Some consequences of the Majoron being the dark radiation

We discuss some phenomenological consequences in a scenario where a singlet Majoron plays the role of dark radiation. We study the interrelations between neutrino mass generation and the scalar potential arising from this identification. We find the extra scalar has to be light with a mass at or below the GeV level. The mixing of this scalar with the Standard Model Higgs impacts low energy phenomena such as the muonic hydrogen Lamb shift and muon anomalous magnetic moment. Demanding that the light scalar solves the puzzle in the muon magnetic moment requires the scalar to be lighter still with mass at or below the 10 MeV level. The cross-sections for the production of heavy neutrinos at LHC14 are also given.