标题： 量子色动力学中味非奇异性分裂函数的四圈贡献——费米子贡献 显示英文标题

标题： Flavour Non-Singlet Splitting Functions at Four Loops in QCD -- The Fermionic Contributions

摘要： 我们已经确定了四阶$n_f$贡献，这些贡献影响着规范量子色动力学中具有$n_f$轻子味的强子夸克分布的所有味差异演化的两个分裂函数。 这些函数的解析表达式既以广义规范群为基础，又分别在 Mellin$N$空间和动量分数$x$空间中呈现。 在小的$x$极限下会出现双重对数项，但两种分裂函数在小的$x$情况下的增长被限制在极小的$x$值范围内，即$x \lesssim 10^{-6}$。 大$x$极限包含了四圈夸克虚异常维度的$n_f$部分。 利用这一结果，我们还得到了相应胶子量在大类包含性可观测量（包括胶子融合产生希格斯玻色子）中的$n_f$贡献以及由软胶子发射导致的所有阈值增强对数。 显示英文摘要

摘要： We have determined the fourth-order $n_f$ contributions to the two splitting functions governing the evolution of all flavor differences of quark distributions of hadrons in perturbative quantum chromodynamics with $n_f$ light flavors. The analytic forms of these functions are presented in both Mellin $N$-space and momentum-fraction $x$-space for a general gauge group. In the small-$x$ limit double logarithms occur, but the small-$x$ rise of both splitting functions is confined to extremely small $x$-values, $x \lesssim 10^{-6}$. The large-$x$ limit includes the $n_f$-part of the four-loop quark virtual anomalous dimension. Using this result we obtain also the $n_f$ contributions to the corresponding gluonic quantity and the complete threshold-enhanced logarithms from soft-gluon emission for a large class of inclusive observables, including Higgs boson production in gluon-gluon fusion.