Abstract
The Collins-Soper kernel relates transverse momentum-dependent parton distribution functions (TMDPDFs) at different energy scales. For small parton transverse momentum $q_T\sim \Lambda_\text{QCD}$, this kernel is non-perturbative and can only be determined with controlled uncertainties through experiment or first-principles calculations. This work presents the first exploratory determination of the Collins-Soper kernel using the lattice formulation of Quantum Chromodynamics. In a quenched calculation, the $N_f=0$ kernel is determined at scales in the range 250 MeV $< q_T < 2$ GeV, and an analysis of the remaining systematic uncertainties is undertaken.
Highlights
Understanding the structure of matter has been a defining goal of physics for centuries
Some important aspects of this structure related to the transverse momentum of quarks and gluons in a hadron state are encoded in transverse-momentum-dependent parton distribution functions (TMDPDFs) [1,2,3]
These quantities can be constrained for the proton by Drell-Yan production and semi-inclusive deep inelastic scattering (SIDIS) of electrons off protons; the best current constraints are achieved via global fits to experimental data [4,5,6,7,8,9,10,11,12,13,14,15], with improvements expected in the coming years from measurements at COMPASS [16], the Thomas Jefferson National Accelerator Facility [17], RHIC [18], and an Electron-Ion Collider [19]
Summary
Understanding the structure of matter has been a defining goal of physics for centuries. [23,24,25,26,27], and the large-momentum effective theory (LaMET) framework [28,29] provides a promising pathway toward the determination of TMDPDFs by matching these matrix elements to the desired light-cone correlation functions at large hadron momentum [30,31,32,33,34,35,36,37] [32,33] how this approach may be used to extract the Collins-Soper kernel nonperturbatively from computations of matrix elements of nonlocal quark bilinear operators with staple-shaped Wilson lines This approach is implemented numerically for the first time, in a proof-of-principle calculation in quenched QCD. IV outlines the requirements for a fully controlled calculation of the Collins-Soper kernel to be achieved by this method
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