SIMPonium bound states of complex scalar dark matter: Relic density and astrophysical signatures

TL;DR

The paper investigates SIMPonium bound states in a sub-GeV complex-scalar SIMP dark matter model with a massless dark-photon mediator A^μ, focusing on bound-state formation, radiative de-excitation, and decay, and their impact on relic density and indirect detection. It derives a minimal Lagrangian with a Higgs-portal to connect to the SM, and solves coupled Boltzmann equations for free χ and SIMPonium yields, finding freeze-out at $x_f \approx 20$ for free χ and $x_f \approx 250$ for SIMPonium, while reproducing the observed relic density $\Omega h^2 \approx 0.12$. It computes photon spectra from final-state radiation and radiative decays across astrophysical environments, obtaining a total flux for $m_χ = 150$ MeV in the range $E_γ^2 dφ/(dΩ dE_γ) \in [10^{-27}, 10^{-17}]$ MeV cm$^{-2}$ s$^{-1}$ sr$^{-1}$ for $E_γ \in [10^{-3}, 10^{2}]$ MeV, below current detectability. Overall, bound-state dynamics mainly reshapes the dark-sector abundance and yields only feeble indirect-detection signals, consistent with the lack of observed sub-GeV DM signatures in GC, dwarfs, and clusters.

Abstract

We study a strongly interacting complex scalar dark matter candidate $(χ)$, subject to an attractive potential mediated by a vector boson $A^μ$. Such interactions allow $χ$ to form bound states: SIMPonium. In this work, we systematically investigate the bound state dynamics of our dark sector, including the formation and decay of SIMPonium and it's influence on the thermal history. Our analysis shows in absence of any bound state formation $χ$ freezes out at $x\approx 16$ and the presence of SIMPonium in the thermal bath slightly modifies the freeze out behaviour of the free $χ$ particles, which freezes out at $x \approx 20$. While the bound state itself remains in chemical equilibrium for a longer duration and freezes out at a significantly later time, $x \approx 250$. We compute the indirect energy spectra arising from free dark matter annihilation and SIMPonium decay, where the resulting Standard Model particles subsequently produce both final state radiation and radiative decay spectra. We find that the total differential photon flux from dark matter with mass $m_χ= 150\,\mathrm{MeV}$ lies in the range $E_γ^2 \frac{dφ}{dΩ\, dE_γ} \in [10^{-27},\,10^{-17}] \,\mathrm{MeV\,cm^{-2}\,s^{-1}\,sr^{-1}}$ , for photon energies in the interval $E_γ\in [10^{-3},\,10^{2}] \,\mathrm{MeV}$. The predicted signal is therefore exceedingly feeble and remains well below the sensitivity of current experimental facilities.

Figures (17)

• Figure 1: Feynman diagram illustrating the $4\chi \rightarrow 2\chi$ number changing process.
• Figure 2: Evolution of the number densities of free dark matter ($Y_\chi$), SIMPonium ($Y_B$), and dark matter abundance in the absence of bound state formation ($Y_{\text{free}}$). The observed relic density $\Omega h^2 = 0.12 \pm 0.0012$ is indicated by the purple dotted line.
• Figure 3: Feynman diagram for bound state formation via emission of a vector boson in the process $\chi^* \chi \rightarrow B_n A^\mu$.
• Figure 4: Panel (a) shows the SIMPonium formation cross section (for $v_{\text{rel}} = 3000~\text{km/s}$) as a function of the dark matter mass, varied from 0 to 1000 MeV, for the ground state and the first and second excited states. Panel (b) illustrates the dependence of the cross section on the relative velocity $v_{\text{rel}}$ in $\text{km/s}$, where the red, green, and blue curves correspond to $m_\chi = 10~\text{MeV}$, $150~\text{MeV}$, and $500~\text{MeV}$, respectively. Solid, dashed, and dotted lines represent the $n = 1$, $n = 2$, and $n = 3$ states, respectively. The red-shaded region represents dwarf galaxies, the yellow corresponds to the galactic center, and the blue indicates galactic clusters.
• Figure 5: Feynman diagram illustrating the de-excitation of an excited SIMPonium state to the ground state via emission of a vector boson in the process $B_{n'} \rightarrow B_n A^\mu$.