Prospecting effective Yang-Mills-Higgs models for the asymptotic confining flux tube

TL;DR

This paper investigates a broad class of effective Yang-Mills-Higgs models with adjoint scalars, demonstrating their ability to replicate key confining string properties observed in lattice simulations of pure Yang-Mills theory.

Contribution

It identifies conditions under which these models exhibit stable, asymptotic confining flux tube properties consistent with lattice results, despite complex field and potential configurations.

Findings

Models reproduce N-ality and flux-tube profiles.

Profiles are independent of quark representation N-ality.

Casimir scaling is observed in the models.

Abstract

In this work, we analyze a large class of effective Yang-Mills-Higgs models constructed in terms of adjoint scalars. In particular, we reproduce asymptotic properties of the confining string, suggested by lattice simulations of $SU(N)$ pure Yang-Mills theory, in models that are stable in the whole range of Higgs-field mass parameters. These properties include $N$-ality, Abelian-like flux-tube profiles, independence of the profiles with the $N$-ality of the quark representation, and Casimir scaling. We find that although these models are formulated in terms of many fields and possible Higgs potentials, a collective behavior can be established in a large region of parameter space, where the desired asymptotic behavior is realized.