Pseudo-Nambu-Goldstone dark matter and two-Higgs-doublet models

We study a dark matter model with one singlet complex scalar and two Higgs doublets. The scalar potential respects a softly broken global symmetry, which makes the imaginary part of the singlet become a pseudo-Nambu-Goldstone boson acting as a dark matter candidate. The pseudo-Nambu-Goldstone nature of the boson leads to the vanishing of its tree-level scattering amplitude off nucleons at zero momentum transfer. Therefore, although the interaction strength could be sufficiently large to yield a viable relic abundance via thermal mechanism, direct detection is incapable of probing this candidate. We further investigate the constraints from Higgs measurements, relic abundance observation, and indirect detection.