Gravitational waves from first order electroweak phase transition in models with the $U(1)_X^{}$ gauge symmetry

TL;DR

The paper investigates a SM extension with a dark U(1)_X gauge symmetry broken by a dark Higgs, focusing on patterns of the electroweak and dark phase transitions and the gravitational waves produced by strongly first-order transitions. It analyzes a zero- and finite-temperature effective potential, classifies multi-step PT paths, and computes GW spectra via sound waves, incorporating collider Higgs constraints and dark matter considerations. The results show that multi-step EWPTs can yield detectable GWs for a heavy enough dark photon, with $m_X \,\gtrsim \,25$ GeV and $g_X \,\gtrsim \,0.5$, while DM constraints (especially in Model B) constrain or modify the viable regions. The work emphasizes the complementary reach of GW observatories (LISA/DECIGO) and dark-sector searches in testing the dark U(1)_X scenario and its implications for Higgs physics and DM.

Abstract

We consider a standard model extension equipped with a dark sector where the $U(1)_X^{}$ Abelian gauge symmetry is spontaneously broken by the dark Higgs mechanism. In this framework, we investigate patterns of the electroweak phase transition as well as those of the dark phase transition, and examine detectability of gravitational waves (GWs) generated by such strongly first order phase transition. It is pointed out that the collider bounds on the properties of the discovered Higgs boson exclude a part of parameter space that could otherwise generate detectable GWs. After imposing various constraints on this model, it is shown that GWs produced by multi-step phase transitions are detectable at future space-based interferometers, such as LISA and DECIGO, if the dark photon is heavier than 25 GeV. Furthermore, we discuss the complementarity of dark photon searches or dark matter searches with the GW observations in these models with the dark gauge symmetry.

Figures (9)

• Figure 1: Four types of PT path are labeled by A, B, C and D. Here, SYM and EW denotes the symmetric phase $(\varphi_\Phi^{},\varphi_S ^{})=(0,0)_{T\to \infty}$, and the EW phase $(v_\Phi^{},v_S^{})_{T=0}$. Intermediate phases are denoted by I $(0,\varphi_S^{}>v_S^{})$, I' $(0,v _S^{})$ and II $(v_\Phi,0)$. For details, see Refs. Funakubo:2005puProfumo:2014opaChiang:2017nmuVieu:2018nfq.
• Figure 2: The six benchmark points are blobbed on the ($m_X, g_X$)-plane. The solid lines show the cases of $v_S [\text{GeV}]=50$ (blue), $100$ (orange), $200$ (green) from the top.
• Figure 3: Types of multi-step PT on the $(m_H^{},\theta)$ plane for the benchmark point $m_X=200~\text{GeV}$ and $g_X=2$ ($v_S=100~\text{GeV}$). The left (right) frame shows light heavy $H$ cases: $m_H^{}<m_h^{}$ (heavy $H$ cases: $m_H^{}>m_h^{}$). Parameter sets predicting one-step PT with 1st order are marked with blue closed square, one-step PT with 2nd order with blue open square, two-step PT where both transitions are 1st order with green closed star, two-step PT where the latter one is 1st order with green closed triangle, and two-step PT where the former one is 1st order with green open triangle. The blue solid lines show the contours of $\Delta \lambda_{hhh}$ in percentage. The black lines show the combined exclusion limit obtained by $\kappa_Z^{}$ measurement (orange) and direct searches for $H$ (gray). In Model B, the following constraints on DM properties should be imposed. The red lines show the contours of the normalized relic density $\Omega_X^{}/\Omega_{\rm obs}^{}$ in common logarithm (The red bold lines show the cases of $\Omega_X^{}=\Omega_{\rm obs}^{}$). The cyan regions are excluded by DM direct detection by XENON1T in terms of $\log_{10}^{}(\sigma_X^{} \times \Omega_X^{}/\Omega_{\rm obs}^{}$). For more details, see TABLE \ref{['table:legends']}.
• Figure 4: Predicted values of $\alpha$ and $\widetilde{\beta}$ for the benchmark point $m_X^{}=200~\text{GeV}$ and $g_X^{}=2$ ($v_S^{}=100~\text{GeV}$). For two-step PT with 1st order $\to$ 1st order, the former (green closed star) and the latter (green closed triangle) is connected with a red dashed line. Parameter sets excluded by the collider bounds shown in Fig. \ref{['fig:200+1_1']} are marked with darker points. The expected sensitivities of LISA and DECIGO detector designs are computed by using the sound wave contribution for $T_t^{}=100~\text{GeV}$ and $v_b^{}=0.95$.
• Figure 5: Types of multi-step PT for $m_X=100~\text{GeV}$, $g_X=2$ ($v_S=50~\text{GeV}$). See the captions of Figs. \ref{['fig:200+1_1']}--\ref{['fig:200+1_2']}.