Non-adiabatic Level Crossing in Resonant Neutrino Oscillations (2212.06978v1)

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.

• The paper presents an analytical derivation of the electron neutrino detection probability by modeling resonant oscillations with non-adiabatic level crossings.
• It employs a Landau-Zener method with a linear electron density assumption near resonance to quantify the transition probability Pₓ.
• The findings establish parameter boundaries for mixing angles and mass differences that help explain the solar neutrino deficit observed in experiments.

Non-adiabatic Level Crossing in Resonant Neutrino Oscillations

The paper "Non-adiabatic Level Crossing in Resonant Neutrino Oscillations" by Stephen J. Parke elaborates on the analytical formulation of electron neutrino detection probability in the context of resonant oscillation regions, particularly within the sun. The analysis hinges on the resonant conversion of electron neutrinos into muon neutrinos as facilitated by the Mikheyev-Smirnov-Wolfenstein (MSW) effect, which provides a plausible solution to the long-standing solar neutrino problem. This manuscript focuses on the calculation of neutrino transition probabilities when they experience non-adiabatic level crossings and their implications for solar neutrino observations.

Analytical Formulation and Key Results

The central objective of this research is to derive an analytical expression for the probability $P_{\nu_e}$ of detecting electron neutrinos after they propagate through resonant regions. The probability approximates $$\langle P_{\nu_e} \rangle \approx \sin^2 \theta_0 + P_\text{x} \cos 2 \theta_0$$, where $\theta_0$ signifies the vacuum mixing angle and $P_\text{x}$ denotes the Landau-Zener probability of level crossing. The analysis assumes neutrinos are produced above resonance, transitioning through resonance, and ultimately detected in vacuum conditions.

In formulating $P_\text{x}$, Parke simplifies the matter by assuming a linear variation of the electron density near resonance, making the problem amenable to the Landau-Zener approach. The derived expression highlights that $P_\text{x}$ is largely influenced by the electron density gradient at resonance and the neutrino mixing parameters.

Implications for Solar Neutrino Observations

The implications of this analysis are significant in the parameter space associated with the solar neutrino problem. For regions where neutrinos cross the resonance, the non-adiabatic transitions influence detection probabilities, hinting at the conditions under which the MSW effect can explain the solar neutrino deficit observed in experiments such as the Homestake experiment. Probabilities are calculated within various regimes of resonance crossing, providing parameter boundaries—mass squared differences and mixing angles—that align with the expected solar neutrino capture rates.

Future Directions

While the paper provides robust predictions and clarifies resonant neutrino oscillation theory, further detailed experimental verification remains crucial. The sensitivity of neutrino transition probabilities to solar density profiles suggests that future solar neutrino detectors, with improved energy resolution and sensitivity, may be able to validate these results more extensively. Moreover, precision measurements may refine theoretical neutrino models and enhance our understanding of non-adiabatic transitions in complex solar environments.

This work substantively contributes to the field by offering a lucid analytical framework for non-adiabatic transitions in resonant neutrino oscillations and creates an avenue for reconciling theoretical predictions with empirical observations. Expanding this framework to involve multiple resonance scenarios and incorporating data from diverse neutrino sources can progressively elucidate the dynamics of neutrino transformation processes in astrophysical settings.