The color force acting on a quark in the pion and nucleon

TL;DR

This paper investigates the color Lorentz force acting on quarks within pions and nucleons using the instanton liquid model, linking it to form factors and comparing with lattice QCD results.

Contribution

It explicitly derives form factors related to the color Lorentz force in light hadrons within the instanton liquid model, including instanton molecules, and connects them to gravitational and transversity form factors.

Findings

Color force distributions in pions and nucleons are derived.

Results for nucleons agree with recent lattice QCD data.

Instanton molecules significantly influence the non-perturbative color force.

Abstract

In the Operator Product Expansion (OPE) of hard scattering amplitudes, the twist-3 operators describe local colored Lorentz forces acting on a quark, thereby providing a measure of the strength of the gluon fields. Its value is directly accessible from the nucleon twist-3 polarized $g_2$-parton distribution function. In the semiclassical (instanton-based) QCD vacuum models, the leading non-perturbative contribution stems from correlated instanton-anti-instanton pairs, or molecules. We analyze the magnitude of the color force on a struck quark in light hadrons (pion and nucleon), in the context of the instanton liquid model (ILM). We derive explicitly the pertinent form factors associated with the color Lorentz force and show that they are intimately related to the pertinent hadronic gravitational and transversity form factors. Using the ILM enhanced by molecules, we detail the ensuing colored force distribution in the transverse plane for the luminal pions and nucleons. The results for the nucleons are in good agreement with those recently reported from a lattice collaboration.