The Simplest Dark Matter Model at the Edge of Perturbativity

Increasingly sensitive direct detection dark matter experiments are testing important regions of parameter space for WIMP dark matter and pushing many models to the multi-TeV regime. This brings into question the perturbativity of these models. In this context, and in light of the new limits from the LZ experiment, we investigate the status of the simplest thermal dark matter model: a singlet scalar, real or complex, coupled to the Higgs boson. We calculate the next-to-leading order (NLO) corrections to the direct detection rates as well as for the annihilations driving thermal freeze-out. For the complex case, we find that the entire perturbative region is excluded by direct detection. For the real case we find that the mass should be $\gtrsim 20\,{\rm TeV}$ at NLO, compared with the $\gtrsim 30\,{\rm TeV}$ LO limit. We highlight that a three-fold improvement on WIMP spin independent interactions can fully test the real scalar model in the perturbative regime. Finally, for both models, there is still an allowed (albeit narrow) region near the Higgs resonance where couplings are perturbative.