Determining Dark Matter properties with a XENONnT/LZ signal and LHC-Run3
  mono-jet searches
  We develop a method to forecast the outcome of the LHC Run 3 based on the
hypothetical detection of $\mathcal{O}(100)$ signal events at XENONnT. Our
method relies on a systematic classification of renormalisable 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 $\mathcal{O}(100)$ signal
events at XENONnT. In a first scenario, the energy distribution of the signal
events is featureless, as for canonical spin-independent interactions. In this
case, if a mono-jet 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 mono-jet 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 non zero recoil energies.
In this second case, a mono-jet 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
$\mathcal{O}(100)$ signal events at XENONnT combined with the detection, or the
lack of detection, of a mono-jet 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.
