Non-adiabatic Level Crossing in Resonant Neutrino Oscillations

TL;DR

This paper derives an analytic expression for electron neutrino detection probability in resonant oscillation regions, accounting for non-adiabatic effects, and applies it to solar interior oscillations.

Contribution

It provides a new analytic formula for neutrino transition probabilities considering non-adiabatic effects in resonant regions.

Findings

Derived a simple expression for neutrino detection probability.

Applied the formula to solar interior resonance oscillations.

Validated the approach with existing models.

Abstract

Analytic results are presented for the probability of detecting an electron neutrino after passage through a resonant oscillation region. If the electron neutrino is produced far above the resonance density, this probability is simply given by $\langle \,P_{\nu_e} \, \rangle \approx \sin^2 \theta_0+ P_\text{x} \cos 2 \theta_0$, where $\theta_0$ is the vacuum mixing angle. The probability is averaged over the production as well as the detection positions of the neutrino and $P_\text{x} $ is the Landau-Zener transition probability between adiabatic states. Finally, this result is applied to resonance oscillations within the solar interior.