Just how different are SU(2) and SU(3) Landau-gauge propagators in the IR regime?

TL;DR

This study compares Landau-gauge gluon and ghost propagators in SU(2) and SU(3) Yang-Mills theories, finding their infrared behaviors are quantitatively similar, supporting the idea of gauge group independence in the IR regime.

Contribution

First comparative lattice study of SU(2) and SU(3) Landau-gauge propagators with equivalent parameters, revealing their IR behaviors are essentially the same.

Findings

Good agreement between SU(2) and SU(3) propagators in IR region

Infrared behavior appears independent of gauge group SU(N_c)

Supports Schwinger-Dyson predictions of IR independence

Abstract

The infrared behavior of gluon and ghost propagators in Yang-Mills theories is of central importance for understanding quark and gluon confinement in QCD. While simulations of pure SU(3) gauge theory correspond to the physical case in the limit of infinite quark mass, the SU(2) case (i.e. pure two-color QCD) is usually employed as a simplification, in the hope that qualitative features be the same as for the SU(3) case. Here we carry out the first comparative study of lattice (Landau) propagators for these two gauge groups. Our data were especially produced with equivalent lattice parameters in order to allow a careful comparison of the two cases. We find very good agreement between SU(2) ans SU(3) propagators, showing that in the IR limit the equivalence of the two cases is quantitative, at least down to about 1 GeV. Our results suggest that the infrared behavior of these propagators is independent of the gauge group SU(N_c), as predicted by Schwinger-Dyson equations.