[Paper Review] Optimization for Mass Hierarchy

John LoSecco|arXiv (Cornell University)|Jun 4, 2013

Neutrino Physics Research5 references3 citations

TL;DR

This paper proposes optimizing reactor neutrino experiments for mass hierarchy determination by minimizing baseline distance to enhance sensitivity. By analyzing oscillation phase differences at L/E ≈ 8418 m/MeV, it identifies 30 km as optimal for peak energy sensitivity, yielding a 2.3× oscillation enhancement and improved energy resolution over longer baselines.

ABSTRACT

The Delta m^2_13 oscillation frequency for reactor neutrinos differs by 6.4% between normal and inverted mass hierarchy. This frequency difference accumulates to a phase difference over distance and time. The optimal distance is when the maximum phase difference between hierarchies occurs near the peak in the observable reactor neutrino spectrum. Added citations to some related recent work.

Motivation & Objective

• To identify the optimal baseline distance for reactor antineutrino experiments to resolve the neutrino mass hierarchy.
• To minimize detector energy resolution requirements by maximizing oscillation contrast at the spectrum peak.
• To overcome limitations of long-baseline experiments that suffer from low event rates and poor energy resolution.
• To isolate the mass hierarchy-sensitive component of the oscillation probability and quantify its phase dependence.
• To provide a practical, energy-optimized strategy for future experiments using known reactor neutrino spectra and oscillation parameters.

Proposed method

• Derives the transition probability for electron antineutrino disappearance using the PMNS matrix and mass-squared differences.
• Identifies the mass hierarchy-sensitive term in the oscillation probability as proportional to sin²(2θ₁₃)cos²(θ₁₂)sin(2|Δ₃₂|)sin(2Δ₂₁).
• Calculates the difference in oscillation probability between normal and inverted hierarchies as a function of L/E.
• Locates the global maximum of |D_N - D_I| at L/E ≈ 8418 m/MeV using numerical search and phase coherence conditions.
• Evaluates energy-dependent modulation of the reactor neutrino spectrum using a 3.66 MeV peak spectrum from Double Chooz.
• Compares baseline performance at 30 km and 60 km, showing improved peak separation and phase contrast at shorter baselines.

Experimental results

Research questions

• RQ1 What baseline distance maximizes the observable phase difference between normal and inverted neutrino mass hierarchies in reactor experiments?
• RQ2 How does reducing baseline length improve energy resolution and event rate for mass hierarchy determination?
• RQ3 What is the optimal L/E ratio for maximizing the difference in oscillation probabilities between mass hierarchies?
• RQ4 How does the energy spectrum modulation affect the detectability of mass hierarchy at different baselines?
• RQ5 Can a shorter baseline provide sufficient contrast to resolve the mass hierarchy without requiring ultra-high energy resolution?

Key findings

• The optimal L/E ratio for maximum phase difference between mass hierarchies is approximately 8418 m/MeV.
• A baseline of 30 km provides a 180° phase difference at the spectrum peak (3.66 MeV), yielding a 2.3× oscillation enhancement.
• The maximum observable difference in oscillation probability between hierarchies is cos²(θ₁₂)sin²(2θ₁₃) ≈ 0.16, achievable near L/E = 8418 m/MeV.
• Shorter baselines (e.g., 24.9 km) still provide strong separation, with 90% of the maximum contrast achievable at L/E = 5861 m/MeV.
• Operating near the 3.66 MeV peak of the reactor spectrum ensures broad sensitivity across the observable energy range.
• A 30 km baseline increases event rates by a factor of ~2 compared to the solar minimum baseline, due to reduced suppression from Δm²₁₂ oscillations.