We evaluate the Collins-Soper kernel and the reduced soft function in lattice QCD, incorporating O(αs) matching corrections. The calculation relies on the evaluation of the quasi-transverse momentum-dependent wave function with asymmetric staple-shaped quark bilinear operators and four-point meson form factors. These quantities are computed non-perturbatively using two Nf=2+1+1 twisted-mass fermion ensembles with the same lattice spacing of a=0.093 fm: the first ensemble has a lattice size of 243×48 and a pion mass of 346 MeV; the second one has a lattice size of 323×64 and a pion mass of 261 MeV. The Collins-Soper kernel and the soft function are needed for the determination of the transverse momentum-dependent parton distribution functions.
@article{arxiv.2509.26316,
title = {Collins-Soper Kernel and Reduced Soft Function in Lattice QCD},
author = {Constantia Alexandrou and Simone Bacchio and Krzysztof Cichy and Martha Constantinou and Aniket Sen and Gregoris Spanoudes and Fernanda Steffens and Jacopo Tarello},
journal= {arXiv preprint arXiv:2509.26316},
year = {2025}
}