τ−→η(′)π−ντγdecays as background in the search for second class currents

Abstract

Observation of ${\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\eta}}^{(\ensuremath{'})}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\nu}}_{\ensuremath{\tau}}$ decays at Belle-II would indicate either a manifestation of isospin symmetry breaking or genuine second class current (SCC) effects. The corresponding radiative ${\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\eta}}^{(\ensuremath{'})}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\nu}}_{\ensuremath{\tau}}\ensuremath{\gamma}$ decay channels are not suppressed by $G$-parity considerations and may represent a serious background in searches of SCCs in the former. We compute the observables associated to these radiative decays using resonance chiral Lagrangians and conclude that vetoing photons with ${E}_{\ensuremath{\gamma}}>100\text{ }\text{ }\mathrm{MeV}$ should get rid of this background in the Belle-II environment while searching for the ${\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\eta}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\nu}}_{\ensuremath{\tau}}$ channel. Similar considerations hold inconclusive for decays involving the ${\ensuremath{\eta}}^{\ensuremath{'}}$, given the theory's uncertainties in the prediction of the ${\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\eta}}^{\ensuremath{'}}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\nu}}_{\ensuremath{\tau}}$ branching ratio. Still, additional kinematics-based cuts should be able to suppress this background in the ${\ensuremath{\eta}}^{\ensuremath{'}}$ case to a negligible level.