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

Abstract

We study a strongly interacting complex scalar dark matter candidate $(\chi)$, subject to an attractive potential mediated by a vector boson $A^\mu$. Such interactions allow $\chi$ 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 $\chi$ freezes out at $x\approx 16$ and the presence of SIMPonium in the thermal bath slightly modifies the freeze out behaviour of the free $\chi$ 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 $m_\chi = 150\,\mathrm{MeV}$ lies in the range $E_\gamma^2 \frac{d\phi}{d\Omega\, dE_\gamma} \in [10^{-27},\,10^{-17}] \,\mathrm{MeV\,cm^{-2}\,s^{-1}\,sr^{-1}}$ , for photon energies in the interval $E_\gamma \in [10^{-3},\,10^{2}] \,\mathrm{MeV}$. The predicted signal is therefore exceedingly feeble and remains well below the sensitivity of current experimental facilities.