Search for Inelastic Dark Matter in Events with Two Displaced Muons and Missing Transverse Momentum in Proton-Proton Collisions at $\sqrt{s}=13\text{}\text{}\mathrm{TeV}$

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 $138\text{}\text{}{\mathrm{fb}}^{-1}$ 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 $\sigma \left(pp\to {A}^{\prime }\to {\chi }_{1}{\chi }_{2}\right)$ and the decay branching fraction $B\left({\chi }_{2}\to {\chi }_{1}{\mu }^{+}{\mu }^{-}\right)$, where ${A}^{\prime }$ 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.