A renormalization group invariant scalar glueball operator in the (Refined) Gribov-Zwanziger framework

Understand

This paper presents a complete algebraic analysis of the renormalizability of the $d=4$ operator $F^2_{\mu\nu}$ in the Gribov-Zwanziger (GZ) formalism as well as in the Refined Gribov-Zwanziger (RGZ) version.

• The GZ formalism offers a way to deal with gauge copies in the Landau gauge.
• We explicitly show that $F^2_{\mu\nu}$ mixes with other $d=4$ gauge variant operators, and we determine the mixing matrix $Z$ to all orders, thereby only using algebraic arguments.
• The mixing matrix allows us to uncover a renormalization group invariant including the operator $F^2_{\mu\nu}$.