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.
Definition of ABCD bins and yields in data, per match category. The predicted yield in the bin with the smallest backgrounds (bin D) is extracted from the simultaneous four-bin fit by assuming zero signal, which corresponds to $(\text{Obs. B} \times \text{Obs. C}) / (\text{Obs. A})$ in this limit.
Systematic uncertainties in the analysis. The jet uncertainties are larger in 2017 because of noise issues with the ECAL endcap. The tracking inefficiency in 2016 is caused by the unexpected saturation of photodiode signals in the tracker.
Simulated muon reconstruction efficiency of standard (blue squares) and displaced (red circles) reconstruction algorithms as a function of transverse vertex displacement $v_{xy}$. The two dashed vertical gray lines denote the ends of the fiducial tracker and muon detector regions, respectively.
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