Intrinsic glue and Wilson lines within dressed quarks

Caroline S. R. Costa,Peter C. Tandy,Ian C. Cloët,Adam Freese,Bruno El-Bennich,Gastão Krein

doi:10.1103/physrevc.104.045201

Abstract

We construct a quark target model (QTM) to incorporate intrinsic glue into effective low-energy models of QCD, which often contain only quark degrees of freedom. This method guarantees the gauge invariance of observables order by order in the strong coupling. The quark and gluon PDFs for the dressed quarks are obtained in the QTM at leading order. We demonstrate gauge invariance of the results by comparing both covariant and light cone gauges, with the former including an explicit Wilson line contribution. A key finding is that in covariant gauges the Wilson line can carry a significant amount of the light cone momentum. With coupling strength ${\ensuremath{\alpha}}_{s}=0.5$ and dressed quark mass ${M}_{q}=0.4\phantom{\rule{4pt}{0ex}}\mathrm{GeV}$, we find quark and gluon momentum fractions of ${\ensuremath{\langle}x\ensuremath{\rangle}}_{q}=0.81$ and ${\ensuremath{\langle}x\ensuremath{\rangle}}_{g}=0.19$, where the Wilson line contribution to the quark momentum fraction is $\ensuremath{-}0.18$. We use the on-shell renormalization scheme and find that at one loop this Wilson line contribution does not depend on the covariant gauge but does vanish in light cone gauge as expected. This result demonstrates that it is crucial to account for Wilson line contributions when calculating quantum correlation functions in covariant gauges. We also consider the impact of a gluon mass using the gauge invariant formalism proposed by Cornwall, and combine these QTM results with two quark-level models to obtain quark and gluon PDFs for the pion.

Highlights

Many of the open mysteries in nuclear physics—such as the origin of hadron mass and the distribution of spin in the proton—can be addressed through partonic correlation functions, including parton distribution functions (PDFs), transverse momentum distributions (TMDs), and generalized parton distributions (GPDs)
Gauge invariance of the results was demonstrated by explicitly calculating the PDFs in both covariant and light cone gauges
The quark target PDFs were combined with a Nambu– Jona-Lasinio (NJL) model result and a phenomenological parametrization for the pion PDF via a convolution formalism, and the resulting quark and gluon PDFs were evolved via next-to-leading order (NLO) DGLAP equations and compared to empirical and phenomenological results

Summary

Introduction

Many of the open mysteries in nuclear physics—such as the origin of hadron mass and the distribution of spin in the proton—can be addressed through partonic correlation functions, including parton distribution functions (PDFs), transverse momentum distributions (TMDs), and generalized parton distributions (GPDs). Calculating these distributions exactly from quantum chromodynamics (QCD) remains challenging, where even in lattice QCD approximation schemes are needed [1,2,3,4,5,6,7]. The primary emphasis of model calculations has so far been on calculating various quark correlation functions, with

Objectives

Results

Conclusion