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

TL;DR

This paper analyzes radiative tau decays involving eta and eta' mesons as potential backgrounds in searches for second class currents, proposing photon energy cuts to mitigate their impact.

Contribution

It provides a theoretical calculation of radiative decay observables using Resonance Chiral Lagrangians and suggests practical photon veto strategies for experiments.

Findings

Photon vetoes with E_gamma > 100 MeV can suppress backgrounds for eta decays.

Uncertainties in eta' decay predictions make background suppression less conclusive.

Kinematic cuts can reduce eta' decay backgrounds to negligible levels.

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.