Nonperturbative Determination of Collins-Soper Kernel from Quasi Transverse-Momentum Dependent Wave Functions

TL;DR

This paper presents a lattice QCD calculation of the Collins-Soper kernel, essential for understanding the rapidity evolution of TMD distributions, using large-momentum effective theory and one-loop matching.

Contribution

It provides the first lattice-based determination of the Collins-Soper kernel at one-loop accuracy with systematic uncertainty analysis.

Findings

Determined the Collins-Soper kernel up to 0.6 fm transverse separation.

Analyzed systematic uncertainties from operator mixing and scale dependence.

Potential to compute soft functions and other TMD quantities at one-loop accuracy.

Abstract

In the framework of large-momentum effective theory at one-loop matching accuracy, we perform a lattice calculation of the Collins-Soper kernel which governs the rapidity evolution of transverse-momentum-dependent (TMD) distributions. We first obtain the quasi TMD wave functions at three different meson momenta on a lattice with valence clover quarks on a dynamical HISQ sea and lattice spacing $a=0.12$~fm from MILC, and renormalize the pertinent linear divergences using Wilson loops. Through one-loop matching to the light-cone wave functions, we determine the Collins-Soper kernel with transverse separation up to 0.6~fm. We study the systematic uncertainties from operator mixing and scale dependence, as well as the impact from higher power corrections. Our results potentially allow for a determination of the soft function and other transverse-momentum dependent quantities at one-loop accuracy.