Lattice QCD Green's functions in maximally Abelian gauge: infrared Abelian dominance and the quark sector

TL;DR

This study uses lattice QCD simulations to analyze the infrared behavior of quark and gluon propagators in a specific gauge, providing evidence for Abelian dominance in the quark sector.

Contribution

It demonstrates that in the maximally Abelian gauge, diagonal gluons dominate infrared dynamics, supporting the Abelian dominance hypothesis in lattice QCD.

Findings

Infrared enhancement of diagonal gluon propagator

Off-diagonal gluons have minimal impact on quark dynamics

Diagonal gluon background reproduces Landau gauge quark propagator

Abstract

On lattice gauge field configurations with 2+1 dynamical quark flavors, we investigate the momentum space quark and gluon propagators in the combined maximally Abelian plus $U(1)_3\times U(1)_8$ Landau gauge. We extract the gluon fields from the lattice link variables and study the diagonal and off-diagonal gluon propagators. We find that the infrared region of the transverse diagonal gluon propagator is strongly enhanced compared to the off-diagonal propagator. The Dirac operator from the Asqtad action is inverted on the diagonal and off-diagonal gluon backgrounds separately. In agreement with the hypothesis of infrared Abelian dominance, we find that the off-diagonal gluon background hardly gives rise to any non-trivial quark dynamics while the quark propagator from the diagonal gluon background closely resembles its Landau gauge counterpart.