Three loop effective potential for $\langle \frac{1}{2} { A_\mu^a }^2 \rangle$ in the Landau gauge in QCD

TL;DR

This paper calculates the three-loop effective potential for the dimension two gluon operator in Landau gauge QCD, providing refined estimates of the gluon effective mass.

Contribution

It introduces a three-loop calculation of the effective potential for a key operator in QCD using the Local Composite Operator method, extending previous two-loop results.

Findings

Three-loop effective mass estimates are similar to two-loop results for fewer than five quarks.

The method refines understanding of gluon mass generation in QCD.

Results are specific to SU(3) gauge group with varying quark flavors.

Abstract

We apply the Local Composite Operator method to construct the three loop effective potential for the dimension two operator $\frac{1}{2} { A_\mu^a }^2$ in the Landau gauge in Quantum Chromodynamics. For $SU(3)$ we show that the three loop value of the effective mass of the gluon is similar to the two loop estimates when the number of massless quarks is strictly less than five for $SU(3)$.