Breaking the symmetries in self-induced flavor conversions of neutrino beams from a ring

Self-induced flavor conversions of supernova neutrinos have been characterized in the spherically symmetric bulb model, reducing the neutrino evolution to a one-dimensional problem along a radial direction. We lift this assumption, presenting a two-dimensional toy model where neutrino beams are launched in many different directions from a ring. We find that self-interacting neutrinos spontaneously break the spatial symmetries of this model. As a result the flavor content and the lepton number of the neutrino gas would acquire sizable direction-dependent variations, breaking the coherent behavior found in the symmetric case. This finding would suggest that the previous results of the self-induced flavor evolution obtained in one-dimensional models should be critically reexamined.