Symmetry breaking radiative corrections to B to tensor meson form factors at large recoil

Abstract

Abstract In heavy-to-light B decays, the heavy-quark/large-energy symmetry reduces the number of QCD form factors. At large final state meson energy, these form factors receive sizeable perturbative corrections. The hard-gluon vertex corrections are absorbed in the coefficients of soft-form factors, while the hard-spectator interactions generate symmetry-breaking corrections and end-point singularities. At an order of 1/m b, using the heavy-quark/large-energy symmetry, the end-point singularities can also be absorbed in the soft form factors, whereas the symmetry breaking corrections add separately to the form factors. In this work, we calculate these perturbative corrections for B → Tμ + μ − decays, with T representing the tensor mesons K 2 * , f 2 , a 2 all having J P = 2+. We find that the values of the branching ratio (Br) and the zero-position of the forward–backward asymmetry ( A F B ) of B → K 2 * μ + μ − decay receive nearly 5% and 14% contributions, respectively, from these radiative corrections. Compared to these observables, the radiative corrections change the averaged longitudinal lepton polarization asymmetry (⟨P L⟩) by 13%. Therefore, prior to attributing any deviation from the SM predictions of these asymmetries as a hint of NP, one has to take into account the contributions of vertex and hard-spectator corrections.