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Color force acting on a quark in the pion and nucleon

Wei-Yang Liu*, Edward Shuryak†, and Ismail Zahed‡

  • Center for Nuclear Theory, Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794-3800, USA

  • *Contact author: wei-yang.liu@stonybrook.edu
  • †Contact author: edward.shuryak@stonybrook.edu
  • ‡Contact author: ismail.zahed@stonybrook.edu
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Phys. Rev. D 113, 114007 – Published 5 June, 2026

DOI: https://doi.org/10.1103/j3lv-wgrl

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 g2-parton distribution function. In the semiclassical (instanton-based) QCD vacuum models, the leading nonperturbative contribution stems from correlated instanton-antiinstanton 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.

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Phys. Rev. D 113, 114007– Published 5 June, 2026
  • Received 3 December 2025
  • Accepted 24 April 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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