Lepton-pair production in di-pion $\tau$ lepton decays

Abstract

We study the ${\tau }^{-}\to {\nu }_{\tau }{\pi }^{-}{\pi }^0{\ell }^{+}{\ell }^{-}$ ($\ell =e,\mu$) decays, which are $O({\alpha }^2)$-suppressed with respect to the dominant di-pion tau decay channel. Both the inner-bremsstrahlung and the structure- (and model-)dependent contributions are considered. In the $\ell =e$ case, structure-dependent effects are $\mathcal{O}(1\%)$ in the decay rate, yielding a clean prediction of its branching ratio, $2.3\times 10^{-5}$, measurable with BaBar or Belle(-II) data. For $\ell =\mu$, both contributions have similar magnitude and we get a branching fraction of $(1.6\pm 0.3)\times 10^{-7}$, reachable by the end of Belle-II operation. These decays allow to study the dynamics of strong interactions with simultaneous weak and electromagnetic probes; their knowledge will contribute to reducing backgrounds in lepton flavor/number violating searches.