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 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 $138{\mathrm{fb}}^{-1}$ 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 $\sigma (pp\to A^{\prime }\to {\chi }_1{\chi }_2)$ and the decay branching fraction $\mathcal{B}({\chi }_2\to {\chi }_1{\mu }^{+}{\mu }^{-})$, 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.

Figure 1

Feynman diagram of IDM production and decay in $pp$ collisions. The heavier state ${\chi }_2$ can be long-lived and decays to ${\chi }_1$ and to a muon pair via an off-shell dark photon $A^{\prime }$.

Figure 2

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.

Figure 3

Measured $\min \text{−}{d}_{xy}$ distribution in the two-match category, after requiring the $\min \text{−}{d}_{xy}$ muon to pass the isolation requirement $I_{\mathrm{PF}}^{\mathrm{rel}}<0.25$ (i.e., the $B$ and $D$ bins of the $ABCD$ plane). Overlaid with a red histogram is the background predicted from the region of the $ABCD$ plane failing the same requirement (the $A$ and $C$ bins), as well as three signal benchmark hypotheses (as defined in the legends), assuming ${\alpha }_{\mathrm{D}}$ is equal to the electromagnetic (EM) fine-structure constant ${\alpha }_{\mathrm{EM}}$. The red hatched bands correspond to the background prediction uncertainty. The last bin includes the overflow.

Figure 4

Two-dimensional exclusion surfaces for $\mathrm{\Delta }=0.1m_1$ (top) and $0.4m_1$ (bottom), as functions of the DM mass $m_1$ and the signal strength $y$, with $m_{A^{\prime }}=3m_1$. Filled histograms denote observed limits on $\sigma (pp\to A^{\prime }\to {\chi }_2{\chi }_1)\mathcal{B}({\chi }_2\to {\chi }_1{\mu }^{+}{\mu }^{-})$. Solid (dashed) curves denote the observed (expected) exclusion limits at 95% C.L., with 68% C.L. uncertainty bands around the expectation. Regions above the curves are excluded, depending on the ${\alpha }_{\mathrm{D}}$ hypothesis: ${\alpha }_{\mathrm{D}}={\alpha }_{\mathrm{EM}}$ (dark blue) or 0.1 (light magenta). The sensitivity is higher in the region near $m_1\approx 30$ GeV or $m_{A^{\prime }}\approx 90\mathrm{GeV}$ because of the $A^{\prime }$ mixing with the $Z$ boson in that mass range.