Two Higgs doublet model with a complex singlet scalar and Multi-critical Point Principle

TL;DR

The paper investigates a 2HDM extended by a complex singlet S in which the imaginary part χ acts as dark matter, with three neutral Higgs bosons that can be nearly mass-degenerate to suppress direct-detection signals. It imposes the tree-level Multiple Point Principle to enforce degenerate electroweak and singlet vacua and studies the resulting scalar potential, DM phenomenology, and the electroweak phase transition (EWPT), including thermal-loop effects. The results show that the MPP favors large Higgs-doublet–singlet mixing parameters $\delta_1$ and $\delta_2$, which competes with the degenerate-scalar DM suppression that prefers small mixing, yet viable regions exist where DM relic density and LZ constraints are satisfied and a strong first-order EWPT is achieved via thermal loops. This work highlights a nontrivial tension and possible compatibility between fundamental vacuum degeneracy principles and DM phenomenology in an extended scalar sector, with DM viable regions near the Higgs resonance and in the multi-TeV regime alongside a robust EWPT.

Abstract

We study a two Higgs doublet model extended by a complex singlet scalar, in which the imaginary part of the singlet serves as a dark matter (DM) candidate. In this model, degenerate masses of the three neutral Higgs bosons are crucial for achieving consistency with current constraints from DM direct-detection experiments and Higgs searches. This is called the degenerate scalar scenario. To provide a theoretical motivation for such a degenerate Higgs spectrum, we impose the tree-level Multiple Point Principle (MPP), which requires the electroweak and singlet vacua to be degenerate, and analyze its implications for the scalar potential, DM phenomenology, and the electroweak phase transition. We show that the tree-level MPP favors large SU(2)$_L$ doublet-singlet mixing parameters, which compete with the degenerate scalar scenario. Nevertheless, we demonstrate that viable parameter regions still exist in which the observed DM constraints are satisfied. Furthermore, although the tree-level MPP forbids a tree-level-driven first-order electroweak phase transition, we show that thermal loop effects can induce a strong first-order transition compatible with electroweak baryogenesis.

Figures (4)

• Figure 1: Numerical results for $\mathcal{R} \equiv \Delta V_0 / V_0(v_1, v_2, v_S)$ as a function of the singlet VEV $v_S$, where the color indicates the value of the soft-breaking parameter $a_1$. The left panel corresponds to $0<v_S<1000$ GeV, while the right panel focuses on the region with $v_S \lesssim 0.7~\mathrm{GeV}$.
• Figure 2: Parameter points in the $(v_S, a_1)$ plane. Blue points satisfy the theoretical constraint $0<d_2<4\pi$, while red points additionally fulfill the tree-level MPP condition $\Delta V_0=0$.
• Figure 3: Left: Relic abundance $\Omega_\chi h^2$ for BP1 (red solid), BP2 (blue dashed), and BP3 (green dotted). The gray-shaded region corresponds to DM overproduction. Right: Scaled spin-independent direct-detection cross section $\tilde{\sigma}_{\mathrm{SI}}$ (see Eq. \ref{['scale']}) for the same benchmark points. The gray shaded region is excluded by the LZ experiment LZ:2024zvo.
• Figure 4: Left: Relic abundance $\Omega_\chi h^2$ for BP4 (green solid), BP5 (magenta dashed), and BP6 (light blue dotted). The gray-shaded region corresponds to DM overproduction. Right: Scaled spin-independent direct-detection cross section $\tilde{\sigma}_{\mathrm{SI}}$ (see Eq. \ref{['scale']}) for the same benchmark points. The gray shaded region is excluded by the LZ experiment LZ:2024zvo.