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The discovery of dark matter (DM) at XENONnT or LZ would place constraints onDM particle mass and coupling constants. It is interesting to ask when theseconstraints can be compatible with the DM thermal production mechanism. Weaddress this question within the most general set of renormalisable models thatpreserve Lorentz and gauge symmetry, and that extend the Standard Model by oneDM candidate of mass $m_{\rm DM}$ and one particle of mass $M_{med}$ mediatingDM-quark interactions. Our analysis divides into two parts. First, we postulatethat XENONnT/LZ has detected $\mu_S\sim\mathcal{O}(100)$ signal events, and usethis input to calculate the DM relic density, $\Omega_{DM} h^2$. Then, weidentify the regions in the $M_{med} - \Omega_{DM} h^2$ plane which arecompatible with the observed signal and with current CMB data. We find that formost of the models considered here, $\mathcal{O}(100)$ signal events atXENONnT/LZ and the DM thermal production are only compatible for resonant DMannihilations, i.e. for $M_{med}\simeq2 m_{DM}$. In this case, XENONnT/LZ wouldbe able to simultaneously measure $m_{DM}$ and $M_{med}$. We also discuss thedependence of our results on $m_{DM}$, $\mu_S$ and the DM spin, and provideanalytic expressions for annihilation cross-sections and mediator decay widthsfor all models considered in this study.

Compatibility of a dark matter discovery at XENONnT/LZ with the WIMP thermal production mechanism