Correlations of $C$ and $CP$ violation in $\eta \to {\pi }^0{\ell }^{+}{\ell }^{-}$ and ${\eta }^{\prime }\to \eta {\ell }^{+}{\ell }^{-}$

Abstract

Based on recent progress in the systematic analysis of $C$ and $CP$ violation in the light-meson sector, we calculate the $C$-odd transition amplitudes $\eta \to {\pi }^0{\ell }^{+}{\ell }^{-}$ and ${\eta }^{\prime }\to \eta {\ell }^{+}{\ell }^{-}$. Focusing on long-distance contributions driven by the lowest-lying hadronic intermediate states, we work out the correlations between these beyond-the-Standard-Model signals and the Dalitz-plot asymmetries in $\eta \to {\pi }^0{\pi }^{+}{\pi }^{-}$ and ${\eta }^{\prime }\to \eta {\pi }^{+}{\pi }^{-}$, using dispersion theory.

Comments: 35 pages, 7 figures, 3 tables; v2: section 5 revised, discussion extended, version published in JHEP