Towards a unified viewpoint of Gribov--Zwanziger and Serreau--Tissier gauge fixing

TL;DR

This paper develops a unified, renormalizable gauge fixing framework that interpolates between two prominent approaches to Landau gauge fixing, providing insights into infrared Yang--Mills behavior and potential lattice tests.

Contribution

It introduces a local, BRST-invariant action unifying Serreau--Tissier and Gribov--Zwanziger gauge fixings, with algebraic renormalization and infrared matching conditions.

Findings

The gluon propagator interpolates between massive and decoupling forms.

A radiatively generated gluon screening mass emerges from the replica sector.

The framework enables controlled studies of infrared correlators and lattice test proposals.

Abstract

We investigate a unified Landau--gauge fixing that continuously interpolates between the viewpoints of the Serreau--Tissier (ST) copy-averaged formulation and the (Refined) Gribov--Zwanziger (RGZ) restriction to the first Gribov region. By combining the ST weight with a GZ-type horizon term and localizing both through the replica trick and the BRST-invariant $A_\mu^h$ formulation, we obtain a single, local, BRST-invariant, power-counting renormalizable action. Algebraic renormalization shows that all counterterms are reabsorbed by a common set of field and parameter renormalizations, therefore the unification is algebraic rather than merely additive. The replica sector yields a radiatively generated gluon screening mass, while the RGZ parameters are fixed by the horizon and condensate gap equations; we also give infrared matching conditions that link both descriptions at small momentum. We present a compact BRST-superspace rewriting of the RGZ block and a simple hybrid superspace that hosts the ST replicas and RGZ side by side; these add no dynamics and organize the Ward-identity analysis. The resulting gluon propagator interpolates among the massive Faddeev--Popov--ST and the RGZ decoupling forms. This framework offers a controlled way to study how infrared Yang--Mills correlators depend on the balance between copy averaging and horizon suppression, and it suggests practical lattice tests through tunable copy weighting.