Phase transitions and gauge artifacts in an Abelian Higgs boson plus singlet model

While the finite-temperature effective potential in a gauge theory is a gauge-dependent quantity, in several instances a first-order phase transition can be triggered by gauge-independent terms. A particularly interesting case occurs when the potential barrier separating the broken and symmetric vacua of a spontaneously broken symmetry is produced by tree-level terms in the potential. Here, we study this scenario in a simple Abelian Higgs model, for which the gauge-invariant potential is known, augmented with a singlet real scalar. We analyze the possible symmetry-breaking patterns in the model, and illustrate in which cases gauge artifacts are expected to manifest themselves most severely. We then show that gauge artifacts can be pronounced even in the presence of a relatively large, tree-level singlet-Higgs cubic interaction. When the transition is strongly first order, these artifacts, while present, are more subtle than in the generic situation