Complex scalar dark matter with effective Higgs portals beyond radiation domination

TL;DR

The paper tackles the challenge of obtaining the correct DM relic density for a complex scalar DM with a Higgs portal given stringent direct-detection limits. It introduces a dimension-5 Higgs-portal operator and analyzes DM production during both a standard radiation-dominated era and a reheating epoch, incorporating inflaton decay via $\Gamma_\phi$ and the initial Hubble scale $H_I$; relic density is governed by semi-annihilation and constrained by Fermi-LAT data on semi-annihilation and by EFT validity requiring $\Lambda_{NP} > T_{max}$ and $2 m_\Phi < \Lambda_{NP}$. The results show that freeze-out during reheating expands viable parameter space beyond the RD case, with viable regions clustering near the Higgs resonance or at masses above TeV when $\Lambda_{NP}$ is chosen appropriately. Collider signals at HL-LHC and FCC-ee are found to be small, indicating direct and indirect searches are the primary tests for these scenarios, with future improvements needed for collider reach.

Abstract

The increasingly stringent bounds on the Higgs-portal coupling, arising from dark matter (DM) direct-detection searches, confront the minimal renormalizable complex scalar DM scenario with thermal production, where freeze-out occurs in the standard radiation-dominated era. This limitation can be alleviated by introducing a dimension-5 Higgs-portal operator in the minimal renormalizable complex scalar DM model and/or by modifying the standard cosmological history of the Universe. In this article, we analyze complex scalar DM production in both the reheating and radiation-dominated epochs within an effective field theory (EFT) framework. While both scenarios exhibit sizeable regions of parameter space consistent with existing constraints, freeze-out during reheating opens up additional viable regions that are otherwise ruled out by DM overabundance in the radiation-dominated scenario. Notably, the renormalizable Higgs-portal coupling is constrained by relic density, direct- and indirect-detection limits, whereas the EFT coupling associated with the dimension-5 operator is constrained by relic density and indirect-detection bounds arising from DM semi-annihilation. We further study the production cross section of complex scalar DM at hadron and lepton colliders.

Figures (7)

• Figure 1: The Feynman diagrams correspond to the self- and semi-annihilation of DM, where $\text{SM}=\{\rm h,~W^{\pm},~Z,~quarks~and~leptons\}$.
• Figure 2: In this figure, we show the variation of the relic density, $\Omega_{\Phi} h^2$, with the DM mass, $m_{\Phi}^{}$, for scenarios when freeze-out occurs during the standard radiation domination epoch and during reheating phase. They are, represented by the thick blue and dashed (yellow, green, magenta) lines, respectively. In addition, the right y-axis in this figure show the DM-nucleon scattering cross section. The thick magenta line represents the $\Phi$-nucleon scattering cross section. The dot-dashed magenta line indicating the $\rm LZ-2025$ limit on $\Phi$-nucleon scattering cross section. For this figure, we have considered different parameters as $\Lambda^{}_{\text{NP}}=20\,\text{TeV},~\lambda_{\Phi}^{} = 1, ~\mu_3 = 2 m_{\Phi}^{}, ~\lambda_{\Phi\text{H}}^{} = 10^{-2},~\lambda_{\Phi\text{H}}^{\prime} = 1$ and $\mathcal{H}_\text{I}^{}=10^{-4}\,\text{GeV}$.
• Figure 3: The orange points in fig . \ref{['fig:dd2']} and \ref{['fig:dd3']} indicate parameter regions consistent with the observed relic density in the $m_{\Phi}^{}$–$\Lambda^{}_{\text{NP}}$ plane. The magenta color-coded lines correspond to the $m_{\Phi}^{}$–$\sigma^{\text{SI}}_{\Phi\text{N}}$ plane (x-axis and right y-axis) in both plots. In the left panel, these points correspond to freeze-out during the radiation-dominated epoch, while in the right panel, they correspond to freeze-out during the reheating epoch. In both plots, the thick magenta line represents the $\Phi$-nucleon scattering cross section considering parameters as $\lambda_{\Phi}^{} = 1, ~\mu_3 = 2 m_{\Phi}^{}, ~\lambda_{\Phi\text{H}}^{} = 10^{-3}$, and $~\lambda_{\Phi\text{H}}^{\prime} = 1$. In addition, the right y-axis in figures shows the CSDM-nucleon scattering cross section, with the dot-dashed magenta line indicating the $\rm LZ-2025$ limit on DM-nucleon scattering. The gray-shaded region is excluded due to the EFT validity criterion, $\Lambda^{}_{\text{NP}}>2m_{\Phi}^{}$.
• Figure 4: Left: The different contours depict the parameter space in the $m_{\Phi}^{}-\lambda_{\Phi\text{H}}^{}$ plane along which relic density is satisfied. The different color codes indicate various values of $\lambda_{\Phi\text{H}}^{\prime}$. The gray-shaded region is excluded by the $\rm LZ-2025$ data while the neutrino-floor for direct DM detection Billard:2021uyg is represented by the gray dashed line. Right: The different contours depicts the relic density allowed parameter space in the $m_{\Phi}^{} - \Gamma_{\phi}$ plane, considering the genesis of DM during the reheating era. The right $y$-axis, depicted with magenta color, indicates the variation of $T_{\text{max}}$ with $\Gamma_{\phi}$ (left y-axis), for $\mathcal{H}_\text{I}^{} = 10^{-3}~\text{GeV}$. The black star points do not satisfy the $\rm LZ-2025$ bound on $\sigma^{\text{SI}}_{\Phi\text{N}}$. The dashed lines correspond to $\Lambda^{}_{\text{NP}}=T_{\text{max}}$. For both plots, we have considered the remaining parameters as $\lambda_{\Phi}^{}=1$, and $\mu_3=2m_{\Phi}^{}$.
• Figure 5: In the left and right panels of this figure, we show the variation of DM self- and semi-annihilation into SM particles (depicted via dotted lines) as a function of $m_{\Phi}^{}$, respectively. The different parameters are fixed at $\lambda_{\Phi}^{}=1$, $\mu_3=2m_{\Phi}^{}$, $\lambda_{\Phi\text{H}}^{}=10^{-3}$, $\lambda_{\Phi\text{H}}^{\prime}=1$, $\Gamma_{\phi}=10^{-16}~\text{GeV}$, and $\mathcal{H}_\text{I}^{}=10^{-3}~\text{GeV}$. The magenta color–coded right y-axes represents the $\Lambda^{}_{\text{NP}}$ scale. The blue and yellow points in the left panel correspond to the self-annihilation of CSDM into $b\bar{b}$ and $W^+W^-$, respectively, while the green points in the right panel corresponds to the semi-annihilation of CSDM into $\Phi^* h$. The cyan dotted (CTA) and blue thick (Fermi-LAT) lines, along with the red and green thick Fermi-LAT lines, represent the projected and observed upper limits on the DM self- and semi-annihilation cross sections, respectively, as shown in the figure legend. The magenta long dashed lines show the relic-allowed parameter space in the $m_{\Phi}^{}-\Lambda^{}_{\text{NP}}$ plane, with the variation of $\Lambda^{}_{\text{NP}}$ indicated along the right y-axis. All magenta points below the gray dot-dashed line are excluded by the EFT validity condition $\Lambda^{}_{\text{NP}} > T_{\text{max}}$, relevant for semi-annihilation, while the relic-density–allowed magenta points within the magenta-shaded region are disfavoured by $2m_{\Phi}^{} < \Lambda^{}_{\text{NP}}$. The olive points must satisfy $2m_{\Phi}^{} < \Lambda^{}_{\text{NP}}$ due to the $\Lambda^{}_{\text{NP}}$ dependence of the semi-annihilation cross section. The black dashed line represents $\Lambda^{}_{\text{NP}}=v_{\rm SM}^{}$Buchmuller:1985jzBrivio:2017vriGrzadkowski:2010es, where $v_{\rm SM}^{}$ denotes the EWSB vev.