One-loop corrections to the Higgs boson invisible decay in a complex singlet extension of the SM

The search for dark matter (DM) at colliders is founded on the idea of looking for something invisible. There are searches based on production and decay processes where DM may reveal itself as missing energy. If nothing is found, our best tool to constrain the parameter space of many extensions of the Standard Model (SM) with a DM candidate is the Higgs boson. As the measurements of the Higgs couplings become increasingly precise, higher-order corrections will start to play a major role. The tree-level contribution to the invisible decay width provides information about the portal coupling. Higher-order corrections also gives us access to other parameters from the dark sector of the Higgs potential that are not present in the tree-level amplitude. In this work we will focus on the complex singlet extension of the SM in the phase with a DM candidate. We calculate the one-loop electroweak corrections to the decay of the Higgs boson into two DM particles. We find that the corrections are stable and of the order of a few percent. The present measurement of the Higgs invisible branching ratio, BR$(H→$ invisible $)