G-parity breaking in $τ^- \to η^{(\prime)} π^- ν_τ$ decays induced by the $η^{(\prime)}γγ$ form factor

Abstract

Breaking of G-parity or new weak (second class) currents can be responsible for $τ^- \to η^{(\prime)} π^- ν_τ$ decays. Forthcoming measurements of $τ$ 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 $τ^- \to η^{(\prime)} π^- ν_τ$ decays induced by the emission of two virtual photons and its later conversion into an $η^{(\prime)}$ 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 $τ^- \to η^{(\prime)} π^- ν_τ$ .

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