Investigating a strong first-order electroweak phase transition in the RxSM at future linear $e^+e^-$ colliders and LISA

Abstract

The general real singlet extension of the Standard Model (SM), the RxSM, is one of the simplest theories Beyond-the-Standard Model (BSM) that can accommodate a strong first-order electroweak phase transition (SFOEWPT). We investigate the possible thermal histories of the scalar potential in the RxSM, and the regions of the model parameter space in which SFOEWPT can be realised. We then explore complementary avenues to probe such scenarios experimentally: either using searches for a stochastic background of gravitational waves (GWs), or using searches for di-Higgs production processes at future collider experiments, focusing on the case of a high-energy $e^+e^-$ collider. An important aspect of our work is that one-loop corrections to all relevant trilinear scalar couplings are consistently included both in the calculation of dynamics of the electroweak phase transition (EWPT) and in collider processes. We find entirely different phenomenological signatures for different parts of the RxSM parameter space giving rise to SFOEWPTs. On the one hand, if the SFOEWPT is driven by the singlet field, the 125 GeV Higgs boson is very SM-like and signs of BSM physics would be difficult to find at colliders, but strong GW signals could be produced. On the other hand, in scenarios where a SFOEWPT is driven by the doublet field, BSM deviations in properties of the detected Higgs boson, particularly in its trilinear self-coupling, typically lead to observable signals at colliders, while detectable GW signals are much more challenging to achieve. This work highlights the complementarity of collider experiments and cosmological observations to determine the dynamics of the EWPT and reconstruct the shape of the Higgs potential realised in Nature.

Figures (7)

• Figure 1: Tracing of the different minima of the potential as a function of the temperature for the six thermal histories possible in the RxSM. Blue lines represent the minima of the EW doublet and orange lines those of the singlet field, while red vertical lines indicate the critical temperature $T_c$. The solid lines represent the path followed by the Universe.
• Figure 2: RxSM parameter scan results for $\xi_n\equiv v_n/T_n$. Left:$\{m_H,\cos \alpha\}$ plane; right: $\{v_S,m_H\}$ plane.
• Figure 3: Parameter scan results for BP1, with $\xi_n$ indicated by the colour of the scatter points. The different thermal histories are labelled following \ref{['fig:thermalhistories']}. Coloured regions are excluded perturbative unitarity (light blue), NLO stability of the EW vacuum (grey), and direct searches for heavy Higgs bosons ATLAS:2020tlo (light red). In region B, $\xi_n\in [0,1]$.
• Figure 4: Parameter scan results for points in benchmark plane 1 with a SFOEWPT (regions C and D of \ref{['fig:BP1diags']}). Left: SNR at LISA (assuming $v_{\mathrm{w}}=0.95$ and three years of observation time) in the plane $\{m_H,\cos\alpha\}$. The red line indicates the region with $\mathrm{SNR} > 10$. Right:$\xi_n$ in the plane $\{m_H,\kappa_\lambda^{(1)}\}$ for points with $\mathrm{SNR} > 10$.
• Figure 5: Left: parameter scan results for benchmark plane 2, with $\xi_n$ shown by the colour coding of the scatter points. The labelling of different thermal histories follows that of \ref{['fig:thermalhistories']}. Coloured regions are excluded by vacuum trapping (pink), NLO stability of the potential (grey), or experimental searches (red by Ref. ATLAS:2018sbw, and orange by Ref. CMS:2021yci). Right: Temperature-dependent one-loop effective potential at the nucleation temperature, $V_\text{eff}(T_n)$, for a benchmark point with a thermal history of type E. This point is defined by $m_H=639 \;\text{GeV}\xspace$, $c_{\alpha}=0.9777$, $v_S=289 \;\text{GeV}\xspace$, $\kappa_S=-205 \;\text{GeV}\xspace$, $\kappa_{SH}=-1403 \;\text{GeV}\xspace$, where we find $T_n=64\;\text{GeV}\xspace$ and a $\mathrm{SNR} = 4.5$. Here $S$ and $\Phi^0$ denote the singlet field and the CP-even neutral component of the doublet, respectively.