Effective potential for highly relativistic neutrinos in a weakly magnetized medium and their oscillation

We have calculated the effective potential experienced by highly relativistic neutrinos in a weakly magnetized electron–positron plasma, where a momentum-dependent finite-width correction to the propagator of W is considered to account for the threshold effect. Magnetars are believed to be sources of TeV–PeV neutrinos which are produced due to photomeson and proton–proton interactions in their atmosphere. We have studied the resonant-oscillation process ν _e ↔ ν _μ,τ of the highly relativistic neutrinos in the atmosphere of SGR 1806-20, which is a magnetar. It is shown that, for high-energy neutrinos propagating within the magnetar atmosphere, the resonance condition can never be satisfied. On the other hand, if GeV neutrinos are produced deep inside the magnetar atmosphere, where the temperature is about 50 keV or more, then these neutrinos can undergo resonant oscillation.