[Paper Review] Flavor sensitivity to theta_13 and the mass hierarchy for neutrinos from solar WIMP annihilation

Ralf Lehnert, T. Weiler|arXiv (Cornell University)|Feb 12, 2010

Dark Matter and Cosmic Phenomena3 citations

TL;DR

This paper demonstrates that neutrinos from solar WIMP annihilation in the 0.3–10 GeV energy range exhibit strong flavor sensitivity to the neutrino mixing angle 𝜃₁₃ and the sign of Δm²₃₂ (mass hierarchy) due to adiabatic-to-nonadiabatic transitions at the second matter resonance. With as few as 200 events in this 'sweet region,' future large-volume detectors could probe 𝜃₁₃ down to 0.5°, distinguish mass hierarchy, and identify dominant WIMP annihilation modes.

ABSTRACT

The effect of the higher-energy 2nd resonance and the associated adiabatic-to-nonadiabatic transition on neutrino propagation in solar matter is presented. For WIMP-annihilation neutrinos injected with energies in the "sweet region" between 300 MeV and 10 GeV at the Sun's center, a significant and revealing dependence on the neutrino mass hierarchy and the mixing angle theta_13 down to 0.5 degrees is found in the flavor ratios arriving at Earth. In addition, the amplification of flavor ratios in the sweet region allows a better discrimination among possible annihilation modes of the solar dark matter. Under mild assumptions on WIMP properties, it is estimated that 200 neutrino events in the sweet region would be required for inferences of theta_13, the mass hierarchy, and the dominant WIMP annihilation mode. Future large-volume, low-energy neutrino detectors are likely needed if the measurement is to be made.

Motivation & Objective

• To investigate the sensitivity of WIMP-annihilation neutrinos to the neutrino mixing angle 𝜃₁₃ and mass hierarchy in the 0.3–10 GeV energy range.
• To explore how the adiabatic-to-nonadiabatic transition at the second matter resonance in the Sun's core affects flavor ratios at Earth.
• To assess the detectability of these effects with future low-energy, large-volume neutrino detectors.
• To enable discrimination among dominant WIMP annihilation modes through flavor ratio analysis.
• To quantify the number of neutrino events required for meaningful inference of 𝜃₁₃, mass hierarchy, and annihilation modes.

Proposed method

• Modeling neutrino propagation through the Sun using the matter-coupled mixing matrix 𝑈ₘ, which accounts for the MSW effect at the second resonance.
• Applying the density matrix formalism to compute flavor evolution across the adiabatic-to-nonadiabatic transition at the second resonance.
• Using tribimaximal mixing parameters to compute the relative changes in flavor ratios (𝑊_𝜇/𝑊_𝑒) across the resonance for both normal and inverted mass hierarchies.
• Calculating the differential flavor fluxes at Earth via the transformation 𝑊_𝛼 = 𝑈 𝑃 𝑈ᵀ_𝑚(𝑟=0)𝑤_𝛼, where 𝑤_𝛼 are production flavor ratios at the Sun's center.
• Estimating the required number of detectable events (200 in the sweet region) to infer 𝜃₁₃, mass hierarchy, and dominant WIMP annihilation modes.
• Analyzing the impact of detector type, particularly magnetized vs. unmagnetized, on distinguishing neutrino and antineutrino events to enhance signal sensitivity.

Experimental results

Research questions

• RQ1 Can the adiabatic-to-nonadiabatic transition at the second matter resonance in the Sun’s core provide a measurable signal for small 𝜃₁₃ values?
• RQ2 Does the sign of Δm²₃₂ (normal vs. inverted mass hierarchy) lead to distinct flavor ratio patterns in WIMP-annihilation neutrinos at Earth?
• RQ3 What is the minimum number of detectable neutrino events required to infer 𝜃₁₃, mass hierarchy, and dominant WIMP annihilation modes?
• RQ4 How does the flavor ratio evolution in the 0.3–10 GeV range differ between neutrinos and antineutrinos under varying mass hierarchies?
• RQ5 To what extent can future large-volume, low-energy neutrino detectors resolve the resonance-induced flavor structure in WIMP-annihilation neutrinos?

Key findings

• The second matter resonance at ~0.2 GeV energy produces a strong, non-adiabatic signal for nonzero 𝜃₁₃, with sensitivity down to 0.5°, even for small mixing angles.
• The adiabatic-to-nonadiabatic transition at the second resonance is significantly more sensitive to 𝜃₁₃ than the first resonance due to the larger enhancement of a small mixing angle to 45°.
• The flavor ratio change across the second resonance is approximately twice as large for antineutrinos in the inverted mass hierarchy compared to neutrinos in the normal hierarchy, due to differing mass eigenstate assignments.
• A minimum of 200 detectable neutrino events in the 0.3–10 GeV 'sweet region' is estimated to be sufficient for simultaneous inference of 𝜃₁₃, mass hierarchy, and dominant WIMP annihilation mode.
• The signal is most effectively probed by large-volume, low-energy neutrino detectors, with magnetized detectors offering a factor-of-two advantage in signal discrimination by separating neutrino and antineutrino events.
• The resonance structure does not alter the total neutrino spectrum but strongly modifies the flavor distribution, making flavor ratios a key observable for probing neutrino parameters.