Probing the Dark Sector with Dark Matter Bound States

A model of dark sector where $O({\rm few~GeV})$ mass dark matter particles $\chi$ couple to a lighter dark force mediator $V$, $m_V \ll m_\chi$, is motivated by the recently discovered mismatch between simulated and observed shapes of galactic haloes. Such models, in general, provide a challenge for direct detection efforts and collider searches. We show that for a large range of coupling constants and masses, the production and decay of the bound states of $\chi$, such as $0^{-+}$ and $1^{--}$ states, $\eta_D$ and $\Upsilon_D$, is an important search channel. We show that $e^+e^-\to \eta_D +V$ or $\Upsilon_D +\gamma$ production at $B$-factories for $\alpha_D > 0.1$ is sufficiently strong to result in multiple pairs of charged leptons and pions via $\eta_D\to 2V \to 2(l^+l^-)$ and $\Upsilon_D\to 3V \to 3(l^+l^-)$ $(l=e,\mu,\pi)$. The absence of such final states in the existing searches performed at \babar\ and Belle sets new constraints on the parameter space of the model. We also show that a search for multiple bremsstrahlung of dark force mediators, $e^+e^-\to \chi\bar\chi+nV$, resulting in missing energy and multiple leptons, will further improve the sensitivity to self-interacting dark matter.