Probing Lorentz invariance with a high-energy neutrino flare

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Preprint
Report number	KCL-PH-TH/2024-22 ; CERN-TH-2024-056 ; arXiv:2408.15949
Title	Probing Lorentz invariance with a high-energy neutrino flare
Author(s)	Bustamante, Mauricio (Bohr Inst.) ; Ellis, John (King's Coll. London ; CERN) ; Konoplich, Rostislav (Manhattan Coll., Riverdale ; New York U.) ; Sakharov, Alexander S. (Manhattan Coll., Riverdale ; CERN)
Imprint	2024-08-28
Number of pages	16
Note	16 pages, 7 figures, plus an appendix
Subject category	hep-th ; Particle Physics - Theory ; hep-ph ; Particle Physics - Phenomenology ; hep-ex ; Particle Physics - Experiment ; gr-qc ; General Relativity and Cosmology ; astro-ph.HE ; Astrophysics and Astronomy
Abstract	Time-of-flight measurements of high-energy astrophysical neutrinos can be used to probe Lorentz invariance, a pillar of modern physics. If Lorentz-invariance violation (LIV) occurs, it could cause neutrinos to slow down, with the delay scaling linearly or quadratically with their energy. We introduce non-parametric statistical methods designed to detect LIV-induced distortions in the temporal structure of a high-energy neutrino flare as it travels to Earth from a distant astrophysical source, independently of the intrinsic timing properties of the source. Our approach, illustrated using the 2014/2015 TeV-PeV neutrino flare from the blazar TXS 0506+056 detected by IceCube, finds that the LIV energy scale must exceed 10^{14} GeV (linear) or 10^9 GeV (quadratic). Our methods provide a robust means to investigate LIV by focusing solely on a neutrino flare, without relying on electromagnetic counterparts, and account for realistic energy and directional uncertainties. For completeness, we compare our limits inferred from TXS 0506+056 to the sensitivity inferred from multi-messenger detection of tentative coincidences between neutrinos and electromagnetic emission from active galactic nuclei and tidal disruption events.
Other source	Inspire
Copyright/License	preprint: (License: arXiv nonexclusive-distrib 1.0)

$\textbf{\textit{Broken Lorentz invariance changes the time distribution of a flare of high-energy astrophysical neutrinos.}} Higher-energy neutrinos emitted by a transient source, like the blazar TXS 0506+056, would travel more slowly than lower-energy neutrinos. Their time distribution grows more uniform, flatter, and more skewed. \textbf{\textit{The absence of these features in a detected flare places robust limits on the energy scale of Lorentz-invariance violation.}} \vspace*{-1.2cm}$ $\textbf{\textit{Probability density function of the neutrino energy, $E_\nu$.}} Each curve corresponds to a different muon track detected by IceCube as associated to the TXS 0506+056 2014/2015 flare~\cite{IceCube:2018cha}, characterized here by its central reconstructed muon energy proxy, $\hat{E}_{\mu,i}$. For each event, the probability density is built by accounting for the connection between neutrino energy and muon energy proxy, and between the latter and the observed muon energy proxy of the event. See Sec.~\ref{sec:flares-uncertainty} and Appendix~\ref{sec:pdf_neutrino_energy} for details.$ $\textbf{\textit{Sketch of the effects of Lorentz-invariance violation on the arrival times of neutrinos in a flare.}} In this figure we assume---for illustration only---that, in the absence of LIV during neutrino propagation, the arrival times of high-energy neutrinos at Earth would be distributed normally, preserving the time distribution emitted by their astrophysical source. Yet, in our calculations, we do not assume any shape for the emission time profile. Under LIV, the distribution of arrival times may deviate from the distribution at emission, and become more uniform, less peaky, and more asymmetric. See Sec.~\ref{sec:methods-measures} for details.$ Show more plots

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