Gerlach Marvin, Nierste Ulrich, Shtabovenko Vladyslav, Steinhauser Matthias
Institut für Theoretische Teilchenphysik, Karlsruhe Institute of Technology (KIT), 76128 Karlsruhe, Germany.
Phys Rev Lett. 2022 Sep 2;129(10):102001. doi: 10.1103/PhysRevLett.129.102001.
We extend the theoretical prediction for the width difference ΔΓ_{q} in the mixing of neutral B mesons in the Standard Model to next-to-next-to-leading order in α_{s}. To this aim, we calculate three-loop diagrams with two |ΔB|=1 current-current operators analytically. In the matching between |ΔB|=1 and |ΔB|=2 effective theories, we regularize the infrared divergences dimensionally and take into account all relevant evanescent operators. Further elements of the calculation are the two-loop renormalization matrix Z_{ij} for the |ΔB|=2 operators and the O(α_{s}^{2}) corrections to the finite renormalization that ensures the 1/m_{b} suppression of the operator R_{0} at two-loop order. Our theoretical prediction reads ΔΓ_{s}/ΔM_{s}=(4.33±0.93)×10^{-3} if expressed in terms of the bottom mass in the MS[over ¯] scheme and ΔΓ_{s}/ΔM_{s}=(4.20±0.95)×10^{-3} for the use of the potential-subtracted mass. While the controversy on |V_{cb}| affects both ΔΓ_{s} and ΔM_{s}, the ratio ΔΓ_{s}/ΔM_{s} is not affected by the uncertainty in |V_{cb}|.
我们将标准模型中中性B介子混合时宽度差ΔΓₑ的理论预测扩展到αₛ的次下领先阶。为此，我们解析计算了带有两个|ΔB| = 1流-流算符的三环图。在|ΔB| = 1和|ΔB| = 2有效理论的匹配中，我们通过维数正规化来处理红外发散，并考虑所有相关的瞬逝算符。计算的其他要素包括|ΔB| = 2算符的二环重整化矩阵Zᵢⱼ以及对有限重整化的O(αₛ²)修正，这确保了在二环阶对算符R₀的1/mₑ抑制。如果用MS[上划线]方案中的底夸克质量表示，我们的理论预测为ΔΓₛ/ΔMₛ = (4.33 ± 0.93)×10⁻³；对于使用势减法质量，ΔΓₛ/ΔMₛ = (4.20 ± 0.95)×10⁻³。虽然关于|Vₑᵦ|的争议同时影响ΔΓₛ和ΔMₛ，但比率ΔΓₛ/ΔMₛ不受|Vₑᵦ|不确定性的影响。
