[Paper Review] Search for Lorentz Violation in km$^3$-Scale Neutrino Telescopes

CA Argüelles, GH Collin+3 more|arXiv (Cornell University)|Aug 9, 2016

Noncommutative and Quantum Gravity Theories2 references3 citations

TL;DR

This paper investigates Lorentz violation in high-energy neutrino oscillations using km³-scale neutrino telescopes like IceCube and ANTARES. It derives oscillation probability formulas for the νμ–ντ sector under isotropic Lorentz-violating Hamiltonians, showing that such effects could be probed at sensitivities of ~10⁻²⁴ to 10⁻³² GeV for a- and c-type terms, respectively, using atmospheric neutrino data above 1 TeV.

ABSTRACT

Kilometer$^3$-scale neutrino detectors such as IceCube, ANTARES, and the proposed Km3Net neutrino observatory in the Mediterranean have measured, and will continue to characterize, the atmospheric neutrino spectrum above 1 TeV. Such precise measurements enable us to probe new neutrino physics, in particular, those that arise from Lorentz violation. In this paper, we first relate the effective new physics hamiltonian terms with the Lorentz violating literature. Second, we calculate the oscillation probability formulas for the two-level $ν_μ-ν_τ$ sector. Finally, we comment on some of the challenges and outlook for this analysis.

Motivation & Objective

• To explore the implications of Lorentz violation in high-energy neutrino oscillations using data from km³-scale neutrino telescopes.
• To relate effective Lorentz-violating Hamiltonian terms to the Standard-Model Extension (SME) framework.
• To calculate oscillation probabilities in the νμ–ντ sector under isotropic Lorentz violation, focusing on the vacuum oscillation regime.
• To estimate the sensitivity of current and future neutrino detectors to Lorentz-violating parameters at the 10⁻²⁴ to 10⁻³² GeV scale.
• To set the stage for future data-driven searches by modeling event expectations and incorporating systematic uncertainties.

Proposed method

• Derives the effective Hamiltonian including Lorentz-violating terms from the minimal Standard-Model Extension (SME), focusing on dimension-four operators with aμβ and cλσμβ coefficients.
• Imposes isotropic Lorentz violation by restricting all Lorentz indices to time components, simplifying the Hamiltonian to H = H_std + aαβ − (4/3)Ecαβ.
• Replaces the factor −4cαβ/3 with cαβ for consistency, enabling direct comparison with oscillation probability calculations.
• Constructs the two-level Hamiltonian for the νμ–ντ system, separating vacuum and Lorentz-violating contributions, with the latter scaling as En.
• Derives the νμ survival probability using a modified mixing angle formalism, incorporating both CPT-conserving (a-term) and CPT-violating (c-term) effects.
• Introduces a rescaling parameter R and effective mixing angle Θ that depend on the magnitude and phase of Lorentz-violating parameters, enabling quantitative analysis of oscillation suppression or enhancement.

Experimental results

Research questions

• RQ1 What are the observable signatures of Lorentz violation in high-energy atmospheric neutrino oscillations as measured by km³-scale detectors?
• RQ2 How do Lorentz-violating terms in the neutrino Hamiltonian affect νμ disappearance probabilities at energies above 1 TeV?
• RQ3 What are the sensitivity limits of current and future neutrino telescopes to isotropic Lorentz-violating parameters aαβ and cαβ?
• RQ4 How do the CPT-conserving a-term and CPT-violating c-term contribute differently to oscillation probabilities in the νμ–ντ sector?
• RQ5 What are the implications of neglecting matter effects in the νμ–ντ oscillation framework under Lorentz violation?

Key findings

• The paper derives a modified νμ survival probability formula that includes both standard vacuum oscillations and Lorentz-violating contributions, with explicit dependence on the real and imaginary parts of the c-term.
• For Re(cμμ) = 10⁻²⁵ GeV, the νμ disappearance probability shows measurable deviations from standard oscillations at L/E ≈ 1000 km/TeV, indicating potential detectability.
• The sensitivity to Lorentz-violating parameters is estimated at ~10⁻²⁴ GeV for the a-term and ~10⁻³² GeV for the c-term at 1 PeV neutrino energy, based on back-of-the-envelope scaling.
• The oscillation probability is significantly modulated by the relative phase η and mixing angle ξ, which depend on the imaginary and real parts of the δμτ term.
• The simplified isotropic model allows for analytical treatment of oscillation probabilities and enables direct comparison with IceCube and ANTARES data.
• The framework sets a foundation for future data-driven searches by modeling event expectations and incorporating systematic uncertainties from atmospheric neutrino fluxes.