In this talk, we report the first complete results of the four-loop non-singlet splitting functions in QCD. Splitting functions govern the scale evolution of parton distribution functions, which enter the theoretical predictions for all physical processes at high-energy hadron colliders. According to their flavor group structure, splitting functions are classified into non-singlet and singlet components. In the non-singlet case, a direct multiplicative renormalization formula applies, leaving the integration-by-parts (IBP) reduction and the solution of master integrals as the primary bottleneck. After many years of effort, we obtained recently the first complete four-loop non-singlet splitting functions. The results are in fully analytic form. We also report on progress in the singlet case, where twist-two operators mix with un-physical operators. We present a systematic procedure to derive the counterterm Feynman rules for these un-physical operators, which provides a path toward the complete four-loop singlet splitting functions.
Biography: Tongzhi Yang is a faculty member at the Institute of Quantum Matter, South China Normal University since July 2025. He received his BSc from Zhejiang University in 2015 and his PhD from the same institution in 2020. His research focuses on perturbative QCD, with recent emphasis on the development of integration-by-parts techniques and their applications to compute anomalous dimensions and Wilson coefficients relevant to collider phenomenology. Prior to his current position, he was a postdoctoral researcher at the University of Zurich from 2020 to 2025.
Prof. Huaxing Zhu