Lattice QCD calculation of the Collins-Soper kernel from quasi TMDPDFs

TL;DR

This paper reports a lattice QCD calculation of the nonperturbative Collins-Soper kernel, highlighting the challenges and uncertainties in extracting it due to power corrections and matching issues.

Contribution

It provides a first lattice QCD determination of the Collins-Soper kernel at moderate transverse momenta, emphasizing the importance of systematic uncertainties.

Findings

Different extraction methods yield significantly different results.

Power corrections and perturbative matching are non-negligible.

Uncertainty estimates vary widely depending on the approach.

Abstract

This work presents a lattice quantum chromodynamics (QCD) calculation of the nonperturbative Collins-Soper kernel, which describes the rapidity evolution of quark transverse-momentum-dependent parton distribution functions. The kernel is extracted at transverse momentum scales in the range 400 MeV $< q_T < 1.7$ GeV in a calculation with dynamical fermions and quark masses corresponding to a larger-than-physical pion mass, $m_\pi=538(1)$ MeV. It is found that different approaches to extract the Collins-Soper kernel from the same underlying lattice QCD matrix elements yield significantly different results and uncertainty estimates, revealing that power corrections, such as those associated with higher-twist effects, and perturbative matching between quasi and light-cone beam functions, cannot be neglected.