Determining dark matter properties with a XENONnT/LZ signal and LHC Run 3 monojet searches

We develop a method to forecast the outcome of the LHC Run 3 based on the hypothetical detection of O(100) signal events at XENONnT. Our method relies on a systematic classification of renormalizable single-mediator models for dark matter-quark interactions and is valid for dark matter candidates of spin less than or equal to one. Applying our method to simulated data, we find that at the end of the LHC Run 3 only two mutually exclusive scenarios would be compatible with the detection of O(100) signal events at XENONnT. In the first scenario, the energy distribution of the signal events is featureless, as for canonical spin-independent interactions. In this case, if a monojet signal is detected at the LHC, dark matter must have spin 1/2 and interact with nucleons through a unique velocity-dependent operator. If a monojet signal is not detected, dark matter interacts with nucleons through canonical spin-independent interactions. In a second scenario, the spectral distribution of the signal events exhibits a bump at nonzero recoil energies. In this second case, a monojet signal can be detected at the LHC Run 3; dark matter must have spin 1/2 and interact with nucleons through a unique momentum-dependent operator. We therefore conclude that the observation of O(100) signal events at XENONnT combined with the detection, or the lack of detection, of a monojet signal at the LHC Run 3 would significantly narrow the range of possible dark matter-nucleon interactions. As we argued above, it can also provide key information on the dark matter particle spin.