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

TL;DR

This paper analyzes rare tau decay modes involving lepton pairs and pions, providing precise predictions for their branching ratios and exploring their potential to probe strong interaction dynamics and background reduction in new physics searches.

Contribution

It offers the first detailed calculation of $ au^- o u_{ au} o u_{ au} ext{pions} ext{leptons}$ decays including structure-dependent effects, with predictions for branching ratios relevant for current and future experiments.

Findings

Branching ratio for $ au^- o u_{ au} ext{pions} e^+ e^-$ is $2.3 imes 10^{-5}$.

Branching ratio for $ au^- o u_{ au} ext{pions} \mu^+ \mu^-$ is $(1.6 imes 10^{-7})$.

Structure-dependent effects are significant for muonic decay mode, influencing experimental measurements.

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, $2.3\times10^{-5}$, measurable with BaBar or Belle(-II) data. For $\ell=\mu$, both contributions have similar magnitude and we get a branching fraction of $(1.6\pm0.3)\times10^{-7}$, 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.