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−π0 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−π0 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.