G-parity breaking in ${\tau }^{-}\to {\eta }^{(\mathrm{\prime })}{\pi }^{-}{\nu }_{\tau }$ decays induced by the ${\eta }^{(\mathrm{\prime })}\gamma \gamma$ form factor

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