Observation of $ \tau^- \rightarrow \pi^- \nu_{\tau} e^+ e^-$ and search for $\tau^- \rightarrow \pi^- \nu_{\tau} \mu^+ \mu^-$

TL;DR

This paper reports the first observation of the rare tau decay into a pion, neutrino, and electron-positron pair, measuring its branching fraction and setting limits on the muon pair decay mode, using data from the Belle experiment.

Contribution

First measurement of branching fractions for $ au^- ightarrow ext{pion}^- u_ au ext{lepton}^+ ext{lepton}^-$ decays, including the first observation of the electron mode.

Findings

First observation of $ au^- ightarrow ext{pion}^- u_ au e^+ e^-$ with 7.0$\sigma$ significance.

Measured partial branching fraction for $M_{ ext{pion} e e}>1.05$ GeV/$c^2$ as $(5.90 imes 10^{-6})$.

Set an upper limit of $1.14 imes 10^{-5}$ on the $ au^- ightarrow ext{pion}^- u_ au ext{mu}^+ ext{mu}^-$ decay.

Abstract

We present the first measurements of branching fractions of rare tau-lepton decays, $\tau^- \rightarrow \pi^- \nu_{\tau} \ell^+ \ell^-$ ($\ell = e$ or $\mu$), using a data sample corresponding to 562 fb$^{-1}$ collected at a center-of-mass energy of 10.58 GeV with the Belle detector at the KEKB asymmetric-energy $e^+ e^-$ collider. The $\tau^- \rightarrow \pi^- \nu_\tau e^+ e^-$ decay is observed for the first time with 7.0$\sigma$ significance. The partial branching fraction determined by the structure-dependent mechanisms mediated by either a vector or an axial-vector current for the mass region $M_{\pi e e}>1.05$ GeV/$c^2$ is measured to be $\mathcal{B}(\tau^-\rightarrow \pi^- \nu_\tau e^+ e^-)[M_{\pi^- e^+ e^-}>1.05~{\rm GeV}/c^2] = (5.90 \pm 0.53 \pm 0.85 \pm 0.11) \times 10^{-6}$, where the first uncertainty is statistical, the second is systematic, and the third is due to the model dependence. In the full phase space, due to the different detection efficiencies for the structure-dependent mechanisms mediated by axial-vector and vector currents, the branching fraction varies from $\mathcal{B}_{A}(\tau^-\rightarrow \pi^- \nu_\tau e^+ e^-) = (1.46 \pm 0.13 \pm 0.21) \times 10^{-5}$ to $\mathcal{B}_{V}(\tau^-\rightarrow \pi^- \nu_\tau e^+ e^-) = (3.01 \pm 0.27 \pm 0.43) \times 10^{-5}$, respectively. An upper limit is set on the branching fraction of the $\tau^- \rightarrow \pi^- \nu_\tau \mu^+ \mu^-$ decay, $\mathcal{B}(\tau^-\rightarrow \pi^- \nu_\tau \mu^+ \mu^-) < 1.14 \times 10^{-5}$, at the 90% confidence level.