In the Standard Model, the $b \to s$ and $b \to d$ flavor-changing neutral currents (FCNC) are induced by loop effects. Rare semileptonic $B$-meson decays originated by these currents are standard channels for testing the Standard Model precisely and in searching for possible physics beyond it.
Here, we consider the rare $B^+ \to \pi^+ \ell^+ \ell^-$ decay, where $\ell = \mu,\, \tau$ is a charged lepton, and present its dilepton invariant-mass spectrum and decay rate based on the effective electroweak Hamiltonian approach for the $b \to d \ell^+ \ell^-$ transitions in the Standard Model, taking into account weak annihilation and long-distance contributions, of which the later is from the light vector mesons.
Our prediction for the total branching fraction of $B^+ \to \pi^+ \mu^+ \mu^-$ agrees with the latest LHCb result within the experimental and theoretical uncertainties. Moreover, including the annihilation diagrams and contributions from the $\rho^0$- and $\omega$-resonances together gives better agreement with the experimental data in the low $q^2$-part of the dimuon mass spectrum.
We also present theoretical predictions for the total and partial branching fractions for $B^+ \to \pi^+ \tau^+ \tau^-$ in the Standard Model.
These results are potentially useful in testing the lepton flavor universality in the FCNC $B \to \pi \ell^+ \ell^-$ decays.