AI 中文总结
研究利用有效场论计算$B^-\toτ^-\barν_τ(\gamma)$轻子衰变速率，含QED修正，建立因子分解定理并评估，考虑多种修正，结果显示部分贡献抵消，结构依赖修正可忽略，给出不确定性估计及轻子味普适性比率预测。
AI 中文摘要
我们使用一系列有效场论（EFTs）来计算轻子衰变$B^-\to\tau^-\bar\nu_\tau(\gamma)$的速率，包括实和虚量子电动力学（QED）修正，并在$B$介子静止参考系中对电磁辐射施加$E_{\rm cut}\ll\Lambda_{\rm QCD}$的截断。我们建立了该速率的因子分解定理并在$\mathcal{O}(\alpha)$阶进行评估，重新求和微扰理论中所有阶的主导对数修正。大质量$m_\tau$使我们能将τ轻子视为重费米子，得到一种结构上与μ子情况不同且更简单的EFT构造。我们的分析包括主导的$\Lambda_{\rm QCD}/m_\tau$修正以及$E_{\rm cut}/\Lambda_{\rm QCD}$中的主导修正。结果表明某些本应显著的贡献相互抵消，与μ子通道不同，涉及$BB^\ast\gamma$跃迁的结构依赖修正数值上可忽略，对$E_\mathrm{cut}$的剩余对数依赖较弱。我们估计结构依赖的QED修正计算中的当前不确定性约为速率的0.5%。作为副产品，我们给出了τ和μ子通道轻子味普适性比率的最新预测。
英文摘要
Using a sequence of effective field theories (EFTs), we calculate the rate for the leptonic decay $B^-\toτ^-\barν_τ(γ)$ including real and virtual QED corrections, with a cut $E_{\rm cut}\llΛ_{\rm QCD}$ imposed on electromagnetic radiation in the $B$-meson rest frame. We establish a factorization theorem for the rate and evaluate it at $\mathcal{O}(α)$, resumming the leading logarithmic corrections to all orders in perturbation theory. The large mass $m_τ$ allows us to treat the tau lepton as a heavy fermion below $μ\sim m_B\sim m_τ$, leading to an EFT construction that is structurally different and noticeably simpler than that for the muon case. In particular, hadron-structure dependent QED corrections can be described in terms of QED-induced $B^-\toτ^-$ form factors, which should be calculable on the lattice. Our analysis includes the leading $Λ_{\rm QCD}/m_τ$ corrections as well as the leading corrections in $E_{\rm cut}/Λ_{\rm QCD}$. We show that contributions of the form $Λ_{\rm QCD}m_B/m_τ^2$, which are naively sizable, cancel among each other. Contrary to the muon channel, structure-dependent corrections involving $BB^\astγ$ transitions are numerically negligible for the tau case. The remaining logarithmic dependence on $E_\mathrm{cut}$ is mild. We estimate that the present uncertainty in the calculation of the structure-dependent QED corrections is about 0.5\% of the rate. As a byproduct, we present a state-of-the-art prediction for the lepton flavor universality ratio of the tau and muon channels.
Comments25 pages, 4 figures
