Patterns of $C$- and $CP$-violation in hadronic $η$ and $η'$ three-body decays

Abstract

We construct hadronic amplitudes for the three-body decays η (′) → π + π − π 0 and η ′ → ηπ + π − in a non-perturbative fashion, allowing for C-and CP -violating asymmetries in the π + π − distributions. These amplitudes are consistent with the constraints of analyticity and unitarity. We find that the currently most accurate Dalitz-plot distributions taken by the KLOE-2 and BESIII collaborations confine the patterns of these asymmetries to a relative per mille and per cent level, respectively. Our dispersive representation allows us to extract the individual coupling strengths of the C-and CP -violating contributions arising from effective isoscalar and isotensor operators in η (′) → π + π − π 0 and an effective isovector operator in η ′ → ηπ + π − , while the strongly different sensitivities to these operators can be understood from chiral power counting arguments.