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Theoretical Studies of C and CP Violation in $\Eta \To \Pi^+ \Pi^- \Pi^0$ Decay

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Theoretical Studies of C and CP Violation in $\Eta \To \Pi^+ \Pi^- \Pi^0$ Decay University of Kentucky UKnowledge Theses and Dissertations--Physics and Astronomy Physics and Astronomy 2020 Theoretical Studies of C and CP Violation in $\eta \to \pi^+ \pi^- \pi^0$ Decay Jun Shi University of Kentucky, [email protected] Author ORCID Identifier: https://orcid.org/0000-0001-9484-616X Digital Object Identifier: https://doi.org/10.13023/etd.2020.388 Right click to open a feedback form in a new tab to let us know how this document benefits ou.y Recommended Citation Shi, Jun, "Theoretical Studies of C and CP Violation in $\eta \to \pi^+ \pi^- \pi^0$ Decay" (2020). Theses and Dissertations--Physics and Astronomy. 74. https://uknowledge.uky.edu/physastron_etds/74 This Doctoral Dissertation is brought to you for free and open access by the Physics and Astronomy at UKnowledge. It has been accepted for inclusion in Theses and Dissertations--Physics and Astronomy by an authorized administrator of UKnowledge. For more information, please contact [email protected]. STUDENT AGREEMENT: I represent that my thesis or dissertation and abstract are my original work. Proper attribution has been given to all outside sources. I understand that I am solely responsible for obtaining any needed copyright permissions. I have obtained needed written permission statement(s) from the owner(s) of each third-party copyrighted matter to be included in my work, allowing electronic distribution (if such use is not permitted by the fair use doctrine) which will be submitted to UKnowledge as Additional File. I hereby grant to The University of Kentucky and its agents the irrevocable, non-exclusive, and royalty-free license to archive and make accessible my work in whole or in part in all forms of media, now or hereafter known. I agree that the document mentioned above may be made available immediately for worldwide access unless an embargo applies. I retain all other ownership rights to the copyright of my work. I also retain the right to use in future works (such as articles or books) all or part of my work. I understand that I am free to register the copyright to my work. REVIEW, APPROVAL AND ACCEPTANCE The document mentioned above has been reviewed and accepted by the student’s advisor, on behalf of the advisory committee, and by the Director of Graduate Studies (DGS), on behalf of the program; we verify that this is the final, approved version of the student’s thesis including all changes required by the advisory committee. The undersigned agree to abide by the statements above. Jun Shi, Student Dr. Susan Gardner, Major Professor Dr. Christopher Crawford, Director of Graduate Studies THEORETICAL STUDIES OF C AND CP VIOLATION IN η ! π+π−π0 DECAY DISSERTATION A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the College of Arts and Sciences at the University of Kentucky By Jun Shi Lexington, Kentucky Director: Dr. Susan Gardner, Professor of Physics Lexington, Kentucky 2020 Copyright c Jun Shi 2020 https://orcid.org/0000-0001-9484-616X ABSTRACT OF DISSERTATION THEORETICAL STUDIES OF C AND CP VIOLATION IN η ! π+π−π0 DECAY A violation of mirror symmetry in the η ! π+π−π0 Dalitz plot has long been recognized as a signal of C and CP violation. In this thesis, we show how the isospin of the underlying C- and CP-violating structures can be reconstructed from their kinematic representation in the Dalitz plot. Our analysis of the most recent experi- mental data reveals, for the first time, that the C- and CP-violating amplitude with total isospin I = 2 is much more severely suppressed than that with total isospin I = 0. In searching for C- and CP-violating sources beyond the SM, we enumerate the leading-dimension, CP-violating effective operators that share the gauge symmetry and particle content of the Standard Model (SM), carefully separating the operators that are P-odd from those that are C-odd below the electroweak scale. The P-odd and CP-odd effective operators that generate permanent electric dipole moments have been the subject of much investigation in the literature; we now focus on C-odd and CP-odd operators and study their effects systematically. We emphasize that while for flavor-changing interactions the C-odd and CP-odd operators appear in mass dimension 6, for flavor-conserving interactions the C-odd and CP-odd operators appear in mass dimension 8, though some operators can be of mass dimension 6 in numerical effect. In the flavor-changing case, the C-odd and CP-odd operators and P- odd and CP-odd operators probe different linear combinations of common low-energy coefficients in SM effective field theory. Remarkably, however, in the flavor-conserving case, we find that low-energy coefficients probed by a P-odd and CP-odd observable, such as by the permanent electric dipole moment of the neutron, and by a C-odd and CP-odd observable, as probed by mirror symmetry breaking in the η ! π+π−π0 Dalitz plot, can be completely different. Finally, from the C-odd and CP-odd flavor-conserving operators, we determine the operators with definite isospin that can contribute to η ! π+π−π0 decay. We illustrate how these operators can be represented in chiral perturbation theory, for the eventual determination of their contribution to mirror-symmetry breaking in the η ! π+π−π0 Dalitz plot. KEYWORDS: CP violation, beyond the SM, effective field theory, η ! π+π−π0 decay, effective operators Jun Shi August 5, 2020 THEORETICAL STUDIES OF C AND CP VIOLATION IN η ! π+π−π0 DECAY By Jun Shi Dr. Susan Gardner Director of Dissertation Dr. Christopher Crawford Director of Graduate Studies August 5, 2020 Date ACKNOWLEDGMENTS I would like to first show my deepest gratitude to my supervisor Prof. Susan Gardner. I appreciate the opportunity she kindly offered for continuing my study in University of Kentucky which will leave a indelible and special memory in the rest of my life. Susan is remarkably knowledgeable and shows fantastic enthusiasm in discovering the mysteries of high energy physics and astronomy. It is my great honor to do my research under her direction. It is wholeheartedly appreciated that her great advice for my study proved monumental towards the accomplishment of this project. Her virtuous character, unswerving enthusiasm and fighting spirit will affect my whole life and guide me through my future career. I also want to show my great thankfulness to other members of my PhD Advisory Committee - Prof. Keh-Fei Liu, Prof. Brad-Plaster and Prof. Anne-Frances Miller. Thank you for all your help and being so nice to me. I appreciate Prof. Jeffery Todd Hastings being the outside examiner of my defense. I am indebted to all the help from the former DGS Prof. Tim Gorringe, the present DGS Prof. Christopher Crawford in my graduate study. Plenty thanks are given to Diane Riddell, Libby Weir, Suann Reese, Maxwell Ankrah and Max Brown for their kind help. I also want to show my gratitude to the lecture professors that I have assisted, Prof. Michael Eides, Prof. Susan Gardner, Prof. Terrence Draper, Prof. Wolfgang Korsch, Prof. Tim Gorringe and Dr. Ivan Horvath. Thanks to my friends Qing Chen, Sinong Liu, Xinshuai Yan, Gen Wang, Yi-Bo Yang, Xuguang Ai, Tongxi Hu, Austin Hinkel, Nick Floyd, Parisa Alimohamadi and so many others, it has been a wonderful life in University of Kentucky. Last but not least, I wish to acknowledge the support and great love of my parents, my parents in law, my husband Jian Liang and my son Xiaokuan Liang. They kept iii me going on and this work would not have been possible without them. iv TABLE OF CONTENTS Acknowledgments . iii List of Tables . viii List of Figures . ix Chapter 1 Introduction . 1 1.1 Histories of C, P, and T in Particle Physics . 1 1.2 Baryon Asymmetry in Universe . 2 1.3 BAU effects from the Standard Model . 3 1.4 Why search for CP violation in η ! π+π−π0 decay . 4 1.5 Organization of this thesis . 5 Chapter 2 C, P, and T in Physics . 7 2.1 Parity and time reversal in classical physics . 7 2.1.1 Parity . 7 2.1.2 Time reversal . 8 2.1.3 Maxwell equations . 8 2.1.4 Spin, dipole moments, and helicity . 9 2.2 C, P, and T in quantum mechanics . 10 2.2.1 Parity and charge conjugation . 11 2.2.2 Time reversal . 12 2.3 C, P, and T in quantum field theory . 13 2.3.1 Conventions . 13 2.3.2 The Photon Field . 13 2.3.3 Klein-Gordon field . 14 2.3.4 Dirac Field . 16 2.3.5 Charge conjugation . 19 2.3.6 Gluon field . 20 2.3.7 CPT theorem . 22 2.3.8 Summary of C, P, and T in QFT . 22 Chapter 3 CP Violation in and beyond the Standard Model . 24 3.1 CP-violating observables . 24 3.1.1 Direct CP violation . 24 3.1.2 Indirect CP violation . 29 3.1.3 Interference CP violation . 30 3.2 CP violation in the SM . 31 3.2.1 CKM matrix . 31 v 3.2.2 The strong CP problem . 34 3.3 CP violation beyond the SM . 36 3.3.1 two Higgs-doublet model . 36 3.3.2 Left-right symmetric model . 38 3.3.3 Weak scale supersymmetry . 41 3.4 Summary . 42 Chapter 4 Beyond the Standard Model Physics as an Effective Field Theory 43 4.1 Effective field theory . 43 4.2 Standard Model effective field theory .
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