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

Abstract

A new estimate is presented of the dileptonic $B$ decays $B\to \pi {\ell }^{+}{\ell }^{-}(\ell =e,\mu ,\tau )$ in naive factorization within the standard-model (SM) framework. Using a combination of several approaches, we investigate the behavior of the $B\to \pi$ 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 $S{U}_F(3)$ symmetry breaking ansatz. Employing the fitted BCL parameterizations, we evaluate, as an illustrative example, several of the observables of the charged decay modes $B^{-}\to {\pi }^{-}{\ell }^{+}{\ell }^{-}$, including the dilepton invariant mass distribution and branching ratio. For the dielectron and dimuon modes, the branching ratios are estimated at $\mathcal{B}(B^{-}\to {\pi }^{-}{e}^{+}{e}^{-})=(2.263_{-0.192}^{+0.227})\times 10^{-8}$ and $\mathcal{B}(B^{-}\to {\pi }^{-}{\mu }^{+}{\mu }^{-})=(2.259_{-0.191}^{+0.226})\times 10^{-8}$. 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, $\mathcal{B}(B^{-}\to {\pi }^{-}{\tau }^{+}{\tau }^{-})=(1.017_{-0.139}^{+0.118})\times 10^{-8}$, which is one order of magnitude larger than the existing theoretical predictions.

Comments: 31 pages, 7 figures, 7 tables, minor corrections made for typos and omissions