Unpolarized quark and gluon TMD PDFs and FFs at N3LO
Ming-xing Luo, Tong-Zhi Yang, Hua Xing Zhu, Yu Jiao Zhu
Abstract
A bstract In this paper we calculate analytically the perturbative matching coefficients for unpolarized quark and gluon Transverse-Momentum-Dependent (TMD) Parton Distribution Functions (PDFs) and Fragmentation Functions (FFs) through Next-to-Next-to-Next-to-Leading Order (N 3 LO) in QCD. The N 3 LO TMD PDFs are calculated by solving a system of differential equation of Feynman and phase space integrals. The TMD FFs are obtained by analytic continuation from space-like quantities to time-like quantities, taking into account the probability interpretation of TMD PDFs and FFs properly. The coefficient functions for TMD FFs exhibit double logarithmic enhancement at small momentum fraction z . We resum such logarithmic terms to the third order in the expansion of α s . Our results constitute important ingredients for precision determination of TMD PDFs and FFs in current and future experiments.