Soft-Photon Corrections to $\bar{B}$ → Dτ ⁻ $\bar{v}$ $_{T}$ Relative to $\bar{B}$ → Dμ⁻ $\bar{v}$$_{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.