Exact formula of probability and CP violation for neutrino oscillations in matter

Abstract

Within the framework of the standard three neutrino scenario, we derive an exact and simple formula of the oscillation probability P (ν e → ν µ ) in constant matter by using a new method. From this formula, it is found that the matter effects can be separated from the pure CP violation effects. Furthermore, the oscillation probability can be written in the form, P (ν e → ν µ ) = A cos δ + B sin δ + C, in the standard parametrization without any approximation. We also demonstrate that the approximate formula in high-energy can be easily reproduced from this as an example. *

In situdetermination of Earth matter density in a neutrino factory

“…We used the formula (5) but with the exact expression of the oscillation probability [44] to compute the number of events with suitable modification of the range of integration over neutrino energy. In our analysis in this paper we use only the signal events by the charged current (CC) reaction.…”

Supernova constraints on neutrino oscillation and EoS for proto-neutron star

“…Since supernova neutrino temperatures for ν μ,τ andν μ,τ are the same, any observables which arise from the neutrino oscillation do not depend on δ CP [24,25]. Therefore, the supernova nucleosynthesis is only sensitive to θ 13 and the mass hierarchy.…”

Why is the neutrino oscillation formula expanded in Δm 21 2 /Δm 31 2 still accurate near the solar resonance in matter?

“…This is important considering that simulation of LBL experiments and performing χ 2 -fits require a fast and simple method to compute a large number of oscillation probabilities. Therefore even though the numerical calculation is always viable, there are still many studies on analytic approximation formulae for neutrino oscillation in matter [13,[30][31][32][33][34][35][36][37][38][39][40][41].…”