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We evaluate long-distance electromagnetic (QED) contributions to $\bar{B}{}^0\to D^+ \tau^{-} \bar{\nu}_{\tau}$ and $B^- \to D^0 \tau^{-} \bar{\nu}_{\tau}$relative to $\bar{B}{}^0 \to D^+ \mu^{-} \bar{\nu}_{\mu}$ and $B^- \to D^0\mu^{-} \bar{\nu}_{\mu}$, respectively, in the standard model. We point outthat the QED corrections to the ratios $R(D^{+})$ and $R(D^{0})$ are notnegligible, contrary to the expectation that radiative corrections are almostcanceled out in the ratio of the two branching fractions. The reason is thatlong-distance QED corrections depend on the masses and relative velocities ofthe daughter particles. We find that theoretical predictions for$R(D^{+})^{\tau/\mu}$ and $R(D^{0})^{\tau/\mu}$ can be amplified by $\sim4\%$and $\sim3\%$, respectively, for the soft-photon energy cut in range $20$-$40$MeV.

Soft-Photon Corrections to $\bar{B} \to D \tau^{-} \bar{\nu}_{\tau}$ Relative to $\bar{B} \to D \mu^{-} \bar{\nu}_{\mu}$