[Paper Review] Day-Night and Energy Variations for Maximal Neutrino Mixing Angles

Alan H. Guth, Lisa Randall+1 more|arXiv (Cornell University)|Mar 24, 1999

Neutrino Physics Research4 citations

TL;DR

This paper demonstrates that maximal solar neutrino mixing (θ₁₂ = 45°) does not eliminate the day-night effect, contrary to prior assumptions. Even with maximal mixing, neutrino regeneration in Earth’s matter leads to coherent interference, producing a measurable day-night asymmetry with energy-dependent suppression, enabling discrimination among large mixing angle solutions via sensitive energy-resolved measurements.

ABSTRACT

It has been stated in the literature that the case of maximal mixing angle for u_e leads to no day-night effect for solar neutrinos and an energy independent flux suppression of 1/2. While the case of maximal mixing angle and \Delta m^2 in the MSW range does lead to suppression of the electron neutrinos reaching the earth from the sun by P_S=1/2, the situation is different for neutrinos that have passed through the earth. We make the pedagogical point that, just as with smaller mixing angles, the earth regenerates the | u_1> state from the predominantly | u_2 > state reaching the earth, leading to coherent interference effects. This regeneration can lead to a day-night effect and an energy dependence of the suppression of solar electron neutrinos, even for the case of maximal mixing. For large mixing angles, the energy dependence of the day-night asymmetry depends heavily on Delta m^2. With a sufficiently sensitive measurement of the day-night effect, this energy dependence could be used to distinguish among the large mixing angle solutions of the solar neutrino problem.

Motivation & Objective

• To challenge the long-standing claim that maximal mixing eliminates the day-night effect in solar neutrino oscillations.
• To investigate how neutrino regeneration in Earth’s matter affects the survival probability of electron neutrinos when mixing is maximal.
• To explore whether energy-dependent variations in the day-night asymmetry can distinguish between different large mixing angle solutions.
• To clarify the role of Δm² in shaping the energy dependence of the day-night effect under maximal mixing.
• To provide a pedagogical clarification of coherent interference effects in neutrino oscillations through matter for the maximal mixing case.

Proposed method

• Analyzes neutrino propagation through Earth’s matter using the standard three-flavor oscillation framework with matter potential.
• Applies the MSW (Mikheyev-Smirnov-Wolfenstein) formalism to compute electron neutrino survival probabilities for day and night conditions.
• Evaluates the day-night asymmetry as a function of neutrino energy and Δm² for the maximal mixing case (θ₁₂ = 45°).
• Considers coherent interference between the |u₁⟩ and |u₂⟩ states during neutrino passage through Earth, showing regeneration of the |u₁⟩ component.
• Compares the energy dependence of the day-night asymmetry under maximal mixing to that of smaller mixing angles.
• Uses numerical evaluation of oscillation probabilities to demonstrate that suppression is not energy-independent when Earth matter effects are included.

Experimental results

Research questions

• RQ1 Does maximal mixing (θ₁₂ = 45°) truly eliminate the day-night effect in solar neutrino oscillations?
• RQ2 How does neutrino regeneration in Earth’s matter affect the survival probability of electron neutrinos when mixing is maximal?
• RQ3 What is the energy dependence of the day-night asymmetry for maximal mixing, and how does it vary with Δm²?
• RQ4 Can the energy-resolved day-night asymmetry distinguish between different large mixing angle solutions?
• RQ5 What role does coherent interference between |u₁⟩ and |u₂⟩ states play in generating the day-night effect under maximal mixing?

Key findings

• The assumption that maximal mixing leads to no day-night effect is incorrect; coherent interference from Earth regeneration produces a measurable asymmetry.
• Even with maximal mixing, the suppression of solar electron neutrinos is not energy-independent due to matter effects in Earth.
• The day-night asymmetry exhibits a strong energy dependence that is sensitive to the value of Δm², especially for large mixing angles.
• For sufficiently sensitive detectors, measuring the energy dependence of the day-night asymmetry can distinguish among large mixing angle solutions.
• Neutrino regeneration in Earth transforms the predominantly |u₂⟩ state into a component with |u₁⟩ character, enabling interference and observable effects.
• The survival probability P(e→e) is not fixed at 1/2 in the presence of Earth matter; it varies with energy and Δm², even under maximal mixing.