Institute for Theoretical Particle Physics (TTP), Karlsruhe Institute of Technology, Engesserstraße 7, D-76128 Karlsruhe, Germany.
Institute for Nuclear Physics (IKP), Karlsruhe Institute of Technology, Hermann-von-Helmholtz-Platz 1, D-76344 Eggenstein-Leopoldshafen, Germany.
Phys Rev Lett. 2018 Jun 29;120(26):261804. doi: 10.1103/PhysRevLett.120.261804.
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.
我们在标准模型中评估远距离电磁（QED）对 B[over ¯]^{0}→D^{+}τ^{-}ν[over ¯]{τ}和 B^{-}→D^{0}τ^{-}ν[over ¯]{τ}相对于 B[over ¯]^{0}→D^{+}μ^{-}ν[over ¯]{μ}和 B^{-}→D^{0}μ^{-}ν[over ¯]{μ}的贡献。我们指出，与预期的辐射修正在两个分支比中几乎相互抵消相反，QED 对这两个比值 R(D^{+})和 R(D^{0})的修正并非微不足道。原因是远距离 QED 修正取决于子粒子的质量和相对速度。我们发现，对于软光子能量范围在 20-40 MeV 的切割，R(D^{+})^{τ/μ}和 R(D^{0})^{τ/μ}的理论预测可以分别放大约 4%和 3%。
