Power-enhanced leading-logarithmic QED corrections to B_q → μ ⁺ μ ⁻

We provide a systematic treatment of the previously discovered power- enhanced QED corrections to the leptonic decay B_q→ μ⁺μ⁻ (q = d, s) in the frame- work of soft-collinear effective theory (SCET). Employing two-step matching on SCETI and SCET_II, and the respective renormalization group equations, we sum the leading- logarithmic QED corrections and the mixed QED-QCD corrections to all orders in the couplings for the matrix element of the semileptonic weak effective operator Q₉. We pro- pose a treatment of the B-meson decay constant and light-cone distribution amplitude in the presence of process-specific QED corrections. Finally we include ultrasoft photon radiation and provide updated values of the non-radiative and radiative branching fractions of B_q→ μ⁺μ⁻ decay that include the double-logarithmic QED and QCD corrections.