Soft-Photon Corrections to B^sup ¯^→Dτ−ν^sup ¯^τ Relative to B^sup ¯^→Dμ−ν^sup ¯^μ

We evaluate long-distance electromagnetic (QED) contributions to B¯0→D+τ−ν¯τ and B−→D0τ−ν¯τ relative to B¯0→D+μ−ν¯μ and B−→D0μ−ν¯μ, respectively, in the standard model. We point out that the QED corrections to the ratios R(D+) and R(D0) are not negligible, contrary to the expectation that radiative corrections are almost canceled out in the ratio of the two branching fractions. The reason is that long-distance QED corrections depend on the masses and relative velocities of the daughter particles. We find that theoretical predictions for R(D+)τ/μ and R(D0)τ/μ can be amplified by ~4% and ~3%, respectively, for the soft-photon energy cut in the range 20–40 MeV.