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

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 $SU(3)$.