Global fit of pseudo-Nambu-Goldstone Dark Matter

We perform a global fit within the pseudo-Nambu-Goldstone dark matter (DM) model emerging from an additional complex scalar singlet with a softly broken global U(1) symmetry. Leading to a momentum-suppressed DM-nucleon cross section at tree level, the model provides a natural explanation for the null results from direct detection experiments. Our global fit combines constraints from perturbative unitarity, DM relic abundance, Higgs invisible decay, electroweak precision observables and latest Higgs searches at colliders. The results are presented in both frequentist and Bayesian statistical frameworks. Furthermore, post-processing our samples, we include the likelihood from gamma-ray observations of $\mathit{Fermi}$-LAT dwarf spheroidal galaxies and compute the one-loop DM-nucleon cross section. We find two favoured regions characterised by their dominant annihilation channel: the Higgs funnel and annihilation into Higgs pairs. Both are compatible with current $\mathit{Fermi}$-LAT observations, and furthermore, can fit the slight excess observed in four dwarfs in a mass range between about 30-300 GeV. While the former region is hard to probe experimentally, the latter can partly be tested by current observations of cosmic-ray antiprotons as well as future gamma-ray observations.