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 $q_T\sim {\mathrm{\Lambda }}_{\mathrm{QCD}}$ 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.

• Received 12 November 2018

DOI:https://doi.org/10.1103/PhysRevD.99.034505

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Published by the American Physical Society