Conformal neutrinos: An alternative to the see-saw mechanism

We analyze a scenario where the right-handed neutrinos make part of a strongly coupled conformal field theory and acquire an anomalous dimension γ<1 at a large scale Λ. Their Yukawa couplings to the Higgs become irrelevant at the fixed point and they are suppressed at low scales giving rise naturally to a small (sub-meV) Dirac neutrino mass which breaks the conformal invariance. We derive an upper bound on γ from loop-induced flavor changing neutral currents. Neutrino Yukawa couplings can be sizable at electroweak scales and therefore the invisible decay of the Higgs in the neutrino channel can be comparable to the cc¯ and ττ¯ modes and predict interesting Higgs phenomenology. If lepton number is violated in the conformal theory an irrelevant Majorana mass operator for right-handed neutrinos appears for γ>1/2 giving rise to an inverse see-saw mechanism. In this case light sterile neutrinos do appear and neutrino oscillation experiments are able to probe our model.