论文标题
$ z_m^{\ rm OS} $和$ z_2^{\ rm OS} $的确切结果，带有两个质量尺度，最多三个循环
Exact results for $Z_m^{\rm OS}$ and $Z_2^{\rm OS}$ with two mass scales and up to three loops
论文作者
论文摘要
我们考虑壳体质量和波函数重量化常数$ z_m^{\ rm OS} $和$ z_2^{\ rm OS} $最高三环订单，允许第二个非零夸克质量。我们从谐波粒子和迭代积分方面获得了分析结果，并带有其他字母$ \ sqrt {1-τ^2} $和$ \ sqrt {1-τ^2}/τ$，从参考文献中扩展了发现。 [1]仅显示数值表达式。此外，我们提供订单$ {\ cal o}（ε^2）$和$ {\ cal o}（ε）$在两环和三环订单处，这对于未来的四环计算是至关重要的。零质量，相等质量和大质量案例周围扩展的紧凑结果允许快速进行高精度的数值评估。
We consider the on-shell mass and wave function renormalization constants $Z_m^{\rm OS}$ and $Z_2^{\rm OS}$ up to three-loop order allowing for a second non-zero quark mass. We obtain analytic results in terms of harmonic polylogarithms and iterated integrals with the additional letters $\sqrt{1-τ^2}$ and $\sqrt{1-τ^2}/τ$ which extends the findings from Ref. [1] where only numerical expressions are presented. Furthermore, we provide terms of order ${\cal O}(ε^2)$ and ${\cal O}(ε)$ at two- and three-loop order which are crucial ingrediants for a future four-loop calculation. Compact results for the expansions around the zero-mass, equal-mass and large-mass cases allow for a fast high-precision numerical evaluation.
