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

A search for dark matter in events with a displaced nonresonant muon pair and missing transverse momentum is presented. The analysis is performed using an integrated luminosity of 138 fb${}^{-1}$ of proton-proton (pp) collision data at a center-of-mass energy of 13 TeV produced by the LHC in 2016-2018. No significant excess over the predicted backgrounds is observed. Upper limits are set 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 states in the dark sector with near mass degeneracy. This is the first dedicated collider search for inelastic dark matter.