Self-dual gauge fields, domain wall fermion zero modes and the Kugo-Ojima confinement criterion

TL;DR

This paper introduces a new gauge fixing method for domain wall fermions, applies it to calculate QCD properties, and explores the implications for color confinement and topological charge effects.

Contribution

It proposes a novel gauge fixing condition and applies it to compute QCD observables, linking zero modes and confinement criteria.

Findings

Charge form factor fitted by dipole form under topological charge assumption.

Difference in Kugo-Ojima parameter attributed to anomaly effects.

Method provides new insights into confinement and topological effects in QCD.

Abstract

A new gauge fixing that imposes the U(1) real and quaternion real condition on the correlator of domain wall fermion on the left wall and right wall is proposed. The method is applied to the calculation of the mass function, the QCD effective coupling and the charge form factor of the proton. By assuming topological charge change $|Q|=1$, the charge form factor of the proton is approximately fitted by the dipole form factor. The difference of the Kugo-Ojima color confinement parameter in quenched simulation and in unquenched simulation is expected to be due to an anomaly caused by the vertex of two fermion zero modes and the Bose ghost/gluon.