论文标题
关于$ \ overline {\ mathrm {ms}} $与沉重夸克的动力学质量之间的关系
On the relation between the $\overline{\mathrm{MS}}$ and the kinetic mass of heavy quarks
论文作者
论文摘要
我们计算了重夸克与三个环的动力学质量与动力学质量之间的关系。使用POL与$ \ Overline {\ rm MS} $质量之间的已知关系，我们获得了$ \ overline {\ rm MS} $与Kinetic Masses之间的精确转换关系。动力学质量是通过光谱函数的矩定义的，用于散射，涉及接近阈值的沉重夸克。这就需要计算向前散射幅度的假想部分，最高为三环阶。我们详细讨论了扩展程序和对掌握积分的减少。对于后一种分析结果。我们将结果应用于魅力和底部夸克质量。在后一种情况下，我们计算并包括有限的魅力夸克质量效应。此外，我们确定以四循环顺序转换公式的大$β_0$。对于底部的夸克，我们估计$ \叠加{\ rm MS} $和动力学群众之间转换的不确定性约为15 meV，这是两到三个因子的改进，与两环公式相比。改进的精度对于提取Belle II的Cabibbo-Kobayashi-Maskawa矩阵元素$ | v_ {cb} | $的提取至关重要。
We compute the relation between the pole mass and the kinetic mass of a heavy quark to three loops. Using the known relation between the pole and the $\overline{\rm MS}$ mass we obtain precise conversion relations between the $\overline{\rm MS}$ and kinetic masses. The kinetic mass is defined via the moments of the spectral function for the scattering involving a heavy quark close to threshold. This requires the computation of the imaginary part of a forward scattering amplitude up to three-loop order. We discuss in detail the expansion procedure and the reduction to master integrals. For the latter analytic results are provided. We apply our result both to charm and bottom quark masses. In the latter case we compute and include finite charm quark mass effects. Furthermore, we determine the large-$β_0$ result for the conversion formula at four-loop order. For the bottom quark we estimate the uncertainty in the conversion between the $\overline{\rm MS}$ and kinetic masses to about 15 MeV which is an improvement by a factor two to three as compared to the two-loop formula. The improved precision is crucial for the extraction of the Cabibbo-Kobayashi-Maskawa matrix element $|V_{cb}|$ at Belle II.
