Speaker
Hakan Akdag
(Bonn University)
Description
We construct hadronic amplitudes for the three-body decays
$\eta^{(\prime)}\to\pi^+\pi^-\pi^0$ and $\eta'\to\eta\pi^+\pi^-$ in a non-perturbative fashion,
allowing for $C$- and $CP$-violating asymmetries in the $\pi^+\pi^-$ 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 $\eta^{(\prime)}\to\pi^+\pi^-\pi^0$ and an effective isovector operator in $\eta'\to\eta\pi^+\pi^-$, while the strongly different sensitivities to these operators can be understood from chiral power counting arguments.
Primary author
Hakan Akdag
(Bonn University)
