Triggering collective oscillations by three-flavor effects

Collective flavor transformations in supernovae, caused by neutrino-neutrino interactions, are essentially a two-flavor phenomenon driven by the atmospheric mass difference and the small mixing angle {theta}{sub 13}. In the two-flavor approximation, the initial evolution depends logarithmically on {theta}{sub 13} and the system remains trapped in an unstable fixed point for {theta}{sub 13}=0. However, any effect breaking exact {nu}{sub {mu}-{nu}{tau}}equivalence triggers the conversion. Such three-flavor perturbations include radiative corrections to weak interactions, small differences between the {nu}{sub {mu}}and {nu}{sub {tau}}fluxes, or nonstandard interactions. Therefore, extremely small values of {theta}{sub 13} are in practice equivalent, the fate of the system depending only on the neutrino spectra and their mass ordering.