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 has strong fluctuation whose modulus is compatible with that of the color diagonal ghost propagator. 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 α G = 0. But the ghost propagator renormalized by the loop containing a product of color antisymmetric ghost is expected to behave as \({\langle c\bar c \rangle _r =-\frac{G(q^2)}{q^2}}\) with \({G(q^2)\propto q^{-2\alpha_G}}\) with α G = 0.5, if the fixed point scenario is valid. I interpret the α G = 0 solution should contain a vertex correction. The infrared exponent of our lattice Landau gauge gluon propagator of the RBC/UKQCD is α D = − 0.5 and that of MILC is about − 0.7. A possible interpretation of the origin of the fluctuation is given.