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

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