The Radiative Decay Mode of the Free Neutron by Robert L. Cooper A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Physics) in The University of Michigan 2008 Doctoral Committee: Professor Timothy E. Chupp, Chair Emeritus Professor Glenn F. Knoll Professor David W. Gidley Professor Gordon L. Kane Professor Jianming Qian c Robert L. Cooper 2008 All Rights Reserved To my wife and to my mother ii ACKNOWLEDGEMENTS First and foremost, this dissertation would have been impossible without the constant support, guidance, and large dose of patience from my collaborators. Scott Dewey, Alan Thompson, Fred Wietfeldt, Betsy Beise, Kevin Coakley, and Herbert Breuer have all contributed so much to my intellectual growth, and I am immensely grateful for the opportunity to work with them. As I take my next step towards a postdoc, I have learned from Pieter Mumm and Brian Fisher about being a postdoc. Both would strongly encourage me to forget everything I learned in this case, but it's that humbleness that has endeared them to me so much. My fellow graduate students at NIST; \Piston", Chris, Da, Andrew, Liang, Dima, and their significant others have enriched my life in innumerable ways. To them, all that I can say is, \asps." I am grateful for the deep intellectual conversations with Jim Byrne. I have learned so much from him about physics and the historical significance of the work we're doing. I have had many theoretical conversations with Susan Gardner, and she has inspired me in more ways than she probably realizes. I have been fortunate to have had nearly three advisors in graduate school; Tim Chupp, Jeff Nico, and Tom Gentile. Jeff's light-hearted demeanor was a joy to work with. I never realized lobotomized gibbons were responsible for so much physics before meeting Jeff. I truly appreciate Tom's serious dedication to his craft that is unfettered by ego and driven by the desire to understand the problem at hand. My advisor, Tim, has given me a long leash in graduate school to pursue many projects iii that interested me. I am grateful for the ability to be curious, ask tough questions and to be supported when I have wanted to investigate something for myself. Most of all, Tim has taught me the importance of intellectual excellence, and that if a problem is worth doing, it should be done as well. Eric Tardiff, Behzad Ebrahimi, and Monisha Sharma from the Chupp group have been dear friends whom I have leaned on through graduate school. Furthermore, I am glad that when Eric spoke, I listened. I hope our paths cross in the future. My college friends; Jamey, Dave, Kevin, Pat, Matt, Ryan, and their significant others have been with me from the beginning, and I can honestly say that with their presence, I've had more fun than a graduate student should. I would not be here without the constant support of my parents. They have always believed in me, and that support has allowed me to give 100 % effort to my work. I really can't say enough to acknowledge everything they have done for me. I have saved the best for last. Amy, my wife, has been an unending source of support, love, and inspiration. I am grateful for her infinite patience and sunny attitude. She has been a constant source of strength, and I can't acknowledge enough about how awesome she is. iv TABLE OF CONTENTS DEDICATION :::::::::::::::::::::::::::::::::::::::::: ii ACKNOWLEDGEMENTS :::::::::::::::::::::::::::::::::: iii LIST OF FIGURES :::::::::::::::::::::::::::::::::::::: viii LIST OF TABLES ::::::::::::::::::::::::::::::::::::::: xiii LIST OF APPENDICES ::::::::::::::::::::::::::::::::::: xiv CHAPTER I. Introduction .......................................1 1.1 History of the Weak Interaction and Neutron Beta decay . .1 1.2 Neutron Decay and Lifetime . .4 1.2.1 CKM unitarity . .5 1.2.2 Connection to radiative final states . .6 1.3 Previous Radiative Decay Measurements . .9 1.4 Motivation . 10 1.5 Overview of the Dissertation . 12 II. Theoretical Development ............................... 14 2.1 The Weak Interaction and Beta decay . 15 2.1.1 Structure of the weak interaction . 15 2.1.2 Symmetries of the weak interaction . 18 2.1.3 Differential decay rate . 19 2.2 Neutron Lifetime and Radiative Corrections . 21 2.2.1 Higher order contributions . 21 2.2.2 Ideal experiment . 23 2.2.3 Radiative corrections . 24 2.2.4 Current state of the neutron lifetime . 26 2.3 Radiative Decay Matrix Element and Decay Rate . 28 2.3.1 Ideal radiative decay experiment . 29 2.3.2 Classical treatment . 29 2.3.3 Field theory treatment . 32 2.4 Correlation Coefficients in Radiative Decay . 35 2.4.1 Parameter measurements . 35 2.4.2 Polarized neutron radiative decay . 38 2.5 Photon Polarization . 39 III. Experimental Setup .................................. 41 v 3.1 General Description . 41 3.2 Neutron Beam Line . 43 3.3 Proton and electron detection . 46 3.4 Photon detection . 51 3.4.1 Avalanche photodiodes . 52 3.4.2 Scintillators . 55 3.4.3 Detector assembly . 58 3.5 Data Acquisition System . 61 3.6 Rate Estimates . 63 IV. Analysis .......................................... 65 4.1 Data Reduction . 66 4.1.1 First iteration . 66 4.1.2 False triggers . 67 4.1.3 Photon analysis and second iteration . 68 4.1.4 Raw energy spectra . 70 4.2 Analysis Cuts . 72 4.2.1 Electron-delayed proton cuts . 73 4.2.2 Photon cuts . 75 4.3 Repγ =Rep Ratio Extraction . 76 V. Simulations ........................................ 84 5.1 Event Generation . 85 5.1.1 Conditionally integrated sampling . 85 5.1.2 von Neumann rejection . 86 5.2 Tracking . 88 5.2.1 Runge-Kutta . 89 5.2.2 Adiabatic transport . 91 5.2.3 Drift mechanisms . 93 5.3 Electromagnetic Field Calculation . 93 5.3.1 Implementing dielectrics . 95 5.3.2 Solving the lattice . 96 5.4 Detector Response . 98 5.5 Results . 99 VI. Systematics ........................................ 105 6.1 Photon Detector Uncertainties . 105 6.1.1 Photon detector calibration . 107 6.1.2 Threshold effects . 108 6.1.3 Photon detector efficiency . 109 6.2 Charged Particle Energy . 110 6.2.1 SBD calibration . 110 6.2.2 Electron energy threshold . 111 6.2.3 Proton energy spectrum . 112 6.3 Timing Cuts . 113 6.4 Correlated Backgrounds . 114 6.4.1 External bremsstrahlung . 115 6.4.2 Electronic artifacts . 115 6.5 Model Uncertainties . 116 6.5.1 Registration uncertainties . 117 6.5.2 APD bias leakage . 118 vi 6.5.3 Electron backscattering . 118 VII. Conclusion ........................................ 122 7.1 Results of First Experimental Run . 122 7.1.1 Importance to nuclear physics . 123 7.1.2 Photon energy spectrum . 124 7.2 Future Work . 125 7.2.1 Motivation for a second run . 126 7.2.2 12-element detector . 127 7.2.3 APD direct detection . 130 7.2.4 Absolute decay rate measurements . 131 7.2.5 Run 2 systematics . 132 7.2.6 Status . 134 APPENDICES :::::::::::::::::::::::::::::::::::::::::: 135 BIBLIOGRAPHY :::::::::::::::::::::::::::::::::::::::: 139 vii LIST OF FIGURES Figure 1.1 jVudj can be extracted from the neutron lifetime and λ. There is significant uncer- tainty in the value of the neutron lifetime, and the landscape is not well constrained by λ either. It is interesting to note that pairs of lifetime / λ data points are con- sistent with unitarity. .7 1.2 The sources of uncertainty for each extraction of jVudj. While the neutron's theoret- ical uncertainties are very small, the experimental uncertainty (EXP) is much worse than in nuclear 0+ ! 0+ superallowed decays. The numbers represent the uncer- tainty attributed to the corrections. The correction δR is the radiative correction to the total phase space of the decay. The correction ∆R is radiative corrections due to higher order interactions. The corrections δC and δNS are due to Coulomb and nuclear structure effects. Figure from reference [1]. .8 1.3 The schematic of the experimental apparatus used in the ILL measurement. The components in set up are: 1 - vacuum chamber, 2, 4 - 7, 11 - electrostatic grid, 3 - MCP proton detector, 8, 9 - plastic collimators, 10 - LiF diaphragm, 12 - CsI(Tl) photon detectors, 13 - lead cup, 14 electron detector. 11 2.1 The origin of induced couplings can be motivated by imagining the neutron and proton as \bare" Dirac particles. The leading order beta decay amplitude is given by (a). The corrections to diagram (a) from pion loop (b) and pion exchange (c) are expected to contribute a large correction. 17 2.2 Single photon exchange loop diagrams that correct the tree-level neutron decay. The left-hand side with the dark circle represents the full sum of all corrections that maintain a proton, electron, and antineutrino in the final state. The first term on the right-hand side is the tree-level diagram while the remaining diagrams are the single photon exchange loop diagrams added coherently. The light circles are the parameterization of the weak vertex physics. 22 2.3 An experiment that is sensitive to photons with energy Eγ > ∆E registers no photons in the final state for these diagrams which represent total rates. The dark box on the left-hand side represents the full incoherent sum of.