Non-perturbative Propagators, Running Coupling and Dynamical Mass Generation in Ghost-Antighost Symmetric Gauges in QCD

TL;DR

This paper provides non-perturbative solutions for QCD propagators and the running coupling using Dyson-Schwinger equations, showing agreement with lattice results and insights into confinement and mass generation.

Contribution

It introduces a truncated Dyson-Schwinger framework with ansaetze that produce renormalization point independent results, aligning with lattice data and exploring boundary condition effects.

Findings

Gluon propagator vanishes weakly at small momenta

Ghost propagator is infrared singular, supporting confinement criteria

Running coupling has an infrared fixed point at alpha(0)=8.92/N_c

Abstract

We present approximate non-perturbative solutions for the propagators as well as the running coupling of QCD from a coupled system of renormalised, truncated Dyson--Schwinger equations. We employ ansaetze for the dressed vertices such that the running coupling and the quark mass function are independent of the renormalisation point. Our solutions are in good agreement with the results of recent lattice calculations. We find a weakly vanishing gluon propagator at small momenta and an infrared singular ghost propagator in agreement with Zwanziger's horizon condition and the Kugo-Ojima confinement criterion. The running coupling possesses an infrared fixed point at alpha(0) = 8.92/N_c. To investigate the influence of boundary conditions on the propagators we solved the ghost and gluon DSEs also on a four-torus. Our results show typical finite volume effects but are still close to the continuum solutions for sufficiently large volumes. For the quark propagator we find dynamically generated quark masses that agree well with phenomenological values. The effects of unquenching the system are found to be small. In particular the infrared behaviour of the ghost and gluon dressing functions found in pure Yang-Mills theory is almost unchanged as long as the number of light flavors is smaller than four.