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.
Highlights
Mandelstam’s seminal work [1] established that the rainbow-ladder truncation of the gap and bound-state equations is an adequate approximation to describe dynamical chiral symmetry breaking (DCSB) [2,3,4,5,6,7,8,9,10,11,12] in quantum chromodynamics (QCD)
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 DysonSchwinger equation
In this work we propose a model that describes effectively a massive gluon interaction in the infrared region, where we are inspired by the functional structure of generalized quantum electrodynamics (GQED) proposed long ago by Podolsky [50,51]
Summary
Mandelstam’s seminal work [1] established that the rainbow-ladder truncation of the gap and bound-state equations is an adequate approximation to describe dynamical chiral symmetry breaking (DCSB) [2,3,4,5,6,7,8,9,10,11,12] in quantum chromodynamics (QCD). In this work we propose a model that describes effectively a massive gluon interaction in the infrared region, where we are inspired by the functional structure of generalized quantum electrodynamics (GQED) proposed long ago by Podolsky [50,51]. The goal was to eliminate the infinities that arise in higher-order corrections of point charges and the associated coupling Since this extension of the Lagrangian preserves gauge invariance in a consistent treatment [52,53], GQED has come to be viewed more as a prototype of a theory that contains massless as well as massive photons that do not break gauge invariance.
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