Copositive criteria for a two-component dark matter model

TL;DR

This paper investigates a two-component scalar dark matter model stabilized by a $Z_2\times Z'_2$ symmetry and analyzes vacuum stability via copositive criteria applied to the $4\times4$ quartic-coupling matrix. By exploring four representative sign configurations of the quartic couplings and enforcing the observed relic density and LZ direct-detection bounds, the authors map the viable regions in the quartic parameter space, focusing on $\lambda_{13}$, $\lambda_{23}$, $\lambda_{14}$, and $\lambda_{24}$ with Higgs-singlet mixing between $h_1$ and $h_2$. The study finds that direct detection strongly constrains the parameter space and that copositivity can further tighten or exclude regions depending on the sign pattern, with interference between Higgs-mediated and quartic processes playing a crucial role. The results underscore the utility of copositivity for analytic vacuum-stability constraints in multi-component scalar DM models and illuminate how Higgs-portal dynamics shape viable TeV-scale scenarios.

Abstract

We consider a two-component scalar dark matter model in this work, where the scalars are stabilized by extra $Z_2 \times Z'_2$ symmetry. To guarantee the stability of the vacuum, we consider the copositive criteria and different choices of the signs of the couplings will contribute to different viable parameter spaces. Based on the copositive criteria, we systematically analyze the possible conditions and pick up 17 different cases with fixing some parameters to be negative. We randomly scan the parameter space under dark matter relic density constraint and direct detection constraint and focus on the quartic couplings with $λ_{13}$,$λ_{23}$,$λ_{14}$ and $λ_{24}$. The shapes of the viable parameter space for $|λ_{14}|-|λ_{24}|$ are almost similar among these cases, while for $|λ_{13}|$ and $|λ_{23}|$, the larger value are excluded as long as $λ_{13}\leqslant 0$ and $λ_{23}\leqslant 0$ due to the large interference effect of the $2 \to 2$ processes.

Figures (10)

• Figure 1: Feynman diagrams of dark matter annihilation processes related to new particles.
• Figure 2: Viable parameter space of $(\lambda_{13},\lambda_{14})$ under direct detection constraint in the absence of $S_2$ with $m_1= 1$ TeV.
• Figure 3: Results of case (1) with $\lambda_{12}=1,\lambda_{13},\lambda_{14} \geqslant 0$, where we fix $\lambda_{23}=3.14,\lambda_{24}=0.0787$ in the left picture, and $\lambda_{23}=2.4,\lambda_{24}=0.0603$ in the right picture. The colored lines correspond to the viable parameter space of $(\lambda_{13},\lambda_{14})$ satisfying relic density constraint with $m_1=1,2,3$ TeV, and the respective dashed lines are the upper bound of $\lambda_{14}$ arising from direct detection constraint.
• Figure 4: Results of case (2) with $\lambda_{12}=1,\lambda_{13},\lambda_{14} \leqslant 0$, where we fix $\lambda_{23}=3.14,\lambda_{24}=0.0787$ in the left picture, and $\lambda_{23}=2.4,\lambda_{24}=0.0603$ in the right picture. The blue-shadowed region corresponds to the parameter space satisfying the copositive criteria of case ii. The colored lines correspond to the viable parameter space of $(|\lambda_{13}|,|\lambda_{14}|)$ satisfying relic density constraint with $m_1=1,2,3$ TeV, and the respective dashed lines are the upper bound of $|\lambda_{14}|$ arising from direct detection constraint.
• Figure 5: Results of case (3) with $\lambda_{12}=-1,\lambda_{13},\lambda_{14} \leqslant 0$, where we fix $\lambda_{23}=3.14,\lambda_{24}=0.0787$ in the left picture, and $\lambda_{23}=2.4,\lambda_{24}=0.0603$ in the right picture. The blue-shadowed region corresponds to the parameter space satisfying the copositive criteria of case iii. The colored lines correspond to the viable parameter space of $(|\lambda_{13}|,|\lambda_{14}|)$ satisfying relic density constraint with $m_1=1,2,3$ TeV, and the respective dashed lines are the upper bound of $|\lambda_{14}|$ arising from direct detection constraint.