Analytical Calculation of Matter Effects in Two Mass-Scale Neutrino Oscillations

Abstract

We consider three active flavor neutrino oscillations where both the masssquare differences play a role in atmospheric neutrino problem. We calculate the matter effects arising due to propagation through earth. We demonstrate that these effects improve the fit to the electron data vis-a-vis vacuum oscillations but make the fit to the muon data far worse, thus worsening the overall fit. The results of our analytical calculation verify the numerical investigations of this scheme presented earlier by Fogli et al.

Neutrino Mass Hierarchy Above GUT Scale

“…Because of the longer distance the flux NOνA is peaked at higher energy compared to that of T2K. Matter term, which is proportional to neutrino energy, causes a 25% change in P μe whereas the change in P μe of T2K is only about 10% [22]. If 31 positive P μe increases, whereas if 31 is negative it decreases [23].…”