Observation of τ−→π−ντe+e− and search for τ−→π−ντμ+μ−

We present the first measurements of branching fractions of rare tau-lepton decays, $ au^- ightarrow pi^- u_ au 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 $ au^- ightarrow pi^- u_ au 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 $mathcalB( au^- ightarrow pi^- u_ au e^+ e^-)[M_pi^- e^+ e^->1.05~ m GeV/c^2] = (5.90 pm 0.53 pm 0.85 pm 0.11) imes 10^-6$, 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 $mathcalB_A( au^- ightarrow pi^- u_ au e^+ e^-) = (1.46 pm 0.13 pm 0.21) imes 10^-5$ to $mathcalB_V( au^- ightarrow pi^- u_ au e^+ e^-) = (3.01 pm 0.27 pm 0.43) imes 10^-5$, respectively. An upper limit is set on the branching fraction of the $ au^- ightarrow pi^- u_ au mu^+ mu^-$ decay, $mathcalB( au^- ightarrow pi^- u_ au mu^+ mu^-) < 1.14 imes 10^-5$, at the 90% confidence level.