Three loop MS renormalization of the Curci–Ferrari model and the dimension two BRST invariant composite operator in QCD

The massless Curci–Ferrari model with Nf flavours of quarks is renormalized to three loops in the MS scheme in an arbitrary covariant gauge with parameter α. The renormalization of the BRST invariant dimension two composite operator, 12Aa 2μ−αc̄aca, which corresponds to the mass operator in the massive Curci–Ferrari model, is determined by renormalizing the Greenʹs function where the operator is inserted in a ghost two-point function. Consequently the anomalous dimension of the QCD Landau gauge operator, 12Aa 2μ, and the (gauge independent) photon mass anomalous dimension in QED are both deduced at three loops.