Unpolarized quark and gluon TMD PDFs and FFs at N3LO

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 ((NLO)-L-3) in QCD. The (NLO)-L-3 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 alpha(s). Our results constitute important ingredients for precision determination of TMD PDFs and FFs in current and future experiments.

Automated summary

In this paper, we analytically calculate 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 ((NLO)-L-3) in QCD. Our results provide important ingredients for the precision determination of TMD PDFs and FFs in current and future experiments.