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Among (semi)leptonic rare $B$-decays induced by the $b \to d$ flavor changingneutral current, the decay $B^+ \to \pi^+ \mu^+ \mu^-$ is the only one observedso far experimentally. Related decays involving the $e^+e^-$ and $\tau^+\tau^-$ pairs are the targets for the ongoing experiments at the LHC, inparticular LHCb, and Belle II. The muonic and electronic semileptonic decayshave almost identical branching fractions in the Standard Model (SM). However,the tauonic decay $B^+ \to \pi^+ \tau^+ \tau^-$ differs from the other two dueto the higher reaction threshold which lies slightly below the $\psi(2S)$-resonance. We present calculations of the ditauon ($\tau^+ \tau^-$)invariant-mass distribution and the branching fraction ${\rm Br} (B^+ \to \pi^+\tau^+ \tau^-)$ in the SM based on the Effective Electroweak Hamiltonianapproach, taking into account also the so-called long-distance contributions.The largest theoretical uncertainty in the short-distance part of the decayrates is due to the $B \to \pi$ form factors, which we quantify using threepopular parametrizations. The long-distance contribution can be minimized by acut on the ditauon mass $m_{\tau^+ \tau^-} > M_{\psi (2S)}$. Once available,the branching fractions in the tauonic and muonic (and electronic) modesprovide stringent test of the lepton flavor universality in the $b \to d$transitions. We illustrate this by calculating the ratio $R_\pi (\tau/\mu)\equiv {\rm Br} (B^+ \to \pi^+ \tau^+ \tau^-)/{\rm Br} (B^+ \to \pi^+ \mu^+\mu^-)$ in the SM for the total and binned ratios of the branching fractions.

Branching Fraction of the Decay $B^+ \to \pi^+ \tau^+ \tau^-$ and Lepton Flavor Universality Test via the Ratio $R_\pi (\tau/\mu)$