Running mass, effective energy and confinement: the lattice quark propagator in Coulomb gauge

TL;DR

This study computes the lattice quark propagator in Coulomb gauge, revealing insights into quark mass behavior, renormalization, and confinement mechanisms, with implications for understanding quark confinement in QCD.

Contribution

It provides the first detailed lattice calculation of the quark propagator in Coulomb gauge, analyzing its renormalization, mass function, and implications for confinement mechanisms.

Findings

Quark mass function M(|p|) matches Landau gauge at low momenta.

Full propagator indicates an IR divergent effective energy.

Results suggest Coulomb gauge can improve chiral mass determination.

Abstract

We calculate the lattice quark propagator in Coulomb gauge both from dynamical and quenched configurations. We show that in the continuum limit both the static and full quark propagator are multiplicatively renormalizable. From the propagator we extract the quark renormalization function Z(|p|) and the running mass M(|p|) and extrapolate the latter to the chiral limit. We find that M(|p|) practically coincides with the corresponding Landau gauge function for small momenta. The computation of M(|p|) can be however made more efficient in Coulomb gauge; this can lead to a better determination of the chiral mass and the quark anomalous dimension. Moreover from the structure of the full propagator we can read off an expression for the dispersion relation of quarks, compatible with an IR divergent effective energy. If confirmed on larger volumes this finding would allow to extend the Gribov-Zwanziger confinement mechanism to the fermionic sector of QCD.