$τ^-\toη^{(\prime)}π^-ν_τγ$ decays as backgrounds in the search for second class currents

Abstract

Observation of $τ^-\toη^{(\prime)}π^-ν_τ$ decays at Belle-II would indicate either a manifestation of isospin symmetry breaking or genuine second class currents (SCC) effects. The corresponding radiative $τ^-\toη^{(\prime)}π^-ν_τγ$ decay channels are not suppressed by $G$-parity considerations and may represent a serious background in searches of SCC in the former. We compute the observables associated to these radiative decays using Resonance Chiral Lagrangians and conclude that vetoing photons with $E_γ>100$ MeV should get rid of this background in the Belle-II environment searching for the $τ^-\toηπ^-ν_τ$ channel. Similar considerations hold inconclusive for decays involving the $η^\prime$ given the theory uncertainties in the prediction of the $τ^-\toη^\primeπ^-ν_τ$ branching ratio. Still, additional kinematics-based cuts should be able to suppress this background in the $η^\prime$ case to a negligible level.