Mass-deformed Yang-Mills theory in the covariant gauge and its gauge-invariant extension through the gauge-independent BEH mechanism

TL;DR

This paper explores the mass-deformed Yang-Mills theory in covariant gauges, demonstrating its equivalence to a gauge-invariant gauge-scalar model via a gauge-independent BEH mechanism, and discusses positivity violation implications.

Contribution

It establishes the gauge-invariant extension of mass-deformed Yang-Mills theory through a gauge-independent BEH mechanism and analyzes its non-perturbative properties.

Findings

Reproduces the decoupling solution in Landau gauge Yang-Mills theory.

Shows the equivalence to a gauge-scalar model with a fixed-modulus scalar field.

Demonstrates reflection positivity violation at one-loop level.

Abstract

In this talk we consider the mass-deformed Yang-Mills theory in the covariant gauge which is obtained by just adding a gluon mass term to the Yang-Mills theory with the covariant gauge fixing term and the associated Faddeev-Popov ghost term. First, we reconfirm that the decoupling solution in the Landau gauge Yang-Mills theory is well reproduced from the mass-deformed Yang-Mills theory by taking into account loop corrections. Second, we show that the mass-deformed Yang-Mills theory is obtained as a gauge-fixed version of the gauge-invariantly extended theory which is identified with the gauge-scalar model with a single fixed-modulus scalar field in the fundamental representation of the gauge group. This equivalence is obtained as a consequence of the gauge-independent Brout-Englert-Higgs mechanism proposed recently by one of the authors. Third, we show that the reflection positivity is violated for any value of the parameters in the mass-deformed Yang-Mills theory to one-loop quantum corrections. Finally, we discuss the implications for the existence of positivity violation/restoration crossover in light of the Fradkin-Shenker continuity between Confinement-like and Higgs-like regions in a single confinement phase in the gauge-scalar model on the lattice.