Options

APPENDIX B

Resonance Region Asymmetries

REFERENCES

I85

187

207

,207

210

I X

1.

.2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

IS.

16.

17.

18.

B

LIST OF TABLES

Forward Co\mpton Helicity Amplitudes * .+ 1

Y E- 142 Target Cells

Hodoscope Infomiation

Beam Cuts

h *

Pion Asymmetries AT = A,,, /(Pol,;Pol~J,)

Ratio of to e- for all energies and both spectrometers

Average Additive Dead-time Correction

Target Model for External Radiative Corrections

Estimation of Systematic Error on Total Additive Radiative Correction

f, Term of the Dilution Factor (Method I)

f, Term (Method 11)

Bin boundaries for the eight x bins

AllJife for all energies and spectrometers

A , we for all energies and spectrometers I

A,," for all energies and spectrometers

A i n for all energies and spectrometers . ..

A , "le versus x

9

39

49

77

90

93

98

105

108

1 I3

1 IS

129

130

132

136

138

140

142

X

19. Azn versus x 144

20. 145

21. A," and g,/k', versus x I46

22. Bjorken x range for each data set 148

Systematic error on A," determined fiom A,, and A ,

?

23. A," versus (_)' ~ 149 . //'

* 151

I53

3 .

24. g,4Fl versus Qz

25. g1"(x,Q2) versus x at the.measured (_)"determined from A p and A , *

26.

27.

28.

Systematic error on g," determined from k !" and gZuu' 'at = 2 (GeVIc)' I55

156

1-56

I

g," evaluated from A," and gZNw at 0' = (2, 3 and 10 (GeV/c)?}

Value of the integral ofg," in the measured region (from A," and g2WU )

29, g," evaluated from gJF, at QZ = 12, 3, and 10 (GeV/c)'} ' I57

30. Value of the integral of g," in the measured region (fiom g,/F,) I57

31. Low x integral ofg,"(A,",g2Uu' ) 161 P

' 0 32. High x extrapolation using A In - 0 75 f 0 25 as,x - 1

33. High x extrapolation with final error determination

162

163

34. Latest published redults of recent spin structure experiments * 165

35.

36. Beam Cuts

Summary of E- 142 results

&

37. Target Model for External Radiative Corrections

169

175

I76

38. Comparison of cut 18 with cuts which affect the event selectiorlstatistics 183

39.

40.

Comparison of cut I8 and cut 48 with the new correction factors

Information on Low x point (x=[O 03-0 041) for various cuts

184

186

XI

41. Options for final results of FbII9.I analys~s

42. PRL and Cut 18 wl Quick Corr Factors

43. Same as previous W I just 212

44. Same as. previous w/ (-e// Clustering

45. Same as previous w/ new Beam Cuts (LSpr~ng94)

..

46.

47.

48.

Same as previous w/ Neural cut

Same as previous w/ Ghost cut

Same as previous w/ new Beam and’target polarizations

I ’ e 49. Same as previous wl new Radiative Corrections

% Same as previous wl new Dilution factor

5 1. Same as preious w/ new dead time

52. ,Same as previous w/ E- 143 proton correction

53.

54.

55.

Same ,as previous w/ new contamination correction

Cut 48 with all new factors and all data (recovered runs)

Cut 48 with and. without resolution correction

. .\

56. Cut 46 with and without resolution correction

57. Combinations of Cuts used in Analysis

i88

i89

I90

i90

191

191 *

% ‘ 192

192

193

193

194

194

196

196

197

198

203

.

t

xii

c

LIST OF ILLUSTRATIONS .

, Figure 1 Feynman diagram for deep inelastic e-N scattering \ 1

6 Figure 2 Eady data on 1.2 versus Q’ for x = 0 25 , .

Figure 3 /*; scaling violation 7

33 Figure 4 A , P for SLAC and EMC experiments --

Figure 5 A-Bend beam line at SLAC 26

Figure 6 Elements of the A-Line in ESA 28

Figure 7 Polarization precession angle versus beam energy

Figure 8 polarized Light Source for E- I42

Figure 9 Band Structure for AlGaAs

Figure 10 Schematic of Photocathode

3 -3

-3 4

Figure 11 Top view of Mraller polarimeter setup 36

a Figure 12 ‘He in S state -3 7

Figure 13 E-142 target setup (Only one of five Ti Sapphire lasers shown) 3 8

-7 8 Figure 14 E- 142 Target Cell

Figure 15 E- 142 Spectrometers

Figure 16 “S” Bend configuration of magnets

Figure 17 Solid angle versus momentum

Figure’ 18 Ray traces for the 4 5 I’ and 7 I’ spectrometers

41

‘I2

42

4 3

,

Figure 19

Figure 20

Figure 22

Figure 23 @.

Figure 24

Figure 25

Figure 26

Figure 27 &

Figure 28

Figure 29

Figure 30

Figure 31

Figure 32

Figure 33

Figure 34

Detectors (Top View, not to scale)

Cerenkov detector

0

Shower counter

Leati glass block

Hodoscope fingers ( 2 / 3 overlap)

Lucite ,planes

Trigger schematic legend

Saclay splitter

Shower counfer schematic

Cerenkov trigger schematic

Lucite coincidence and Pion trigger

Main trigger

Efficiency triggers

Trigger OR and the Saclay Trigger Divider

Hodogate

Beam Gate schematic

, Figure 35 Data Acquisition schematic

Figure 36 Cluster block numbering around central block

Figure 37 Fractional energy distribution in a non-edge cluster

Figure 38 Neural network output for pions and electrons

Figure 39 Neural network ( N N 4 95) effect on E/P

Figure 40 Neural Networh etliciency versus energy f o r the 4 5'' at I9 GeV

44

45

47

48

50

5 1

53

54

5 5

56

57

58

59

60

61

62

63

67

69

73

73

74 .

YIV

Figure 41 Neural Network efficiency versus energy for the 7" at 19 GeV 74

75

75

Figure 42 Neural Network efficiency versus energy for the 4 5" at 22 GeV

Figure 43 Neural Network efficiency versus energy for the 7" at 22 GeV

Figure 44 Neural Network efficiency versus energy for the 4 5" at 25 GeV 75

Figure 45 Neural Network efficiency versus energy for the 7" at 25 GeV 75

76

76

Figure 46 Neural Network efficiency versus Trigger OR rate for the 4 5 " at 22 GeV

Figure 47 Neural Network efficiency versus Trigger OR rate for the 7" at 22 GeV

Figure 48 Gate widths where polarization bits are valid 78

Figure 49 4 5 " Trigger OR distribution for 2/2 case and 2/2 but not 3/3

Figure SO 7" Trigger OR distribution for 2/2 case and 212 but not 313

79

79

5,

Figure -51 Measured Msller asymmetry and background 80

Figure 52 Beam polarization versus run number

Figure 53 Tracking algorithm flow chart )i

Figure 54 4 5 O tracking efficiency versus E '

Figure 55 7" tracking efficiency versus E '

Figure 56 4 5 " tracking efficiency versus Trigger Or Rate

Figure 57 7" tracking efficiency versus Trigger Or Rate

Figure 58 ADC spectra for channels -, 25 from the Cerenkov detectors

81

83

84

84

85

85

86

Figure 59 'He and water NMR signals for the polarization measurbment 87

91 Figure 60 Pion asymmetries A - = A,,, / ( / ) o / h c a m / ' o / , ~ ~ , : f , )

Figure 61 Ratio of e ' to e' for all energies in each spectrometer as a hnction of x 94

Figure 62 Measured trigger OR dead-time

x v

98

t

Figure 63 Feynman diagrams of higher order radiative processes

Figure 64 Additive Internal Radiative Correction to A,,3HC for the 4 5 O spectrometer

Figure 65 Additive Internal Radiative Correction to A,,3t'' for the 7" spectrometer

Figure 66 Elastic and quasi-elastic radiative tail contribution to A,,"" for the 4 5"

Figure 67 Elastic and quasi-elastic radiative tail contribution to A,,31ic for the 7"

Figure 68 Schematic of 'He target with NMR pickup coils (not to scale)

Figure 69 Additive Internal +External Radiative Corfection to All3"' for the 4 5 " )

-

Figure 70 Additive Internal + External Radiative Correction to for the 7"

Figure 7 1 Smearing of the momentum spectrum

Figure 72 Resolution corrections for 4 5 " and 7" data versus E '

Figure 73 Comparison of /*> from the FZNMC parameterization versus data

Figure 74 A," averaged over E' and 8 vs x with positivity copstraint, h? and A 2 w u

A

. Figure 75 Left / right beam pulse position and size differences for all A, , runs

Figure 76 Electron rate binned versus beam position and size at the target

Figure 77 A,,"" for each energy and spectrometer

Figure 78 A , "'' for each energy and spectrometer

Figure 79 A,," for each energy and spectrometer

. Figure 80 A ," for each energy and spectrometer

Figure 81 A,'"' virtual photon-'He asymmetry versus x at the measured average cp

Figure 82 A2"" versus x at the measured average (_)'

F'igure 83 A ," versus x at the measured average Q'

Figure 84 f i / i q ' , versus x at the measured average Q'

i00

103

i03

103

103

106

106

106

117

118

123

124

125

126

13 1

133

137

139

141

142

146

147

xvi

4

Figure 85 A I versus Qz

Figure 86 ,q,/b'l versus Q2 (statistical errors only) 5

150

152

Figure 87 g," determined fiom the measured e,, and A , at the measured average Q* 154

Figure 88 g," from A," and glUW at 0' = 2 (GeV/c)' 158

Figure 89 g)" from g,/I*', at Qz = 2 (GeV/c)' 158

163

177

Figure 90 Fit to A ," used in high x extrapolation &

Figure 9 1 Radiative Correction Comparison (rough approximation of errors)

Figure 92 Bel Difference between method 1 and method 2

Figure 93 Comparison of dilution factors for the 4 5: used in the @trick and I+b//Y-l.

179

179

180

181

181

Figure 94 Gate widths where polarization bits are valid

Figure 95 4 5 " Trigger OR distribution for 2/2 case and 2/2 but not 313

Figure 96 7" Trigger OR distribution for 2/2 case and 2/2 but not Y3

Figure 97 PRL with Cut 18 w/ Quick Corr Factors

Figure 98 Same as previou$w/ 2/2 pol . ' Figure 99 Same as previous w/ ( 'ell Clustering

Figure 100 Same as previous w/ new Beam Cuts (.Ypri~igW)

Figure 101 Same as previous w/ Neural cut

Figure 102 Same as previous w/ Ghost cut

Figure 103 Same as previous w/ new Beam and Target polarizations

Figure 104 Same as previous w/ new Radiative Corrections

Figure 105 Same as previous w/ new Dilution factor

Figure 106 Same as previous w/ new dead time 3

189

190

190

191

191

192

192

193

193

194

xvii

1

Figure 107 Same as previous w/ E- 143 proton correction

Figure 108 Same as previous wl new contamination correction

Figure 109 Cut 18 wl (_)trick corrections & Cut 48 w/ all new factors and all data

I94

195

195

Figure 110 A," at x = 0 035 for vanous cuts

Figure I 1 1 Integral of g , of vanous cuts (measured regon)

Figure 112 Cut 48 with and without resolution correction

Figure 113 Cut 46 versus Cut 48 (both without resolution correction)

Figure 1 14 4 5 O I9 GeV Neural Network efficiency

Figure 115 4 5" 22 GeV Neural Network efficiency

Figure 116 4 5 25 GeV Neural Network efficiency

Figure 1 17 7" 19 GeV Neural Network efficiency

Figure 118 7" 22 GeV Neural Network efficiency

Figure 119 7" 25 GeV Neural Network efficiency

196

196

197

198

199

199

200

200

20 1

20 1

I

Figure 120 Smearing of momentum spectrum by using the shower energy resolution 202

xviii