Determination of the Collins-Soper Kernel from Lattice QCD

Maximilian Schlemmer,Alexey Vladimirov,Christian Zimmermann,Michael Engelhardt,Andreas Schäfer

doi:10.1007/jhep08(2021)004

Abstract

We present lattice results for the non-perturbative Collins-Soper (CS) kernel, which describes the energy-dependence of transverse momentum-dependent parton distributions (TMDs). The CS kernel is extracted from the ratios of first Mellin moments of quasi-TMDs evaluated at different nucleon momenta. The analysis is done with dynamical Nf = 2 + 1 clover fermions for the CLS ensemble H101 (a = 0.0854 fm, mπ = mK = 422 MeV). The computed CS kernel is in good agreement with experimental extractions and previous lattice studies.

Highlights

The CS kernel is a fundamental nonperturbative function that characterizes the QCD vacuum [11]
All these suggestions are based on the measurement of quasi-transverse momentum-dependent parton distributions — the correlation of two quark fields in a hadron wave function connected by a staple-shaped gauge link positioned in a space-like plane
To by-pass this severe complication, we study the first moment of quasi-transverse momentum-dependent parton distributions (qTMDs)

Summary

Introduction

The CS kernel is a fundamental nonperturbative function that characterizes the QCD vacuum [11]. Several ways to extract the CS kernel were suggested within the last years [15,16,17,18] All these suggestions are based on the measurement of quasi-transverse momentum-dependent parton distributions (qTMDs) — the correlation of two quark fields in a hadron wave function connected by a staple-shaped gauge link positioned in a space-like plane. It has been shown that in the regime of large hadron momentum and large staple length, a qTMD is a convolution of a physical TMD, a perturbative coefficient function, and a soft factor. One of the fundamental difficulties in the evaluation of quasi-distributions is the necessity to perform a Fourier transformation into momentum-fraction space (introducing the variable x) This transformation is notoriously ill-defined, already for one-dimensional observables (for a review of recent developments, see [19, 20]), and even more so for qTMDs, where one should respect an entangled hierarchy of several scales.

Results

Discussion

Conclusion