Non-perturbative Collins-Soper kernel: Chiral quarks and Coulomb-gauge-fixed quasi-TMD

TL;DR

This paper reports the first lattice QCD calculation of the non-perturbative Collins-Soper kernel using Coulomb-gauge-fixed quasi-TMDs and chiral fermions, providing insights into TMD evolution at various transverse separations.

Contribution

It introduces a novel lattice approach to compute the CS kernel non-perturbatively with Coulomb gauge and chiral fermions, extending the accessible transverse separation range.

Findings

Good agreement with perturbative predictions at small separations

Non-perturbative kernel favors certain global fits at larger separations

Slower decay of signals due to absence of Wilson lines

Abstract

We present the first lattice QCD calculation of the rapidity anomalous dimension of transverse-momentum-dependent distributions (TMDs), i.e. the Collins-Soper (CS) kernel, employing the recently proposed Coulomb-gauge-fixed quasi-TMD formalism as well as a chiral-symmetry preserving lattice discretization. This unitary lattice calculation is conducted using the domain wall fermion discretization scheme, a fine lattice spacing of approximately 0.08 fm, and physical values for light and strange quark masses. The CS kernel is determined analyzing the ratios of pion quasi-TMD wave functions (quasi-TMDWFs) at next-to-leading logarithmic (NLL) perturbative accuracy. Thanks to the absence of Wilson-lines, the Coulomb-gauge-fixed quasi-TMDWF demonstrates a remarkably slower decay of signals with increasing quark separations. This allows us to access the non-perturbative CS kernel up to transverse separations of 1 fm. For small transverse separations, our results agree well with perturbative predictions. At larger transverse separations, our non-perturbative CS kernel clearly favors certain global fits.