Determining the nonperturbative Collins-Soper kernel from lattice QCD

Abstract

At small transverse momentum ${q}_{T}$, transverse-momentum dependent parton distribution functions (TMDPDFs) arise as genuinely nonperturbative objects that describe Drell-Yan like processes in hadron collisions as well as semi-inclusive deep-inelastic scattering. TMDPDFs naturally depend on the hadron momentum, and the associated evolution is determined by the Collins-Soper equation. For ${q}_{T}\ensuremath{\sim}{\mathrm{\ensuremath{\Lambda}}}_{\mathrm{QCD}}$ the corresponding evolution kernel (or anomalous dimension) is nonperturbative and must be determined as an independent ingredient in order to relate TMDPDFs at different scales. We propose a method to extract this kernel using lattice QCD and the large-momentum effective theory, where the physical TMD correlation involving light-like paths is approximated by a quasi-TMDPDF, defined using equal-time correlation functions with a large-momentum hadron state. The kernel is determined from a ratio of quasi-TMDPDFs extracted at different hadron momenta.