On testing in-vacuo dispersion with the most energetic neutrinos: KM3-230213A case study

TL;DR

This paper investigates the potential of using extremely energetic neutrinos, like KM3-230213A, to test in-vacuo dispersion effects predicted by quantum spacetime theories, challenging existing assumptions about optimal energy ranges for such tests.

Contribution

It proposes a novel approach to test in-vacuo dispersion using ultra-high-energy neutrinos, demonstrating how lower-energy transient sources could be linked to high-energy neutrino detections.

Findings

GRB090401B aligns with KM3-230213A directionally

The p-value for the neutrino-GRB coincidence is 0.015

A small number of such coincidences could effectively test in-vacuo dispersion

Abstract

The phenomenology of in-vacuo dispersion, an effect such that quantum properties of spacetime slow down particles proportionally to their energies, has been a very active research area since the advent of the Fermi telescope. One of the assumptions made in this 15-year effort is that the phenomenology of in-vacuo dispersion has a particle-energy sweet spot: the energy of the particle should be large enough to render the analysis immune to source-intrinsic confounding effects but still small enough to facilitate the identification of the source of the particle. We use the gigantic energy of KM3-230213A as an opportunity to challenge this expectation. For a neutrino of a few hundred PeVs a transient source could have been observed at lower energies several years earlier, even assuming the characteristic scale of in-vacuo dispersion to be close to the Planck scale. We report that GRB090401B is in excellent directional agreement with KM3-230213A, and we discuss a strategy of in-vacuo-dispersion analysis suitable for estimating the significance of KM3-230213A as a GRB090401B-neutrino candidate. The $p$-value resulting from our analysis (0.015) is not small enough to warrant any excitement, but small enough to establish the point that a handful of such coincidences would be sufficient to meaningfully test in-vacuo dispersion.