Search for inelastic dark matter in events with two displaced muons and missing transverse momentum in proton-proton collisions at $\sqrt{s} = 13~\mathrm{TeV}$

A search is presented for dark matter in events with a pair of displaced muons and missing transverse momentum. The analysis is performed using $138~\mathrm{fb}^{-1}$ of proton-proton collision data at $13~\mathrm{TeV}$ center-of-mass energy produced by the LHC and collected with the CMS detector from 2016 to 2018. No significant excess is observed over the predicted background. Upper limits are set on the product of the inelastically coupled dark matter production cross section and the decay branching fraction. This is the first search for inelastic dark matter performed at a hadron collider.