Quark Transverse Parton Distribution at the Next-to-Next-to-Next-to-Leading Order

Ming-xing Luo, Tong-Zhi Yang, Hua Xing Zhu, and Yu Jiao Zhu

We report a calculation of the perturbative matching coefficients for the transverse-momentum-dependent parton distribution functions for quark at the next-to-next-to-next-to-leading order in QCD, which involves calculation of nonstandard Feynman integrals with rapidity divergence. We introduce a set of generalized integration-by-parts equations, which allows an algorithmic evaluation of such integrals using the machinery of modern Feynman integral calculation.

Phys. Rev. Lett. 124, 092001 – Published 5 March 2020

The published article is available at https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.124.092001