Transverse momentum dependent distribution functions in the threshold limit

Abstract

We apply the joint threshold and transverse momentum dependent (TMD) factorization theorem to introduce new threshold-TMD distribution functions, including threshold-TMD parton distribution functions (PDFs) and fragmentation functions (FFs). We apply Soft-Collinear Effective Theory and renormalization group methods to carry out QCD evolution for both threshold-TMD PDFs and FFs. We show the universality of threshold-TMD functions among three standard processes, i.e. the Drell-Yan production in $pp$ collisions, semi-inclusive deep-inelastic scattering and back-to-back two hadron production in $e^+e^-$ collisions. In the end, we present the numerical predictions for different threshold-TMD functions and also transverse momentum distributions at $pp$, $ep$, and $e^+e^-$ collisions.