论文标题
未脱光化和两极化的单质量三环厚味操作员矩阵元素$ a_ {gg，q} $和$ΔA_{gg，q} $
The Unpolarized and Polarized Single-Mass Three-Loop Heavy Flavor Operator Matrix Elements $A_{gg,Q}$ and $ΔA_{gg,Q}$
论文作者
论文摘要
我们计算了在非极化和极化情况下计算Gluonic巨大的操作员矩阵元素，即$ a_ {gg，q}（x，μ^2）$和$ΔA__{gg，q}（x，μ^2）$，在三环订单下用于单个质量。这些数量有助于在变化数量方案中匹配Gluon分布。在Larin方案中计算了偏振算子矩阵元件。这些运算符矩阵元素包含有限的二项式和逆二项式总和，中的$ n $空间和迭代的积分在动量分数$ x $ -space中的平方根值字母上的迭代积分。我们得出了从偶数或奇数梅尔蛋白矩的分析延续到复杂平面的必要分析关系，以动量分数$ x $ - 空间呈现分析表达式，并得出数值结果。目前的结果将单质和双质量变化数量方案均完成了Gluon过渡矩阵元件，即三环阶。
We calculate the gluonic massive operator matrix elements in the unpolarized and polarized cases, $A_{gg,Q}(x,μ^2)$ and $ΔA_{gg,Q}(x,μ^2)$, at three-loop order for a single mass. These quantities contribute to the matching of the gluon distribution in the variable flavor number scheme. The polarized operator matrix element is calculated in the Larin scheme. These operator matrix elements contain finite binomial and inverse binomial sums in Mellin $N$-space and iterated integrals over square root-valued alphabets in momentum fraction $x$-space. We derive the necessary analytic relations for the analytic continuation of these quantities from the even or odd Mellin moments into the complex plane, present analytic expressions in momentum fraction $x$-space and derive numerical results. The present results complete the gluon transition matrix elements both of the single- and double-mass variable flavor number scheme to three-loop order.
