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A search for dark matter in events with a displaced muon pair and missingtransverse momentum is presented. The analysis is performed using an integratedluminosity of 138 fb$^{-1}$ of proton-proton (pp) collision data at acenter-of-mass energy of 13 TeV produced by the LHC in 2016-2018. Nosignificant excess over the predicted backgrounds is observed. Upper limits areset on the product of the inelastic dark matter production cross section$\sigma$(pp $\to$ A' $\to$ $\chi_1$$\chi_2$) and the decay branching fraction$\mathcal{B}$($\chi_2$ $\to$ $\chi_1\mu^+\mu^-$), where A' is a dark photon and$\chi_1$ and $\chi_2$ are dark matter states with near mass degeneracy. This isthe first dedicated collider search for inelastic dark matter.

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