Phase Transitions and Gauge Artifacts in an Abelian Higgs Plus Singlet Model

TL;DR

This work investigates gauge artifacts in finite-temperature phase transitions within an Abelian Higgs model augmented by a real singlet scalar, focusing on whether gauge-invariant, tree-level terms can engender a strongly first-order transition without gauge artifacts. The authors compute both one-loop and finite-temperature corrections in $R_\xi$ gauge and compare to a gauge-invariant, ring-improved approach, mapping phase structure for three illustrative parameter sets using CosmoTransitions and the nucleation condition $S_3/T_* \approx 140$ to extract the nucleation temperature $T_*$ and transition strength measures $\alpha$ and $\beta$. They find that the singlet does not automatically suppress gauge artifacts; these artifacts are most pronounced for weakly first-order transitions but are mitigated in strongly first-order cases either via larger gauge couplings or constructive interplay with the cubic singlet term. The results stress the need for gauge-invariant nonperturbative methods to draw robust conclusions about electroweak-like transitions in singlet-extended models, since perturbative gauge-dependent predictions for $T_*$, $\alpha$, and $\beta$ can be misleading in regions with significant gauge artifacts. Overall, the paper clarifies where gauge artifacts arise and guides interpretation of perturbative calculations in gauge theories with extended scalar sectors.

Abstract

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.

Figures (4)

• Figure 1: Contours of the tree-level potential for $m_1/m_2 = 0.4$ and six different values of $\theta$. Red (blue) contour lines denote higher (lower) values of the potential. The Higgs and singlet fields vary along the horizontal and vertical axes, respectively. The origin, which is in the center of each plot, is a maximum in (a), (b), and (f), a saddle point in (c) and (e), and a minimum in (d).
• Figure 2: Gauge dependence in cases 1 (thin green lines) and 2 (black lines) as a function of the gauge parameter $\xi$. The left panels have a small gauge coupling $g=0.5$, while the right have $g=1.0$. Dashed lines represent second-order symmetry breaking transitions, which may be followed by a first-order transition at lower temperature. The marks along the right side of each panel show the corresponding quantity calculated using the gauge-invariant method of Ref. mjrmpatel. The thicker marks include a gauge-invariant treatment of the thermal masses; the thin marks ignore them.
• Figure 3: Gauge dependence in case 2 with $g=0.5$, but with $\theta$ (or equivalently $E$) varied and $\xi$ held fixed. The transition is second-order for $\xi \geq 3$ for all values of $\theta$.
• Figure 4: Similar to Fig. \ref{['fig:thetadep1']}, but for case 3 with $g=0.3$. At $\theta \gtrsim 70^\circ$, the symmetry-breaking transition is second-order for $\xi = 3$ and 5 (dashed lines), followed by a weakly first-order transition. At $\theta \gtrsim 80^\circ$, the symmetry-breaking transition is second order for all plotted values of $\xi$ and the first-order transitions have disappeared. The thick/thin black dotted lines show the gauge-invariant critical temperature and latent heat calculations with/without thermal mass corrections.