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 1/2<\gamma<1 at a large scale \Lambda. Their Yukawa couplings to the Higgs become irrelevant at the fixed point and are suppressed at low scales giving rise naturally to a small (sub-meV) Dirac neutrino mass which breaks the conformal invariance. Similarly the Majorana mass operator becomes irrelevant at the fixed point (not perturbing the conformal theory) and gives rise to a tiny Majorana mass at the scale of conformal breaking. However the effective Majorana mass can be sizable enough at the scale of neutrinoless double \beta-decay experiments to provide positive signals. We also derive an upper bound on \gamma from loop-induced flavor changing neutral currents. Finally 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 c\bar c and \tau\bar\tau modes and predict interesting Higgs phenomenology.