Measuring the Weak Charge of the Proton via Elastic Electron-Proton Scattering

20 MB·

by  Donald Jones

Measuring the Weak Charge of the Proton via Elastic
Electron-Proton Scattering
Donald Charles Jones
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Charlottesville, VA
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6 B.Sc.(Hon), Acadia University, 2008
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[ A Dissertation presented to the Graduate Faculty

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of the University of Virginia in Candidacy for the Degree of
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2 Doctor of Philosophy
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. Department of Physics
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: University of Virginia
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i October, 2015
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Abstract
Measuring the Weak Charge of the Proton via Elastic Electron-Proton
Scattering
The Qweak experiment which ran in Hall C at Jefferson Lab in Newport News, VA, and
completed data taking in May 2012, measured the weak charge of the proton Qp via
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elasticelectron-protonscattering. Longitudinallypolarizedelectronswerescatteredfrom
an unpolarized liquid hydrogen target. The helicity of the electron beam was flipped at
approximately 1 kHz between left and right spin states. The Standard Model predicts
a small parity-violating asymmetry of scattering rates between right and left helicity
states due to the weak interaction. An initial result using 4% of the data was published
in October 2013 [1] with a measured parity-violating asymmetry of −279±35(stat)±
31 (syst) ppb. This asymmetry, along with other data from parity-violating electron
scattering experiments, provided the world’s first determination of the weak charge of
the proton. The weak charge of the proton was found to be Qp = 0.064±0.012, in
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good agreement with the Standard Model prediction of Qp (SM) = 0.0708±0.0003[2].
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The results of the full dataset are expected to be published in early 2016 with an ex-
pected decrease in statistical error from the initial publication by a factor of 4-5. The
level of precision of the final result makes it a useful test of Standard Model predictions
and particularly of the “running” of sin2θ from the Z-mass to low energies. However,
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this level of statistical precision is not useful unless the systematic uncertainties also
fall proportionately. This thesis focuses on reduction of error in two key systematics for
the Qweak experiment. First, false asymmetries arising from helicity-correlated electron
beam properties must be measured and removed. Techniques for determining these false
asymmetries and removing them at the few ppb level are discussed. Second, as a parity-
violating experiment, Qweak relies on accurate knowledge of electron beam polarimetry.
To help address the requirement of accurate polarimetry, a Compton polarimeter built
specificallyforQweak. Comptonpolarimetryrequiresaccurateknowledgeoflaserpolar-
ization inside a Fabry-Perot cavity enclosed in the electron beam pipe. A new technique
was developed for Qweak that reduces this uncertainty to near zero.
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We approve the dissertation of Donald C. Jones.
Supervisor: Prof. Kent Paschke Date of Signature
Committee Member: Prof. Blaine Norum Date of Signature
Committee Member: Prof. Nilanga Liyanage Date of Signature
Committee Chair: Prof. James Fitz-Gerald Date of Signature
“Call unto me and I will answer you, and show you great and hidden things that
you have not known.”
Jeremiah 33:3
Acknowledgements
The route from high school to Bachelors and on to PhD has been a rather circuitous
track for me, and as I consider the key players who helped me reach this goal, I need to
beginbyacknowledgingthosewholaidthefoundationsofeducationandcharacterinmy
life. Without the encouragement and advice of others along the way, I might have been
sidetracked numerous times perhaps permanently. Of course, I begin by acknowledging
my parents, especially my mother. I think about my grade school teachers Ruth Morris,
Shirley Harris and Murray Baker who encouraged me to go beyond high school and
whose advice and confidence spurred me on. Or my older brothers Richard, Paul and
Warren, whonotonlyprovidedencouragement, butalsohelpedmateriallywhenIwould
have otherwise had to quit for financial reasons. Richard has also been a key resource,
helping me with difficult concepts all the way from undergraduate on through graduate
studies. I want to acknowledge these as being key to my success.
I would next like to acknowledge my advisor, Kent Paschke, who I met as an under-
graduate intern at Jefferson Lab. Although he demanded quality scientific output and
I greatly benefited from his tutelage in this respect, perhaps greater was his example
of integrity in research reporting. I learned to question my own conclusions and be
sensitive to self-introduced biases. I always felt under him that one gained the right to
be vocal, confident or opinionated on an issue only after he had well-formulated ideas
that could clearly presented and backed up with data. This was invaluable to a student
who was quick to jump to conclusions, fast to verbalize them and then slower to test
the hypotheses empirically. He not only taught me good research practices, but he also
offered common sense advice for critical decisions relating to education and career and
has always been supportive. I will continue to value his opinion going forward.
Two others with whom I worked most closely and from whose expertise I most benefited
were Dave Gaskell and Mark Dalton. They great resources, helping me to have confi-
dence in tackling tasks on my own and willing to give credit, perhaps more than was
due. These were a pleasure to work alongside.
I want to acknowledge Dave Armstrong, not only for the leadership role he played in
the experiment, but also for taking the effort to break issues down into simple terms
and for taking care not to assume that students were familiar with the science being
discussed. I would like to thank Mark Pitt for his quick insight and leadership during
the course of this difficult experiment. I want to also acknowledge the critical role
Roger Carliniplayed, ensuringthat the experimentran smoothly, providingperspective,
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offering insights and taking, perhaps more than his due, of persecution from the rest,
while maintaining a smile.
Finally, I want to thank my wife, Lydia, who has been a huge source of support and
confidence through this whole process. She has been a tremendous encouragement,
taking on more than her share of home duties to help me more rapidly reach the goal.
Contents
Abstract ii
Acknowledgements v
Contents vii
List of Figures xi
List of Tables xxix
Abbreviations xxxiii
Physical Constants xxxv
1 Introduction to the Standard Model 1
1.1 Electroweak Physics . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 Theoretical Basis for the Qweak Experiment 9
2.1 A Peek at Electroweak Theory . . . . . . . . . . . . . . . . . . . . . 10
2.2 Fundamentals of Electron Scattering . . . . . . . . . . . . . . . . . 12
2.3 Accessing the Weak Sector via Parity Violation . . . . . . . . . . . 18
2.4 Radiative Corrections for the Qweak Experiment . . . . . . . . . . 20
2.4.1 Electromagnetic Corrections . . . . . . . . . . . . . . . . . . 21
2.4.2 Electroweak Corrections . . . . . . . . . . . . . . . . . . . . 22
3 Instrumentation and Operation of the Qweak Experiment 27
3.1 Experimental Overview . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.2 Polarized Electron Source and Injector . . . . . . . . . . . . . . . . 33
3.3 Beam Transport and Monitoring . . . . . . . . . . . . . . . . . . . . 38
3.4 Polarimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.4.1 Møller Polarimeter . . . . . . . . . . . . . . . . . . . . . . . 44
3.4.2 Compton Polarimeter . . . . . . . . . . . . . . . . . . . . . . 46
3.5 Target . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
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Contents viii
3.6 Collimation and Shielding . . . . . . . . . . . . . . . . . . . . . . . 57
3.7 QTORSpectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.8 Main Detector System . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.9 Auxiliary Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.9.1 Background Detectors . . . . . . . . . . . . . . . . . . . . . 63
3.9.2 Focal Plane Scanner . . . . . . . . . . . . . . . . . . . . . . 66
3.9.3 Upstream Luminosity Monitors . . . . . . . . . . . . . . . . 67
3.9.4 Downstream Luminosity Monitors . . . . . . . . . . . . . . . 68
3.10 Tracking System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4 Beam Corrections 77
4.1 Helicity-Correlated False Asymmetries . . . . . . . . . . . . . . . . 77
4.1.1 Minimizing False Asymmetries . . . . . . . . . . . . . . . . . 79
4.1.2 Cancelling False Asymmetries . . . . . . . . . . . . . . . . . 82
4.1.3 Correcting for False Asymmetries . . . . . . . . . . . . . . . 82
4.2 Linear Regression to Remove Helicity-Correlated False Asymmetries 84
4.2.1 Bias in Multivariate Linear Regression . . . . . . . . . . . . 90
4.3 Beam Modulation to Remove Helicity-Correlated False Asymmetries 94
4.3.1 Fast Feedback and Beam Modulation . . . . . . . . . . . . . 99
5 Resolving Issues in the Beam Modulation Analysis 111
5.1 Validating the Modulation Analysis . . . . . . . . . . . . . . . . . . 112
5.1.1 Debugging the Analysis Procedure . . . . . . . . . . . . . . 112
5.1.2 Inconsistency Arising from Redundancy . . . . . . . . . . . 117
5.1.2.1 Residual Sensitivity to Modulation . . . . . . . . . 117
5.1.2.2 Differences in Prescribed Corrections . . . . . . . . 128
5.1.3 Long Timescale Detector to Monitor Sensitivity . . . . . . . 144
5.1.4 Signature of the Inconsistency . . . . . . . . . . . . . . . . . 153
5.2 Determining a Beam Modulation Correction and Error . . . . . . . 159
6 Compton Photon Target 163
6.1 The Fabry-Perot Optical Cavity . . . . . . . . . . . . . . . . . . . . 164
6.2 Laser Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
6.2.1 Methodology and Theory . . . . . . . . . . . . . . . . . . . . 178
6.2.2 Determination of Polarization and Error . . . . . . . . . . . 192
6.2.2.1 Methodology . . . . . . . . . . . . . . . . . . . . . 193
6.2.2.2 Potential Systematic Errors . . . . . . . . . . . . . 198
6.2.2.3 Lessons from Periods of High Polarization Signal . 208
7 Extracting the Weak Charge of the Proton 213
7.1 Extracting the Parity-Violating Asymmetry . . . . . . . . . . . . . 214
7.1.1 Bias Corrections . . . . . . . . . . . . . . . . . . . . . . . . 215
7.1.2 Background Corrections . . . . . . . . . . . . . . . . . . . . 216
Contents ix
7.1.3 Measured Asymmetry . . . . . . . . . . . . . . . . . . . . . 218
7.1.4 Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
7.1.5 The Parity-Violating Asymmetry . . . . . . . . . . . . . . . 224
7.2 From Parity-Violating Asymmetry to Weak Charge . . . . . . . . . 226
8 Concluding Discussion 235
A Maximum Likelihood and the χ2 Statistic 237
B Monitor Differences for Qweak 239
C Effect of FFB Stability on Modulation Analysis 249
D Main Detector Monopole and Dipole Responses 271
E Qweak Terminology 287
Bibliography 291