Rare Semileptonic $B^+ \to \pi^+ \tau^+ \tau^-$ Decay within Perturbative QCD

Rare $B$-meson decays originated by flavor changing neutral currents (FCNCs), $b\to s$ and $b\to d$ quark transitions, are especially sensitive to New physics effects due to the smallness of their decay width. $B$-meson decays due to the $b\to s$ transition have been studied experimentally and theoretically, in a difference to $b\to d$ transitions, in particulear, the $B^+ \to \pi^+ \mu^+ \mu^-$ decay was observed by the LHCb collaboration in 2012 only. This decay is well studied theoretically and predictions are in agreement with experimental data obtained by same collaboration in 2015. It is also of interest to consider a similar decay, where a pair of tauons is chosen as the final pair of leptons. Theoretical predictions for the $B^+ \to \pi^+ \tau^+ \tau^-$ branching fraction are presented based on the effective electroweak Hamiltonian approach, depending on the choice of the parametrization of the formfactors entering the $B \to \pi$ matrix elements. A possibility of the $B \to \pi \tau^+ \tau^-$ observation at the LHC and SuperKEKB is discussed.