$C$ and $CP$ violation in effective field theories and applications to $\eta$-meson decays

Abstract

The quest for sources of the simultaneous violation of $C$ and $CP$ symmetry was popular in the 1960s, but has since been neglected for a long time. We revisit the operators that break $C$ and $CP$ for flavor-conserving transitions in both the Standard Model effective field theory and the low-energy effective field theory, which subsequently can be matched to light-meson physics using chiral perturbation theory. As applications, we discuss in particular the $C$-odd Dalitz plot asymmetries in $\eta \to 3\pi$, but also decays with dilepton pairs in the final state, such as long-distance contributions to the rare semileptonic decays $\eta \to {\pi }^0{\ell }^{+}{\ell }^{-}$ as well as asymmetries in ${\eta }^{(\prime )}\to \gamma {\ell }^{+}{\ell }^{-}$ and ${\eta }^{(\prime )}\to {\pi }^{+}{\pi }^{-}{\ell }^{+}{\ell }^{-}$.

Comments: 15 pages, 4 figures; plenary contribution at the 11th International Workshop on Chiral Dynamics (CD2024)