Roles of the color antisymmetric ghost propagator in the infrared QCD

Abstract

The results of Coulomb gauge and Landau gauge lattice QCD simulation do not agree completely with continuum theory. There are indications that the ghost propagator in the infrared region is not purely color diagonal as in high energy region. After presenting lattice simulation of configurations produced with Kogut-Susskind fermion (MILC collaboration) and those with domain wall fermion (RBC/UKQCD collaboration), I investigate in triple gluon vertex and the ghost-gluon-ghost vertex how the square of the color antisymmetric ghost contributes. Then the effect of the vertex correction to the gluon propagator and the ghost propagator is investigated. Recent Dyson-Schwinger equation analysis suggests the ghost dressing function $G(0)=$ finite and no infrared enhancement or ${\alpha }_G=0$. But the ghost propagator renormalized by the loop containing a product of color antisymmetric ghost is expected to behave as $<c\bar{c}{>}_r=-\frac{G(q^2)}{q^2}$ with $G(q^2)\propto q^{-2(1+{\alpha }_G)}$ with ${\alpha }_G=0.5$, if the fixed point scenario is valid. I interpret the ${\alpha }_G=0$ solution should contain a vertex correction. The infrared exponent of our lattice Landau gauge gluon propagator of the RBC/UKQCD is $\kappa ={\alpha }_G=-0.5$ and that of MILC is about -0.7. The implication for the Kugo-Ojima color confinement criterion, QCD effective coupling and the Slavnov identity are given.

13 pages 10 figures, references added and revised. version to be published in Few-Body Systems

References in corpus (6)

• Infrared Properties of QCD from Dyson-Schwinger equations
• Three-point vertices in Landau-gauge Yang-Mills theory
• Infrared behaviour of the ghost-gluon vertex in Landau gauge Yang-Mills theory
• Effects of the quark field on the ghost propagator of Lattice Landau Gauge QCD
• Infrared features of unquenched finite temperature lattice Landau gauge QCD
• The Color Antisymmetric Ghost Propagator and One-Loop Vertex Renormalization

Cited by in corpus (2)

• Propagator of the lattice domain wall fermion and the staggered fermion
• The self-dual gauge fields and the domain wall fermion zero modes