[Paper Review] Mass-dependent Lorentz Violation and Neutrino Velocity

Miao Li, Tower Wang|arXiv (Cornell University)|Sep 27, 2011

Noncommutative and Quantum Gravity Theories17 references17 citations

TL;DR

This paper proposes a mass-dependent Lorentz violation model to reconcile conflicting neutrino velocity measurements, where neutrino speed exceeds light speed in high-energy experiments (MINOS, OPERA) but not in low-energy ones (SN 1987A, Fermilab). By allowing the effective neutrino mass to run with energy via a non-universal, flavor-sensitive deformation of the mass-energy relation, the model explains superluminal behavior at GeV energies while remaining consistent with stringent SN 1987A constraints.

ABSTRACT

Motivated by a recent and several earlier measurement results of the neutrino velocity, we attempt to resolve the apparent discrepancies between them from the viewpoint of mass-energy relation in special relativity. It is argued that a complicated tachyonic neutrino model or a mass-dependent Lorentz violation theory can do this job.

Motivation & Objective

• To resolve discrepancies between superluminal neutrino velocity measurements (OPERA, MINOS) and subluminal results (Fermilab, SN 1987A) within a relativistic framework.
• To investigate whether a tachyonic neutrino model with energy-dependent mass can explain the observed velocity anomalies.
• To explore a modified mass-energy relation where Lorentz violation depends on particle species and energy scale.
• To assess the viability of discriminative (species-sensitive) models over democratic (universal) models in explaining the data.

Proposed method

• Introduces a modified mass-energy relation via a deformation function f(λ) that breaks Lorentz symmetry in a mass-dependent way.
• Analyzes a tachyonic neutrino model with negative squared mass, showing it fails to reconcile all data without energy-dependent mass running.
• Proposes a running effective neutrino mass: m²_ν(E) = m²_ν(0) - (E²/c⁴) × δ_ν × exp[ -ε_ν (E²_cν/E² + E²/E²_cν) ], allowing transition between ordinary and tachyonic behavior.
• Classifies models into democratic (universal) and discriminative (species-specific) types, favoring the latter due to better consistency with experimental constraints.
• Uses phenomenological fitting of model parameters to match the four key neutrino velocity measurements from literature.
• Applies the model to explain how neutrinos can be superluminal at ~17 GeV (OPERA) and ~3 GeV (MINOS) while remaining subluminal at ~10 MeV (SN 1987A).

Experimental results

Research questions

• RQ1 Can a tachyonic neutrino model with fixed mass reconcile the observed superluminal velocities in OPERA and MINOS with the subluminal constraint from SN 1987A?
• RQ2 How can a mass-dependent Lorentz violation scenario explain the energy, flavor, and baseline dependence of neutrino velocity measurements?
• RQ3 Is a universal (democratic) Lorentz violation model viable, or are species-specific (discriminative) models necessary to satisfy experimental constraints?
• RQ4 What functional form of running neutrino mass can reproduce the observed velocity anomalies while preserving consistency with SN 1987A data?
• RQ5 What are the physical implications of a non-universal, energy-dependent deformation of the mass-energy relation in special relativity?

Key findings

• A standard tachyonic neutrino model with fixed negative mass squared fails to reconcile all experimental data, particularly due to the stringent SN 1987A constraint.
• The model with a running effective neutrino mass, m²_ν(E) = m²_ν(0) - (E²/c⁴) × δ_ν × exp[ -ε_ν (E²_cν/E² + E²/E²_cν) ], successfully fits the OPERA and MINOS data with parameters m_ν(0) = 10⁻¹ eV/c², ε_ν = 0.01, δ_ν = 5×10⁻⁵, and E_cν = 5 GeV.
• The running mass model predicts that neutrinos transition from ordinary particles to tachyons and back as energy increases, crossing zero squared mass near E_cν ≈ 5 GeV.
• The model explains superluminal neutrino velocities at GeV energies (OPERA: (v−c)/c ≈ 2.48×10⁻⁵, MINOS: (v−c)/c ≈ 5.1×10⁻⁵) while remaining consistent with the SN 1987A bound of |v−c|/c < 2×10⁻⁹.
• Discriminative models—where Lorentz violation depends on particle species—are more viable than democratic models, as they allow independent tuning for different particles.
• The model suggests that Lorentz violation may arise from matter field dynamics rather than spacetime structure, offering a phenomenologically consistent alternative to fundamental symmetry breaking.