Towards splitting functions at four-loop order in QCD

In this talk, we provided an update on our progress in computing four-loop splitting functions. The computations are based on off-shell operator matrix elements, where under renormalization physical twist-two operators mix with previously unidentified gauge-variant operators. We presented a method to systematically extract the counterterm Feynman rules resulting from those gauge-variant operators. Then we applied the Feynman rules to derive the full three-loop splitting functions as well as certain four-loop splitting functions with specific color structures.