Particle velocity in noncommutative space-time

TL;DR

This paper explores how low-energy massive particles could be used to detect noncommutative space-time effects, challenging the effectiveness of high-energy photon and neutrino arrival time analyses.

Contribution

It proposes a novel approach focusing on low-energy particles for detecting space-time noncommutativity, contrasting with traditional high-energy methods.

Findings

High-energy gamma-ray and neutrino arrival times are ineffective for detecting noncommutativity.

Low-energy massive particles may serve as better probes for space-time noncommutativity.

The study emphasizes the importance of alternative detection strategies.

Abstract

We investigate a particle velocity in the $\kappa$-Minkowski space-time, which is one of the realization of a noncommutative space-time. We emphasize that arrival time analyses by high-energy $\gamma$-rays or neutrinos, which have been considered as powerful tools to restrict the violation of Lorentz invariance, are not effective to detect space-time noncommutativity. In contrast with these examples, we point out a possibility that {\it low-energy massive particles} play an important role to detect it.