Complementarity of gravitational wave analyses and di-Higgs production in the exploration of the Electroweak Phase Transition dynamics in the RxSM

TL;DR

The paper addresses how the real singlet extension RxSM can realize a strong first-order electroweak phase transition (SFOEWPT) and how to probe it through complementary channels. It combines a one-loop finite-temperature analysis of the Higgs potential and GW production with collider studies of di-Higgs processes at the HL-LHC and at a future $e^+e^-$ collider, implementing the RxSM in BSMPTv3 and using a full on-shell scheme for trilinear couplings. The results reveal two distinct SFOEWPT regimes: a singlet-driven transition that can generate strong gravitational waves detectable by LISA but yields SM-like Higgs properties and little collider signal; and a doublet-driven transition with sizeable deviations in the trilinear Higgs coupling and measurable di-Higgs signals, though GW observability is more limited. The work highlights the necessity of combining GW observations with collider probes to fully explore the RxSM parameter space and elucidate the Higgs potential structure, while highlighting the pivotal role of one-loop corrections in both cosmological and collider contexts.

Abstract

The real singlet extension of the Standard Model (SM), RxSM, is one of the simplest Beyond-the-Standard Model (BSM) theories that can accommodate a strong first-order electroweak phase transition (SFOEWPT). We survey the possible thermal histories of the early Universe in the RxSM, and find that a SFOEWPT can occur in this model as single- or two-step phase transitions. We investigate complementary approaches to probe such scenarios experimentally: either via searches for a stochastic background of gravitational waves (GWs) or via searches for di-Higgs production processes at future collider experiments: the HL-LHC, or a possible high-energy $e^+e^-$ collider. For these analyses we consistently include one-loop corrections to the trilinear Higgs couplings. We find that entirely different phenomenological signals are possible, depending on how the SFOEWPT occurs. In scenarios where such a transition is driven by the Higgs doublet direction in field space, BSM deviations in properties of the detected Higgs boson, particularly in the trilinear scalar coupling, typically lead to observable signals at colliders, while the regions of parameter space with detectable GW signals are very narrow. On the other hand, if the SFOEWPT is triggered by the singlet field direction, the detected Higgs boson is very SM-like and no signs of BSM physics would appear in di-Higgs production processes. However, strong GW signals could be produced for significant parts of the RxSM parameter space with singlet-driven SFOEWPT. This work highlights the crucial importance of exploiting complementary experimental directions to determine the dynamics of the electroweak phase transition and access the shape of the Higgs potential realised in Nature.

Figures (22)

• Figure 1: The tracing of the different minima of the potential with respect to the temperature for six different thermal histories. In blue we show the minima of the EW doublet and in orange the minima of the singlet field. The solid lines represent the path that the universe follows. The red dashed line indicates the critical temperature $T_c$.
• Figure 2: Results for $\xi_n\equiv v_n/T_n$ for the points from our RxSM parameter scan. Top left: $\{\cos \alpha,m_H\}$ plane; top right: $\{\cos \alpha,v_S\}$ plane; bottom left: $\{\kappa_S ,\kappa_{SH}\}$ plane; bottom right: $\{m_H,v_S\}$ plane.
• Figure 3: Parameter scan results in the RxSM for benchmark plane 1. The colour coding shows the ratio $\xi_n=v_n/T_n$. The different thermal histories are labeled following \ref{['thermalhistories']}. We indicate in light blue the region excluded by perturbative unitarity, in grey the region excluded by the stability of the EW vacuum at NLO and in light red the region excluded by direct searches for heavy Higgs bosons in Ref. ATLAS:2020tlo. We note that in region B$0<\xi_n<1$.
• Figure 4: Parameter scan results in the RxSM for the points with a SFOEWPT in the benchmark plane 1. Left: $T_n$ (in GeV); right: SNR at LISA (assuming 3 years of observations) for $v_{\mathrm{w}}=0.95$, where the region delimited in red represents the observable region (i.e. SNR$\;>10$).
• Figure 5: Temperature-dependent one-loop effective potential at the nucleation temperature, $V_\text{eff}(T_n)$, for a benchmark point featuring a SFOEWPT with a thermal history of type D (from \ref{['thermalhistories']}). The BP is defined by $m_H=262 \;\text{GeV}\xspace$, $c_{\alpha}=0.9915$, $v_S=139 \;\text{GeV}\xspace$, $\kappa_S=-833 \;\text{GeV}\xspace$, $\kappa_{SH}=-72 \;\text{GeV}\xspace$, and we obtain $T_n=68\;\text{GeV}\xspace$ as well as a SNR$\;>10$. $\Phi^0$ denotes the CP-even neutral component of the Higgs doublet.