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

Abstract

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

arXiv comment6 pages, 1 figure, Approved for publication in Physical Review D, Appendix with Lengthy expressions can be found in v1

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Cited by in corpus (4)

• Effective-field theory analysis of the ${\tau }^{-}\to {\pi }^{-}{\pi }^0{\nu }_{\tau }$ decays
• Effective-field theory analysis of the ${\tau }^{-}\to {\eta }^{(\prime )}{\pi }^{-}{\nu }_{\tau }$ decays
• ${\tau }^{-}\to {\pi }^{-}\eta {\nu }_{\tau }$ decay induced by QED one-loop effects
• The second-class current decays $\tau \to \pi \eta ({\eta }^{\prime }){\nu }_{\tau }$ in the NJL model including the interaction of mesons in the final state