Neutrino self-interactions

We propose a theory that equips the active neutrinos with interactions among themselves that are at least 3 orders of magnitude stronger than the weak interaction. We introduce an Abelian gauge group U(1)(X) with vacuum expectation value v(x) less than or similar to O(100 MeV). An asymmetric mass matrix implements the active neutrinos as massless mass eigenstates carrying "effective" charges. To stabilize v(x), supersymmetry breaking is mediated via loops to the additional sector with the only exception of xHiggs terms. No Standard Model interaction eigenstate carries U(1)(X) charge. Thus, the dark photon's kinetic mixing is two-loop suppressed. With only simple and generic values of dimensionless parameters, our theory might explain the highenergy neutrino spectrum observed by IceCube including the PeV neutrinos. We comment on the imposing opportunity to incorporate a self-interacting dark matter candidate.