Renormalizing a BRST-invariant composite operator of mass dimension 2 in Yang-Mills theory

TL;DR

This paper investigates the renormalization of a BRST-invariant composite operator of mass dimension 2 in Yang-Mills theory, supporting the idea that such condensates could explain mass gap and confinement.

Contribution

It demonstrates the multiplicative renormalizability of the operator and analyzes its role in the gluon and ghost propagators within Yang-Mills theory.

Findings

Confirmed the operator's multiplicative renormalizability.

Derived the Wilson coefficient for the vacuum condensate.

Connected the results to mass gap and confinement phenomena.

Abstract

We discuss the renormalization of a BRST and anti-BRST invariant composite operator of mass dimension 2 in Yang-Mills theory with the general BRST and anti-BRST invariant gauge fixing term of the Lorentz type. The interest of this study stems from a recent claim that the non-vanishing vacuum condensate of the composite operator in question can be an origin of mass gap and quark confinement in any manifestly covariant gauge, as proposed by one of the authors. First, we obtain the renormalization group flow of the Yang-Mills theory. Next, we show the multiplicative renormalizability of the composite operator and that the BRST and anti-BRST invariance of the bare composite operator is preserved under the renormalization. Third, we perform the operator product expansion of the gluon and ghost propagators and obtain the Wilson coefficient corresponding to the vacuum condensate of mass dimension 2. Finally, we discuss the connection of this work with the previous works and argue the physical implications of the obtained results.