[Paper Review] OPERA, SN1987a and energy dependence of superluminal neutrino velocity

N. D. Hari Dass|arXiv (Cornell University)|Oct 3, 2011

Neutrino Physics Research27 references15 citations

TL;DR

This paper investigates the energy dependence of superluminal neutrino velocities reported by the OPERA collaboration, reconciling them with SN1987a neutrino arrival time data. It proposes a smooth interpolation suggesting a fourth-power energy dependence for δv/c near supernova energies, which remains consistent with both OPERA's 28.1 GeV data and SN1987a's 12-second clustering, while showing that energy-independent or linearly offset velocity models fit OPERA data well near its energy scale.

ABSTRACT

This is a brief note discussing the energy dependence of superluminal neutrino velocities recently claimed by OPERA [1,2]. The analysis is based on the data provided there on this issue, as well as on consistency with neutrino data from SN1987a as recorded by the Kamioka detector [3]. It is seen that it is quite difficult to reconcile OPERA with SN1987a. The so called Coleman- Glashow dispersion relations do not do that well, if applied at all neutrino energies. The so called quantum gravity inspired dispersion relations perform far worse. Near OPERA energies both an energy-independent velocity, as well as a linear energy dependence with an offset that is comparable in value to the observed δv by OPERA at 28.1 GeV works very well. Our analysis shows that precision arrival time data from SN1987a still allow for superluminal behaviour for supernova neutrinos. A smooth interpolation is given that reconciles OPERA and SN1987a quite well. It suggests a fourth power energy dependence for δv of supernova neutrinos. This behaviour is insensitive to whether the velocities are energy-independent, or linearly dependent on energy, near OPERA scale of energies. Suggestions are made for experimental checks for these relations.

Motivation & Objective

• To assess the consistency of OPERA's reported superluminal neutrino velocities with the timing constraints from SN1987a neutrino detection.
• To evaluate the viability of various energy-dependent dispersion relations—particularly Coleman-Glashow and quantum gravity-inspired models—against both OPERA and SN1987a data.
• To propose a phenomenological interpolation model that reconciles OPERA's energy-dependent velocity measurements with the upper limits from SN1987a.
• To suggest experimental tests for the proposed energy dependence, including measurements at different energies and baseline lengths.
• To explore the implications for neutrino propagation, oscillation models, and the foundational principles of relativity if superluminal velocities are confirmed.

Proposed method

• Analyzes OPERA's reported δt values at 13.9, 28.1, and 42.9 GeV to infer energy dependence of δv/c.
• Applies SN1987a neutrino arrival time data (12-second clustering) to constrain possible superluminal velocities at ~10 MeV energies.
• Tests the performance of Coleman-Glashow and quantum gravity-inspired dispersion relations, finding them inadequate for reconciling both datasets.
• Performs a linear fit with an offset to OPERA data alone, yielding a mass scale of 5×10³ TeV and an intercept of 2.0×10⁻⁵, which fits well within OPERA's energy range.
• Constructs a smooth interpolation function between the OPERA-scale linear behavior and SN1987a limits, leading to a proposed E⁴ dependence for δv/c.
• Derives a phenomenological formula: δβ = δβ_OP × (E_GeV² / (E_GeV² + 1.0))², which interpolates between OPERA and SN1987a constraints.

Experimental results

Research questions

• RQ1 Can the energy dependence of superluminal neutrino velocities reported by OPERA be reconciled with the timing constraints from SN1987a?
• RQ2 Do Coleman-Glashow or quantum gravity-inspired dispersion relations adequately describe both OPERA and SN1987a data?
• RQ3 Is there a phenomenological energy dependence for δv/c that simultaneously fits OPERA data and remains consistent with SN1987a arrival time limits?
• RQ4 What are the implications for neutrino oscillation models if δv/c depends on energy in a non-trivial way?
• RQ5 How can future experiments test the proposed E⁴ dependence of δv/c near supernova energies?

Key findings

• The Coleman-Glashow dispersion relation fails to reconcile OPERA and SN1987a data, particularly due to its predicted energy dependence.
• Quantum gravity-inspired dispersion relations perform significantly worse than the proposed interpolation model.
• A linear fit with an offset to OPERA data alone yields a mass scale of 5×10³ TeV and an intercept of 2.0×10⁻⁵, which fits the data very well.
• The proposed interpolation model predicts a fourth-power energy dependence (E⁴) for δv/c near supernova energies, which is consistent with both OPERA and SN1987a.
• At 1 GeV, the model predicts δv/c to be only 1/5 of the value reported by OPERA at 28.1 GeV, indicating a strong energy dependence at higher energies.
• SN1987a arrival time limits still allow for superluminal neutrino velocities, meaning the data do not rule out such behavior, contrary to some assumptions.