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Quark gap equation in light-cone gauge

Roberto Correa da Silveira1, Fernando E. Serna2, and Bruno El-Bennich1,3

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Phys. Rev. D 112, 096015 – Published 12 November, 2025

DOI: https://doi.org/10.1103/cr6p-p5s2

Abstract

An exploratory nonperturbative calculation of the quark propagator in light-cone gauge is motivated by distribution amplitudes whose definition implies a Wilson line. The latter serves to preserve the gauge invariance of the hadronic amplitudes and becomes trivial in light-cone gauge. To that end, we explore the corresponding Dyson-Schwinger equation in its leading truncation and with a dressed vertex derived from a Ward identity in light-cone gauge. The quark’s mass and wave renormalization functions are found to depend on the orientation of the quark momentum relative to the lightlike four-vector below 1 GeV, which expresses the light-cone gauge dependence of the propagator, while a third, complex-valued amplitude exhibits little dependence on that orientation and vanishes in the quark’s rest frame.

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Phys. Rev. D 112, 096015– Published 12 November, 2025
  • Received 7 November 2024
  • Accepted 17 October 2025
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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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