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We calculate the leading radiative corrections to the dark-matter-nucleonscattering in the pseudo-Nambu-Goldstone dark matter model augmented with asecond Higgs doublet (S2HDM). In this model, the cross sections for thescattering of the dark-matter on nuclei vanishes at tree-level in the limit ofzero momentum-transfer due to a U(1) symmetry. However, this symmetry is softlybroken in order to give a mass to the dark-matter particle. As a consequence,non-vanishing scattering cross sections arise at the loop level. We find thatthe current cross-section limits from dark-matter direct-detection experimentscan hardly constrain the parameter space of the S2HDM. However, theloop-corrected predictions for the scattering cross sections can be well withinthe reach of future direct-detection experiments. As a consequence, futurephenomenological analyses of the S2HDM should take into account cross-sectionpredictions beyond tree-level and the experimental constraints from dark-matterdirect-detection experiments.

Direct detection of pseudo-Nambu-Goldstone dark matter in a two Higgs doublet plus singlet extension of the SM