Podolsky propagator in the gap and bound-state equations

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 spacelike 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.

Automated summary

The research proposes a model for the massive gluon propagator that accurately reproduces mass and weak decay constants of pi, K, and eta(c) in excellent agreement with experimental values, while reasonably describing D and D-s. The simplicity of this effective interaction has the potential for useful phenomenological applications and calculations in Minkowski space.