Phase transition and gravitational wave phenomenology of scalar conformal extensions of the Standard Model

TL;DR

This work analyzes phase transition dynamics and gravitational wave phenomenology in scalar classically conformal extensions of the Standard Model. Using finite-temperature effective potentials for multi-scalar setups, it derives transition temperatures $T_c$, $T_n$, and the GW spectrum characterized by $f_{\rm env}$ and $\beta/H_*$, highlighting that strong supercooling can enhance gravitational-wave signals. It finds that minimal one-scalar extensions struggle to satisfy perturbativity and cosmological bounds, while a next-to-minimal two-scalar model can realize electroweak symmetry breaking and produce a sizable GW signal within the reach of LISA and LIGO. The study also notes a viable dark matter candidate in the two-scalar scenario and emphasizes that gravitational waves provide a promising probe of conformal Standard Model extensions.

Abstract

Thermal corrections in classically conformal models typically induce a strong first-order electroweak phase transition, thereby resulting in a stochastic gravitational wave background that could be detectable at gravitational wave observatories. After reviewing the basics of classically conformal scenarios, in this paper we investigate the phase transition dynamics in a thermal environment and the related gravitational wave phenomenology within the framework of scalar conformal extensions of the Standard Model. We find that minimal extensions involving only one additional scalar field struggle to reproduce the correct phase transition dynamics once thermal corrections are accounted for. Next-to-minimal models, instead, yield the desired electroweak symmetry breaking and typically result in a very strong gravitational wave signal.

Figures (7)

• Figure 1: The scalar field potential $\tilde{V}_{\rm eff.}(\phi,T) = V_{\rm eff.}(\phi,T)-V_{\rm eff.}(0,T)$ which accounts for the full one-loop thermal integral and the re-summed daisy diagrams in the proposed two-scalars toy model plotted for different temperatures.
• Figure 2: The phase transition in classically conformal models. The thick solid lines are the isocontours of the phase transition temperature $T_n$, the thin solid lines are instead those of the critical temperature $T_c$. The dashed lines show the temperature corresponding to $\alpha(T)=1$. The grey region is excluded by the requirement that the phase transition occur at temperatures above the BBN one.
• Figure 3: Plot of $\alpha$ as a function of $T_n/T_c$ for $\lambda_p=1$ (top lines) and $\lambda_p=5$ (bottom lines). The solid lines correspond to the result obtained with eq. \ref{['eq:alphaexact']} whereas the dashed lines are for the approximation in eq. \ref{['eq:alphaapp']}.
• Figure 4: The gravitational wave spectrum obtained for the considered model assuming the values of the relative parameters reported in table \ref{['bench']}. The black and grey solid lines show the gravitational wave spectra resulting from the phase transition dynamics for $\lambda_p=1$ and $\lambda_p=2$, respectively. The dashed lines correspond instead to the expected sensitivities for different configurations of the LISA detector (low frequency region) Caprini:2015zlo and the reach of the LIGO experiment after several phases of running (high frequency region) TheLIGOScientific:2016wyq.
• Figure 5: Parameters for the scenario I of the minimal conformal SM extension as a function of $v_\phi^2=v_h^2+v_s^2$. Here the scalar boson detected at the LHC corresponds to the flat direction of the tree level potential, which develops a minimum via the Coleman-Weinberg mechanism. The region on the right hand side of the dashed line is excluded by the LHC Higgs phenomenology as it violates the bound $\cos\theta^*>0.85$Alanne:2014bra.