Electroweak Phase Transition, Gravitational Waves and Collider Probes in Multi-Scalar Dark Matter Scenarios

TL;DR

This work investigates SM extensions with multiple real scalar singlets stabilized by Z2 symmetries to address tight direct-detection constraints on Higgs-portal dark matter. By introducing two- and three-scalar sectors, the model accommodates larger Higgs portal couplings while maintaining the observed relic density, enabling a strong first-order electroweak phase transition and potentially observable stochastic gravitational waves in future space-based detectors. The analysis combines detailed finite-temperature effective potentials, nonperturbative phase-transition dynamics via CosmoTransitions, and GW spectra incorporating bubble collisions, sound waves, and turbulence, showing that the three-scalar scenario yields a stronger GW signal than the two-scalar case. These results highlight a testable connection between dark matter phenomenology, early-Universe cosmology, and gravitational wave signals, with complementary probes from Higgs invisible decays and monojet searches at colliders.

Abstract

We study scalar singlet extensions of the Standard Model (SM), focusing on scenarios where dark matter (DM) is stabilized by a \(\mathbb{Z}_2\) symmetry. In the minimal single-scalar extension of the SM, only a narrow region near the Higgs resonance remains viable, requiring small portal couplings in order to simultaneously satisfy the observed relic abundance and comply with the most recent direct detection limits from the LUX-ZEPLIN (LZ-2024) and XENON1T experiments. To address this limitation, we extend the dark sector by introducing additional real singlet scalars. In both two- and three-singlet extensions, we demonstrate that the observed dark matter relic density can be accommodated with larger Higgs portal couplings. These couplings significantly impact early-Universe dynamics by enhancing the strength of the electroweak phase transition. Both the two- and three-singlet scalar extensions can induce a strong first-order electroweak phase transition, generating stochastic gravitational waves potentially observable at future space-based detectors such as LISA and DECIGO. Notably, the three-singlet scenario induce an even stronger transition compared to the two-singlet case, enhancing the gravitational wave signal strength. Our results highlight the potential of extended scalar sectors as testable frameworks connecting dark matter and gravitational wave signals.

Figures (6)

• Figure 1: Left: Variation of DM relic abundance with dark matter mass $m_{\phi_1}$. Right: Parameter space in $\lambda_{H\phi_1}$ -- $m_{\phi_1}$ plane for which the observed relic density is satisfied. The horizontal black dotted line in the left shows the current relic abundances $\Omega h^2 = 0.12$. The green shaded region in the right panel shows the bound from LZ-2024 LZ:2024zvo.
• Figure 2: (a): Variation of nucleon dark matter effective spin-independent direct detection cross section with dark matter mass. Red points correspond to the three benchmark points in the two-scalar scenario, while blue points represent the three benchmarks for the three-scalar scenario. The shaded green and yellow bands indicate the $1\sigma$ and $2\sigma$ sensitivity regions of the LUX-ZEPLIN (LZ) 2024 experiment, respectively. The experimental exclusion band is adapted from Ref. LZ:2024zvo. (b): Thermally averaged annihilation cross-section $\langle \sigma v \rangle$ of the dark matter candidate $\phi_1$ into $b\bar{b}$ final states as a function of the DM mass $m_{\phi_1}$. The red (blue) points correspond to benchmark scenarios from the two-scalar (three-scalar) models. The solid green curve represents the 95% C.L. upper limit on $\langle \sigma v \rangle$ from Fermi-LAT gamma-ray observations of dwarf spheroidal galaxies Fermi-LAT:2015att.
• Figure 3: Left panel: Constraints on the Higgs portal coupling as a function of dark matter mass, derived from limits on the Higgs invisible decay branching ratio. Right panel: Exclusion limits at $95\%$ confidence level from LHC monojet searches for scalar dark matter.
• Figure 4: Variation of $vev$ of the Higgs field (left) and singlet scalar field $\phi_2$ (right) with temperature for BP1 for two-singlet extensions.
• Figure 5: Variation of $vev$ of the Higgs field (left) and singlet scalar field $\phi_2$ (right) with temperature for BP1 for three-singlet extensions. Note that the singlet scalar field $\phi_3$ follows the same pattern as $\phi_2$.