${\tau }^{-}\to {\eta }^{(\prime )}{\pi }^{-}{\nu }_{\tau }\gamma$ decays as backgrounds in the search for second class currents

Abstract

Observation of ${\tau }^{-}\to {\eta }^{(\prime )}{\pi }^{-}{\nu }_{\tau }$ decays at Belle-II would indicate either a manifestation of isospin symmetry breaking or genuine second class currents (SCC) effects. The corresponding radiative ${\tau }^{-}\to {\eta }^{(\prime )}{\pi }^{-}{\nu }_{\tau }\gamma$ 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 $E_{\gamma }>100$ MeV should get rid of this background in the Belle-II environment searching for the ${\tau }^{-}\to \eta {\pi }^{-}{\nu }_{\tau }$ channel. Similar considerations hold inconclusive for decays involving the ${\eta }^{\prime }$ given the theory uncertainties in the prediction of the ${\tau }^{-}\to {\eta }^{\prime }{\pi }^{-}{\nu }_{\tau }$ branching ratio. Still, additional kinematics-based cuts should be able to suppress this background in the ${\eta }^{\prime }$ case to a negligible level.

arXiv comment61 pages, 20 figures and 2 tables. v2: Improved statistical treatment and appendix A added, discussing the impact of IB contributions. Accepted for publication in PRD

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