Soft-Photon Corrections to B[over ¯]→Dτ^{-}ν[over ¯]_{τ} Relative to B[over ¯]→Dμ^{-}ν[over ¯]_{μ}

We evaluate long-distance electromagnetic (QED) contributions to B[over ¯]^{0}→D^{+}τ^{-}ν[over ¯]_{τ} and B^{-}→D^{0}τ^{-}ν[over ¯]_{τ} relative to B[over ¯]^{0}→D^{+}μ^{-}ν[over ¯]_{μ} and B^{-}→D^{0}μ^{-}ν[over ¯]_{μ}, respectively, in the standard model. We point out that the QED corrections to the ratios R(D^{+}) and R(D^{0}) 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(D^{0})^{τ/μ} can be amplified by ∼4% and ∼3%, respectively, for the soft-photon energy cut in the range 20-40 MeV.