Joint INFN-UNIMI-UNIMIB Pheno Seminars

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

by Tongzhi Yang

Aula Marchetti (U1-07) (University of Milan-Bicocca)

Aula Marchetti (U1-07)

University of Milan-Bicocca

The LHC programs, along with the upcoming collider initiatives such as the Electron-Ion Collider, are positioned to generate precise experimental data crucial for advancing our understanding of proton structures. The proton structures are described by parton distribution functions (PDFs), which have been known to approximate N3LO accuracy. However, to achieve the full N3LO PDFs, it is necessary to know the complete four-loop splitting functions—a task fraught with complexity. Developing efficient methods for computing these functions is of great importance. One of the most efficient techniques involves computing off-shell matrix elements with a twist-two operator insertion. Nonetheless, the off-shell nature of external gluons poses renormalization issues related to gauge invariance. Addressing these concerns entails identifying all non-physical operators that mix with the physical twist-two operators. I will present a new framework that allows us to systematically extract the non-physical operator Feynman rules with all-N dependence. We have applied this framework to re-derive the three-loop singlet splitting functions and demonstrated that the framework is valid to all-loop orders. As a proof of concept, our framework has also successfully yielded state-of-the-art results with certain color structures for four-loop splitting functions in QCD. We compared our full results against the results with fixed moments in the literature and found full agreement.