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Neutrino Self-Interactions

We propose a theory that equips the active neutrinos with interactions among themselves that are at least three orders of magnitude stronger than the weak interaction. We introduce an Abelian gauge group $U(1)_x$ with vacuum expectation value $v_x \lesssim \mathcal{O}(100 \textrm{ MeV})$. 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 high-energy neutrino spectrum observed by IceCube including the PeV neutrinos. We comment on the imposing opportunity to incorporate a self-interacting dark matter candidate.