Soft-Photon Corrections to $\bar{B} \to D τ^{-} \barν_τ$ Relative to $\bar{B} \to D μ^{-} \barν_μ$

Abstract

We evaluate long-distance electromagnetic (QED) contributions to $\bar{B}{}^0 \to D^+ τ^{-} \barν_τ$ and $B^- \to D^0 τ^{-} \barν_τ$ relative to $\bar{B}{}^0 \to D^+ μ^{-} \barν_μ$ and $B^- \to D^0 μ^{-} \barν_μ$, 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 $\sim4\%$ and $\sim3\%$, respectively, for the soft-photon energy cut in range $20$-$40$ MeV.

5 pages, 3 figures; v3: several minor modifications, references added, published version