Author ORCID Identifier

Date Available


Year of Publication


Degree Name

Doctor of Philosophy (PhD)

Document Type

Doctoral Dissertation


Arts and Sciences


Physics and Astronomy

First Advisor

Dr. Susan Gardner


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)

Funding Information

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