A combined study of the gluon and ghost condensates <A^2> and <epsilon^{abc} cbar^b c^c> in Euclidean SU(2) Yang-Mills theory in the Landau gauge

TL;DR

This paper investigates how ghost and gluon condensates affect the mass generation and polarization properties in SU(2) Yang-Mills theory within the Landau gauge, revealing new insights into mass splitting and Abelian dominance.

Contribution

It provides a combined analysis of ghost and gluon condensates, showing their impact on gluon mass parameters and polarization effects in SU(2) Yang-Mills theory.

Findings

Ghost condensate induces a splitting in gluon mass parameters.

Including <A^2> makes the effective masses real, avoiding tachyonic issues.

Diagonal gluon mass is smaller than off-diagonal, suggesting Abelian dominance.

Abstract

The ghost condensate <epsilon^{abc} cbar^b c^c> is considered together with the gluon condensate <A^2> in SU(2) Euclidean Yang-Mills theories quantized in the Landau gauge. The vacuum polarization ceases to be transverse due to the nonvanishing condensate <epsilon^{abc} cbar^b c^c>. The gluon propagator itself remains transverse. By polarization effects, this ghost condensate induces then a splitting in the gluon mass parameter, which is dynamically generated through <A^2>. The obtained effective masses are real when <A^2> is included in the analysis. In the absence of <A^2>, the already known result that the ghost condensate induces effective tachyonic masses is recovered. At the one-loop level, we find that the effective diagonal mass becomes smaller than the off-diagonal one. This might serve as an indication for some kind of Abelian dominance in the Landau gauge, similar to what happens in the maximal Abelian gauge.