#### Author ORCID Identifier

#### Year of Publication

2020

#### Degree Name

Doctor of Philosophy (PhD)

#### Document Type

Doctoral Dissertation

#### College

Arts and Sciences

#### Department

Physics and Astronomy

#### First Advisor

Dr. Susan Gardner

#### Abstract

A violation of mirror symmetry in the $\eta\to\pi^+\pi^-\pi^0$ 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 experimental 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 dimension6 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 $\eta\to \pi^+ \pi^- \pi^0$ 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 $\eta\to\pi^+\pi^-\pi^0$ 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 $\eta\to\pi^+\pi^-\pi^0$ Dalitz plot.

#### Digital Object Identifier (DOI)

https://doi.org/10.13023/etd.2020.388

#### Funding Information

This research was partially supported by the Department of Energy Office of Nuclear Physics under contract DE-FG02-96ER40989, 2015 -- 2019.

#### 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