Discussion on Lorentz Invariance Violation of Non-commutative Field Theory and Neutrino Oscillation

TL;DR

This paper critically examines the possibility of explaining massless neutrino oscillations through Lorentz invariance violation in non-commutative field theory, concluding that such explanations are inconsistent with current experimental data and theoretical conditions.

Contribution

It demonstrates that previous models of neutrino oscillation via Lorentz invariance violation in non-commutative field theory are inconsistent with new theoretical conditions and experimental results.

Findings

Previous models are not self-consistent under new conditions.

Experimental data shows no evidence of Lorentz invariance violation in atmospheric neutrinos.

Lorentz invariance violation cannot naturally explain neutrino oscillations.

Abstract

Depending on deformed canonical anti-commutation relations, massless neutrino oscillation based on Lorentz invariance violation in non-commutative field theory is discussed. It is found that the previous studies about massless neutrino oscillation within deformed canonical anti-commutation relations should satisfy the condition of new Moyal product and new non standard commutation relations. Furthermore, comparing the Lorentz Invariant Violation parameters $\mathit{A}$ in the previous studies with new Moyal product and new non standard commutation relations, we find that the orders of magnitude of non-commutative parameters (Lorentz invariant Violation parameters $\mathit{A}$) is not self-consistent. This inconsistency means that the previous studies of Lorentz invariance violation in non-commutative field theory may not naturally explain massless neutrino oscillation. In other words, it should be impossible to explain neutrino oscillation by Lorentz invariance violation in non-commutative field theory. This conclusion is supported by the latest atmospheric neutrinos experimental results from the Super-Kamiokande Collaboration, which show that no evidence of Lorentz invariance violation on atmospheric neutrinos was observed.