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QED photon-fermion vertex from its Dyson-Schwinger equation in 4D: The full vertex, the transverse form factors, and the perturbative solution

Authors: Oliveira, O.

Ref.: Phys. Rev. D 112(7), 076009 (2025)

Abstract: We investigate the Dyson-Schwinger equation for the photon-fermion one-particle irreducible vertex in QEDinlinear covariant gauges. The longitudinal component of this vertex is described using the Ball-Chiu basis, while its transverse part is expressed with the Kızılersu-Reenders-Pennington basis. Combining the vertex Ward-Takahashi identity with the vertex equation, we derive a set of exact, nonlinear integral equations governing the transverse vertex. These equations hold for any linear covariant gauge and must be solved self-consistently. We discuss several approximations to the exact quations, generalizing results previously obtained at the perturbative one-loop level. Various kinematical configurations are also examined. Furthermore, we compute the perturbative solution of the transverse vertex Dyson-Schwinger equations for all transverse form factors and derive their perturbative asymptotic expressions.

DOI: 10.1103/cvsn-k4q5

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