标题： SM中希格斯自耦合的$β$-函数的QCD诱导的四环贡献及真空稳定性 显示英文标题

标题： Leading QCD-induced four-loop contributions to the $β$-function of the Higgs self-coupling in the SM and vacuum stability

摘要： 我们给出了标准模型中希格斯自耦合$\lambda$的四环级$\beta$-函数的主导顶夸克-宇称和QCD贡献的解析结果，即部分$\propto y_t^4 g_s^6$独立确认了文献[1]中的一个结果。我们还给出了希格斯场的异常维度的贡献$\propto y_t^2 g_s^6$以及顶夸克-宇称$\beta$-函数中的项$\propto y_t g_s^8$，这些项也可以从顶夸克质量的异常维度推导出来。 我们比较了结果与纯QCD中两个和四个标量电流关联函数的RG函数，并发现QCD真空能量的反常维度$\gamma_0$与出现在两个标量电流关联函数的RG方程中的反常维度$\gamma_m^{SS}$之间存在新的关系。 结合最近计算的顶-Yukawa和QCD对$\beta_{g_s}$的贡献 [2,3]，此处提出的$\beta$-函数构成了希格斯自耦合演化的主要四环贡献。 还给出了这些项在顶夸克质量尺度上的数值估计，并分析了对$\lambda$演化至普朗克尺度和真空稳定性问题的影响。 显示英文摘要

摘要： We present analytical results for the leading top-Yukawa and QCD contribution to the $\beta$-function for the Higgs self-coupling $\lambda$ of the Standard Model at four-loop level, namely the part $\propto y_t^4 g_s^6$ independently confirming a result given in [1]. We also give the contribution $\propto y_t^2 g_s^6$ of the anomalous dimension of the Higgs field as well as the terms $\propto y_t g_s^8$ to the top-Yukawa $\beta$-function which can also be derived from the anomalous dimension of the top quark mass. We compare the results with the RG functions of the correlators of two and four scalar currents in pure QCD and find a new relation between the anomalous dimension $\gamma_0$ of the QCD vacuum energy and the anomalous dimension $\gamma_m^{SS}$ appearing in the RG equation of the correlator of two scalar currents. Together with the recently computed top-Yukawa and QCD contributions to $\beta_{g_s}$ [2,3] the $\beta$-functions presented here constitute the leading four-loop contributions to the evolution of the Higgs self-coupling. A numerical estimate of these terms at the scale of the top-quark mass is presented as well as an analysis of the impact on the evolution of $\lambda$ up to the Planck scale and the vacuum stability problem.