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arXiv · 1811.00026

Determining the Nonperturbative Collins-Soper Kernel From Lattice QCD

Markus A. Ebert·Iain W. Stewart·Yong Zhao
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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 $q_T \sim \Lambda_\mathrm{QCD}$ 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.

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Markus A. Ebert, Iain W. Stewart, Yong Zhao. 2018-10-31. Determining the Nonperturbative Collins-Soper Kernel From Lattice QCD. https://doi.org/10.1103/physrevd.99.034505

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