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.
@article{arxiv.2204.00200,
title = {Nonperturbative Determination of Collins-Soper Kernel from Quasi Transverse-Momentum Dependent Wave Functions},
author = {Min-Huan Chu and Zhi-Fu Deng and Jun Hua and Xiangdong Ji and Andreas Schäfer and Yushan Su and Peng Sun and Wei Wang and Yi-Bo Yang and Jun Zeng and Jialu Zhang and Jian-Hui Zhang and Qi-An Zhang},
journal= {arXiv preprint arXiv:2204.00200},
year = {2022}
}