Flavor Nonsinglet Splitting Functions at Four Loops in QCD: Fermionic Contributions
B. A. Kniehl, S. Moch, V.N. Velizhanin, A. Vogt
Abstract
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≲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.