Renormalization of twist-two operators in covariant gauge to three loops in QCD

by Dr 通智 杨 (苏黎世联邦理工大学)

Monday 17 Jul 2023, 10:30 → 11:30 Asia/Shanghai

B105 (CHEP)

Parton densities are crucial for making quantitative predictions in all high-energy hadron collider processes. Typically, the parton densities at an initial energy scale are determined either by fitting them to experimental data or from lattice QCD, and then by the DGLAP evolution equation, the parton densities at other scales can be fixed. The DGLAP evolution kernel, also known as splitting functions, plays a crucial role in the evolution process. To consistently determine N3LO parton densities, which are becoming increasingly important with the inclusion of several matching coefficients at N3LO, it is necessary to know the 4-loop splitting functions. To make the computation possible and save computational resources, finding an efficient method to compute 4-loop splitting functions is of great importance. The method of computing the off-shell matrix elements with a twist-two operator insertion is among the most efficient techniques. Nonetheless, the off-shell nature of external gluons poses renormalization issues related to gauge invariance. Addressing these concerns entails identifying all gauge-variant operators that mix with the physical twist-two operators. 
We recently introduced a new framework in which we systematically extract all gauge-variant operator Feynman rules. We applied this framework to rederive the unpolarized singlet splitting functions to the three-loop order, and we demonstrated that our approach is valid to all loop orders. Furthermore, our framework enables the derivation of all-n operator Feynman rules, which makes the calculation of splitting functions with all-n dependence easier. 
We also successfully applied the same framework to derive four-loop pure singlet splitting functions with two fermionic loops (nf^2) and obtain, for the first time, the four-loop nf^2 pure singlet splitting functions with all-n dependence. Following the same framework, it is promising to finish the complete four-loop splitting functions.

Bio:Tongzhi Yang graduated from Zhejiang University in 2015 and obtained his Ph.D. at the same university in 2020 under the supervision of Mingxing Luo and Huaxing Zhu. He is currently a postdoctoral researcher at the University of Zurich, where he focuses on advancing high-precision predictions in perturbative Quantum Chromodynamics (QCD). His main research accomplishments include: 1. Derive for the first time the matching kernels for N3LO transverse momentum-dependent beam functions and fragmentation functions; 2. Apply for the first time the qT slicing method to derive the fully differential Drell-Yan production at N3LO in QCD; 3. Obtain the state-of-art fixed order analytic predictions for energy correlators; 4. Develop a consistent framework to allow an efficient derivation of higher-order splitting functions. 

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