Prospects on searches for baryonic Dark Matter produced in $b$-hadron decays at LHCb

A model that can simultaneously explain Dark Matter relic density and the apparent matter anti-matter imbalance of the universe has been recently proposed. The model requires $b$-hadron branching fractions to Dark Matter at the per mille level. The $b$-hadrons decay to a dark sector baryon, $\psi_{\rm{DS}}$, which has a mass in the region $940$ MeV/c$^{2} \leq m(\psi_{\rm{DS}}) \leq 4430$ MeV/c$^{2}$. In this paper, we discuss the sensitivity of the LHCb experiment to search for this dark baryon, covering different types of topology and giving prospects for Runs 3 and 4 of the LHC, as well as for the proposed Phase-II Upgrade. We show that the LHCb experiment can cover the entire mass range of the hypothetical dark baryon.