$\ddot{I}{„}^{-}\to \hat{I}{\cdot }^{(\prime )}\ddot{I}{€}^{-}\hat{I}{½}_{\ddot{I}}„{\hat{I}}^3$ decays as backgrounds in the search for second class currents

Abstract

Observation of $\ddot{I}{„}^{-}\to \hat{I}{\cdot }^{(\prime )}\ddot{I}{€}^{-}\hat{I}{½}_{\ddot{I}}„$ decays at Belle-II would indicate either a manifestation of isospin symmetry breaking or genuine second class currents (SCC) effects. The corresponding radiative $\ddot{I}{„}^{-}\to \hat{I}{\cdot }^{(\prime )}\ddot{I}{€}^{-}\hat{I}{½}_{\ddot{I}}„{\hat{I}}^3$ 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 $E_{\hat{I}}^3>100$ MeV should get rid of this background in the Belle-II environment searching for the $\ddot{I}{„}^{-}\to \hat{I}\cdot \ddot{I}{€}^{-}\hat{I}{½}_{\ddot{I}}„$ channel. Similar considerations hold inconclusive for decays involving the $\hat{I}{\cdot }^{\prime }$ given the theory uncertainties in the prediction of the $\ddot{I}{„}^{-}\to \hat{I}{\cdot }^{\prime }\ddot{I}{€}^{-}\hat{I}{½}_{\ddot{I}}„$ branching ratio. Still, additional kinematics-based cuts should be able to suppress this background in the $\hat{I}{\cdot }^{\prime }$ case to a negligible level.

61 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