Unpolarized Quark and Gluon TMD PDFs and FFs at N$^3$LO

Understand

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 $z$.