The anomalous dimension of the gluon-ghost mass operator in Yang-Mills theory

TL;DR

This paper proves that a specific gluon-ghost operator in Yang-Mills theory is multiplicatively renormalizable to all orders and its anomalous dimension is universally determined, confirmed by explicit 3-loop calculations.

Contribution

It establishes the all-order multiplicative renormalizability of the gluon-ghost operator and derives a universal expression for its anomalous dimension across gauges.

Findings

Operator is multiplicatively renormalizable to all orders.

Anomalous dimension is gauge-independent and universally determined.

Explicit 3-loop calculations confirm theoretical predictions.

Abstract

The local composite gluon-ghost operator $({1/2}A^{a\mu}A_{\mu}^{a}+\alpha \bar{c}^{a}c^{a})$ is analysed in the framework of the algebraic renormalization in SU(N) Yang-Mills theories in the Landau, Curci-Ferrari and maximal abelian gauges. We show, to all orders of perturbation theory, that this operator is multiplicatively renormalizable. Furthermore, its anomalous dimension is not an independent parameter of the theory, being given by a general expression valid in all these gauges. We also verify the relations we obtain for the operator anomalous dimensions by explicit 3-loop calculations in the MSbar scheme for the Curci-Ferrari gauge.