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

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.