The Podolsky propagator in gap and bound-state equations

TL;DR

This paper introduces a gauge-invariant, analytically simple model for the gluon propagator based on the Podolsky formalism, successfully describing meson properties and confining interactions within the Dyson-Schwinger and Bethe-Salpeter framework.

Contribution

It proposes a novel, analytically tractable gluon propagator model using Podolsky's formalism that reproduces key features of strong-interaction phenomenology.

Findings

Accurately predicts meson masses and decay constants

Provides a confining interaction model with simple analytical properties

Facilitates calculations in Minkowski space

Abstract

Based on the Generalized Quantum Electrodynamics expression for the Podolsky propagator, which preserves gauge invariance for massive photons, we propose a model for the massive gluon propagator that reproduces well-known features of established strong-interaction models in the framework of the Dyson-Schwinger equation. By adjusting the Podolsky mass and the coupling strength we thus construct a model with simple analytical properties known from perturbative theory, yet well suited to describe a confining interaction. We obtain solutions of the Dyson-Schwinger equation for the quark at space-like momenta on the real axis as well as on the complex plane and solving the bound-state problem with the Bethe-Salpeter equation yields masses and weak decay constants of the $\pi, K$ and $\eta_c$ in excellent agreement with experimental values, while the $D$ and $D_s$ are reasonably well described. The analytical simplicity of this effective interaction has the potential to be useful for phenomenological applications and may facilitate calculations in Minkowski space.