Renormalization of twist-two operators and four-loop splitting functions in QCD

Abstract

The scale evolution of parton distribution functions is governed by the splitting functions. One of the most efficient methods is to extract splitting functions via the computations of off-shell operator matrix elements, where the physical twist-two operators mix with some unknown gaugevariant operators. We proposed a new method to systematically extract the counterterm Feynman rules resulting from those gauge-variant operators. As a first application of the new method, we rederived the three-loop singlet unpolarized splitting functions. As another application, we obtained a new result for the four-loop pure-singlet splitting functions with two closed fermionic loops. We also presented a new result for the 𝑁 𝑓 𝐶 3 𝐹 contribution to the four-loop non-singlet splitting function, where the gauge-variant operators are absent.