Dark matter production from Goldstone boson interactions and implications for direct searches and dark radiation

The stability of the dark matter particle could be attributed to the remnant $Z_2$ symmetry that arises from the spontaneous breaking of a global U(1) symmetry. This plausible scenario contains a Goldstone boson which, as recently shown by Weinberg, is a strong candidate for dark radiation. We show in this paper that this Goldstone boson, together with the CP-even scalar associated to the spontaneous breaking of the global U(1) symmetry, plays a central role in the dark matter production. Besides, the mixing of the CP-even scalar with the Standard Model Higgs boson leads to novel Higgs decay channels and to interactions with nucleons, thus opening the possibility of probing this scenario at the LHC and in direct dark matter search experiments. We carefully analyze the latter possibility and we show that there are good prospects to observe a signal at the future experiments LUX and XENON1T provided the dark matter particle was produced thermally and has a mass larger than ~25 GeV.