The Poker Face of the Majoron Dark Matter Model: LUX to keV Line

We study the viability of pseudo Nambu-Goldstone bosons (Majorons) arising in see-saw models as dark matter candidates. Interestingly the stability of the Majoron as dark matter is related to the scale that sets the see-saw and leptogenesis mechanisms, while its annihilation and scattering cross section off nuclei can be set through the Higgs portal. For $\mathcal{O}(GeV) - \mathcal{O}(TeV)$ Majorons, we compute observables such as the abundance, scattering cross section, Higgs invisible decay width, and emission lines and compare with current data in order to outline the excluded versus still viable parameter space regions. We conclude that the simplest Majoron dark matter models coupling through the Higgs portal, except at the Higgs resonance, are excluded by current direct detection data for Majorons lighter than $225$~GeV and future runnings are expected to rule out decisively the 1GeV-1TeV window. Lastly, we point out that light keV-scale Majorons whose relic density is set by thermal freeze-in from sterile neutrinos can account for the keV line observed by XMM-Newton observatory in the spectrum of 73 galaxy clusters, within a see-saw model with a triplet Higgs.