G-parity breaking in $\ddot{I}{„}^{-}\to \hat{I}{\cdot }^{(\prime )}\ddot{I}{€}^{-}\hat{I}{½}_{\ddot{I}}„$ decays induced by the $\hat{I}{\cdot }^{(\prime )}{\hat{I}}^3{\hat{I}}^3$ form factor

Abstract

Breaking of G-parity or new weak (second class) currents can be responsible for $\ddot{I}{„}^{-}\to \hat{I}{\cdot }^{(\prime )}\ddot{I}{€}^{-}\hat{I}{½}_{\ddot{I}}„$ decays. Forthcoming measurements of $\ddot{I}„$ lepton properties at the Belle II experiment will be able to measure this decay channel for the first time. Isolating new physics contributions from the measured rates will require a careful evaluation of G-parity breaking contributions. Here we evaluate the one-loop contribution to $\ddot{I}{„}^{-}\to \hat{I}{\cdot }^{(\prime )}\ddot{I}{€}^{-}\hat{I}{½}_{\ddot{I}}„$ decays induced by the emission of two virtual photons and its later conversion into an $\hat{I}{\cdot }^{(\prime )}$ meson. As expected, this contribution is very small and may be relevant only for new physics searches contributing at the $10^{-4}$ level to the decay rate of $\ddot{I}{„}^{-}\to \hat{I}{\cdot }^{(\prime )}\ddot{I}{€}^{-}\hat{I}{½}_{\ddot{I}}„$ .

6 pages, 1 figure, Approved for publication in Physical Review D, Appendix with Lengthy expressions can be found in v1