Precise calculation of the dilepton invariant-mass spectrum and the decay rate in B± → π±μ+μ- in the SM

We present a precise calculation of the dilepton invariant-mass spectrum and the decay rate for B-+/- -> pi(+/-)l(+)l(-) (l(+/-) = e(+/-),mu(+/-)) in the Standard Model (SM) based on the effective Hamiltonian approach for the b -> dl(+)l(-) transitions. With the Wilson coefficients already known in next-to-next-to-leading logarithmic (NNLL) accuracy, the remaining theoretical uncertainty in the short-distance contribution resides in the form factors f(+)(q(2)) f(0) (q(2)) and f(T) (q(2)) . Of these, f(+) (q(2)) is well measured in the charged-current semileptonic decays B. -> K, and we use the B-factory data to parametrize it. The corresponding form factors for the B. K transitions have been calculated in the lattice QCD approach for large q(2) and extrapolated to the entire q(2) region using the so-called z expansion. Using an SU(3)(F)-breaking ansatz, we calculate the B. p tensor form factor, which is consistent with the recently reported lattice B. p analysis obtained at large q(2). The prediction for the total branching fraction B(B-+/- -> pi(+/-)mu(+)mu(-)) = (1.88(-0.21)(+0.32)) x 10(-8) is in good agreement with the experimental value obtained by the LHCb Collaboration. In the low-q(2) region, heavy-quark symmetry (HQS) relates the three form factors with each other. Accounting for the leading-order symmetry-breaking effects, and using data from the charged-current process B -> pi lve to determine f(+)(q(2)) we calculate the dilepton invariant-mass distribution in the low-q(2) region in the B-+/- -> pi(+/-)l(+)l(-)decay. This provides a model-independent and precise calculation of the partial branching ratio for this decay.