论文标题
关于电磁偶极子操作员的贡献
On the contribution of the electromagnetic dipole operator ${\cal O}_7$ to the $\bar B_s \to μ^+μ^-$ decay amplitude
论文作者
论文摘要
我们构建了一个分解定理，该定理允许系统地将QCD校正包括在有效的弱汉密尔顿人对$ \ bar b_s \至μ^+μ^ - $衰减幅度中电磁偶极子操作员的贡献。首先，我们重新启动QED框图的已知结果，该结果具有与$ \ bar b_s $ Meson和最终状态下的Light Quark不同速度相关的双层增强。我们提供了对单个动量区域中相关端点差异的取消的详细分析，并显示如何通过适用于相应的裸露分解定理的适当减法来隔离速度对数。这使我们能够以一种直接的方式包含QCD校正，该QCD校正是由软连线性散射核和$ b_s $ -Meson分布分布的硬线性散射核的硬质偶极子操作员的硬匹配系数的重新分配组运行。为了关注双端点对数的贡献，我们得出了一个紧凑的公式，该公式可以恢复领先的QCD校正。
We construct a factorization theorem that allows to systematically include QCD corrections to the contribution of the electromagnetic dipole operator in the effective weak Hamiltonian to the $\bar B_s \to μ^+μ^-$ decay amplitude. We first rederive the known result for the leading-order QED box diagram, which features a double-logarithmic enhancement associated to the different rapidities of the light quark in the $\bar B_s$ meson and the energetic muons in the final state. We provide a detailed analysis of the cancellation of the related endpoint divergences appearing in individual momentum regions, and show how the rapidity logarithms can be isolated by suitable subtractions applied to the corresponding bare factorization theorem. This allows us to include in a straightforward manner the QCD corrections arising from the renormalization-group running of the hard matching coefficient of the electromagnetic dipole operator in soft-collinear effective theory, the hard-collinear scattering kernel, and the $B_s$-meson distribution amplitude. Focusing on the contribution from the double endpoint logarithms, we derive a compact formula that resums the leading-logarithmic QCD corrections.
