Complete analysis on QED corrections to Bq → τ+τ−

Abstract

Motivated by a dynamical enhancement of the electromagnetic corrections by a power of ΛQCD/mb in Bd,s→ μ+μ− at next-to-leading order (NLO), we extend the QED factorization effects on the leptonic B meson decays with light muon leptons to tauonic final states, Bd,s→ τ+τ−, using soft-collinear effective theory (SCET). This extension is necessary owing to the appearance of the large τ mass, which will lead to different power counting in SCET and also different results. We provide a complete NLO electromagnetic corrections to Bd,s→ τ+τ−, which include hard functions and hard-collinear functions below the bottom quark mass scale μb. The power enhanced electromagnetic effects from hard-collinear contributions on Bd,s→ μ+μ− discussed before also exist in Bd,s→ τ+τ−. However the logarithm term arising from contributions of hard-collinear photon and lepton virtualities for Bd,s→ τ+τ− is not large as it is in muon case due to the hard-collinear scale of τ mass, which lead to only approximately 0.04% QED corrections to the branching fraction of Bd,s→ τ+τ− compared with overall reduction about 0.5% in Bd,s→ μ+μ−.