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On the Independent Crossing Approximation in Three Flavor Neutrino Oscillations

In dense matter like the Supernovae and at high energy, neutrinos have two points where the nonadiabatic transitions could occur. With the present values of the oscillation parameters in the standard three flavor scenario, two nonadiabatic transitions can be regarded as independent, i.e., two can be treated by the two flavor formalism separately. However, in the presence of new physics, it is not clear in general whether such independence holds. We examine this question by assuming hypothetical range of the neutrino energy and by varying the mixing angles and the mass squared differences in the standard case. We found the cases where Independent Crossing Approximation breaks down for some unrealistic range of the mass squared difference and the mixing angle. We also discuss the criterion which gives such independence.