Confinement interpretation in a Yang-Mills + Higgs theory when considering Gribov's ambiguity

TL;DR

This paper analyzes the impact of Gribov ambiguity on the gauge field two-point function in SU(2) and SU(2)×U(1) gauge theories with Higgs fields, revealing non-trivial gluon propagator structures influenced by the Higgs representation.

Contribution

It provides a non-perturbative analysis of the gauge field propagator considering Gribov ambiguity in different Higgs representations within Yang-Mills theories.

Findings

Gluon propagator exhibits physical and non-physical mode contributions.

Results depend on the Higgs field's group representation.

Non-perturbative effects significantly alter the gauge field behavior.

Abstract

This work presents concisely the results obtained from the analysis of the two-point function of the gauge field in the $SU(2)$ and $SU(2)\times U(1)$ gauge theories, in the Landau gauge, coupled to a scalar Higgs field in the fundamental or adjoint representation. Non-perturbative effects are considered by taking into account the Gribov ambiguity. In general, in both Yang-Mills models the gluon propagator has non-trivial contributions of physical and non-physical modes, which clearly depends on the group representation of the Higgs field. These results were presented during the Fourth Winter Workshop on Non-perturbative Quantum Field Theory, which took place in Sophia-Antipolis - France.