Supernova neutrino oscillations: Adiabaticity improvement by Majoron fields

If the lepton numbers are associated with global symmetries spontaneously broken at a scale below 1 TeV, neutrino oscillations in supernovae produce classic Majoron fields that perturb the neutrino propagation itself and may change the oscillation patterns in the periods of largest $\nu$ fluxes. The impact of the Majoron fields on the same transitions as $\nu_{e}\to \nu_{X}$ that presumably occur in the Sun is studied in the case of the non-adiabatic MSW solution. It is shown how the back reaction of the Majoron fields may improve the adiabaticity of these oscillations in a supernova environment which has implications on the outgoing $\nu_{e}$ spectrum.