Multi-azimuthal-angle effects in self-induced supernova neutrino flavor
  conversions without axial symmetry
  The flavor evolution of neutrinos emitted by a supernova (SN) core is
strongly affected by the refractive effects associated with the
neutrino-neutrino interactions in the deepest stellar regions. Till now, all
numerical studies have assumed the axial symmetry for the "multi-angle effects"
associated with the neutrino-neutrino interactions. Recently, it has been
pointed out in \cite{Raffelt:2013rqa} that removing this assumption, a new
multi-azimuthal-angle (MAA) instability would emerge in the flavor evolution of
the dense SN neutrino gas in addition to the one caused by multi-zenith-angle
(MZA) effects. Inspired by this result, for the first time we numerically solve
the non-linear neutrino propagation equations in SN, introducing the azimuthal
angle as angular variable in addition to the usual zenith angle. We consider
simple energy spectra with an excess of \nu_e over anti-\nu_e. In these cases,
we find that even starting with a complete axial symmetric neutrino emission,
the MAA effects would lead to significant flavor conversions in normal mass
hierarchy, in cases otherwise stable under the only MZA effects. The final
outcome of the flavor conversions, triggered by the MAA instability, depends on
the initial asymmetry between \nu_e and anti-\nu_e spectra. If it is
sufficiently large, final spectra would show an ordered behavior with spectral
swaps and splits. Conversely, for small flavor asymmetries flavor decoherence
among angular modes develops, affecting the flavor evolution also in inverted
mass hierarchy.
