$B\to π\ell^{+}\ell^{-}$ decays revisited in the standard model

A new estimate is presented of the dileptonic $B$ decays $B\toπ\ell^+\ell^-(\ell=e,μ,τ)$ in naive factorization within the standard-model (SM) framework. Using a combination of several approaches, we investigate the behavior of the $B\to π$ form factors in the entire region of the momentum transfer squared $q^2$. For the vector and scalar form factors, we employ the light cone sum rule (LCSR) with a chiral current correlator to estimate, at twist-2 next-to-leading order (NLO) accuracy, their shapes in small and intermediate kinematical region. Then a simultaneous fit to a Bourrely-Caprini-Lellouch (BCL) parametrization is performed of the sum rule predictions and the corresponding lattice QCD (LQCD) results available at some high $q^2$'s. The same approach is applied for the tensor form factor, except that at large $q^2$ we use as input the LQCD data on the corresponding $B\to K$ form factor in combination with a $SU_F(3)$ symmetry breaking ansatz. Employing the fitted BCL parameterizations, we evaluate, as an illustrative example, several of the observables of the charged decay modes $B^-\toπ^-\ell^+\ell^-$, including the dilepton invariant mass distribution and branching ratio. For the dielectron and dimuon modes, the branching ratios are estimated at $\mathcal{B}(B^-\toπ^-e^+e^-)=(2.263^{+0.227}_{-0.192})\times10^{-8}$ and $\mathcal{B}(B^-\toπ^-μ^+μ^-)=(2.259^{+0.226}_{-0.191}) \times10^{-8}$. The latter shows an excellent agreement with the recent experimental measurement at LHCb and hence puts a stringent constraint on the contribution from possible new physics. We arrive at, for the ditau mode, $\mathcal{B}(B^-\toπ^-τ^+τ^-)=(1.017^{+0.118}_{-0.139})\times10^{-8}$, which is one order of magnitude larger than the existing theoretical predictions.

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