[Paper Review] Shadowing Neutrino Mass Hierarchy with Lorentz Invariance Violation

H. Jurkovich, Pedro Pasquini+1 more|arXiv (Cornell University)|Jun 22, 2018

Noncommutative and Quantum Gravity Theories3 citations

TL;DR

This paper investigates how Lorentz Invariance Violation (LIV) in neutrino propagation—specifically via dimension-4 to dimension-6 operators—affects the sensitivity of long-baseline experiments like DUNE and T2K to the neutrino mass hierarchy. Using a phenomenological Lagrangian and effective Hamiltonian formalism, it shows that a dimension-4 LIV parameter can significantly reduce DUNE’s ability to distinguish between normal and inverted mass hierarchies, while higher-dimensional LIV effects have negligible impact.

ABSTRACT

The effects of Lorentz Invariance Violation(LIV) operators up to dimension 6 in long baseline neutrino experiments are discussed, in specific for DUNE and T2K. A phenomenological Lagrangian is proposed followed by a computation of the effective Hamiltonian of neutrino propagation in matter for mass eigenstates. It is shown that the simplest dimension 4 Lorentz violation parameter can decrease DUNE sensitivity to neutrino mass hierarchy. Also, a $χ^2$ analysis is performed to obtain the expected long-baseline constraints to the LIV operators up to dimension 6.

Motivation & Objective

• To assess the impact of Lorentz Invariance Violation (LIV) on the sensitivity of long-baseline neutrino experiments to the neutrino mass hierarchy.
• To construct a phenomenological Lagrangian incorporating LIV operators up to dimension 6 and derive the corresponding effective Hamiltonian for neutrino propagation in matter.
• To evaluate how LIV parameters—particularly dimension-4—disturb the standard three-neutrino oscillation framework and degrade mass hierarchy sensitivity.
• To simulate experimental constraints on LIV parameters using DUNE and T2K configurations via a χ²-likelihood analysis.
• To provide conservative 90% confidence level bounds on LIV parameters of dimensions 4, 5, and 6 for both DUNE and T2K.

Proposed method

• Formalism is developed using a higher-derivative LIV Lagrangian with terms up to dimension 6, modifying the neutrino energy-momentum dispersion relation.
• The effective Hamiltonian is derived in the mass basis, incorporating LIV corrections as energy-dependent perturbations: $ H_{\text{LIV}} \propto \text{diag}(0, \Delta\gamma^{(d)}_{21}E^{d-3}, \Delta\gamma^{(d)}_{31}E^{d-3}) $.
• Analytical expressions for neutrino oscillation probabilities are computed using perturbation theory, with corrections scaling as $ \eta \sim E^{d-3} $, emphasizing energy dependence.
• A modified version of the Globes probability engine is used to simulate event rates in DUNE and T2K, incorporating systematic errors in signal and background normalization.
• A $ \chi^2 $-based sensitivity analysis is performed, minimizing over oscillation parameters, normalization errors (a, b), and standard model parameters for fixed true $ \delta_{\text{CP}} $ and test LIV values.
• Constraints are extracted at 90% confidence level by scanning over $ \gamma^{(d)} $, with results reported for both DUNE and T2K under normal hierarchy assumption.

Experimental results

Research questions

• RQ1 To what extent does a dimension-4 LIV operator degrade DUNE’s sensitivity to the neutrino mass hierarchy?
• RQ2 How do LIV operators of dimensions 5 and 6 affect the mass hierarchy sensitivity compared to dimension-4?
• RQ3 What are the expected 90% confidence level constraints on LIV parameters of dimensions 4, 5, and 6 from DUNE and T2K experiments?
• RQ4 How does the energy and baseline difference between DUNE and T2K influence their relative sensitivity to LIV effects?
• RQ5 Can the inclusion of LIV in the Hamiltonian lead to observable deviations in neutrino oscillation probabilities that could mimic or mask the true mass hierarchy?

Key findings

• The dimension-4 LIV parameter significantly reduces DUNE’s sensitivity to the neutrino mass hierarchy, as shown by a visible degradation in the $ \chi^2 $-based sensitivity curve in Fig. 1.
• Operators of dimension 5 and 6 have negligible impact on mass hierarchy sensitivity, as their effects are suppressed by higher powers of energy and do not alter the hierarchy determination capability.
• DUNE achieves a conservative 90% confidence level upper limit of $ |\gamma^{(4)}| \leq 8 \times 10^{-24} $, while T2K constrains it to $ 4.1 \times 10^{-21} $, indicating DUNE’s superior sensitivity by three orders of magnitude.
• For dimension-5 LIV, DUNE constrains $ |\gamma^{(5)}| \leq 6.7 \times 10^{-34} \, \text{GeV}^{-1} $, and for dimension-6, $ |\gamma^{(6)}| \leq 1.2 \times 10^{-44} \, \text{GeV}^{-2} $, showing strong suppression with increasing dimension.
• The energy dependence $ \sim E^{d-3} $ makes higher-energy experiments like DUNE (2.5 GeV) more sensitive to higher-dimensional LIV effects than lower-energy experiments like T2K (0.6 GeV).
• The true value of $ \delta_{\text{CP}} $ has a small influence on the LIV parameter constraints, indicating robustness of the sensitivity analysis across different CP phases.