Testing Lorentz invariance with astrophysical neutrinos

The IceCube Neutrino Observatory has reported the observation of two high-energy neutrino events [PRL 111, 021103 (2013)]. Nicknamed Bert & Ernie, these events have energies slightly over 1 PeV ($10^3$ TeV), making them the most energetic neutrinos ever observed. Additionally, in a new report IceCube presents the observation of 26 new events with energies 20-300 TeV [Science 342, 1242856 (2013)]. Besides their high energy, these events are likely to be of astrophysical origin, which is considered an important milestone in the development of neutrino astronomy. The long propagation distance and the high energy of these neutrinos make them sensitive probes of fundamental physics. This paper describes how the observation of these high-energy neutrinos can be used to set stringent limits on some types of Lorentz invariance violation.

• Threshold analyses: althought the evidence favors the astrophysical nature of Bert & Ernie, in a conservative approach we can suposse that these neutrinos were created by the decay of a heavy hadron ${\color{Brown}h}$ in the upper atmosphere in the form ${\color{Brown}h}\to{\color{green}\mu}+{\color{red}{\bar\nu_\mu}}$ (we consider only CPT-even operators so the distinction between neutrinos and antineutrinos is irrelevant). The breakdown of Lorentz symmetry leads to unconventional neutrino dispersion relations, which can block the phase space for hadron decay above a threshold energy $E_\text{th}$. The observation of PeV neutrinos implies that this threshold energy satisfies $1\,\text{PeV}<E_\text{th}$. We use this relation to obtain lower limits (negative values) on possible isotropic modifications of the neutrino dispersion relations.

another unconventional effect that can be triggered by Lorentz violation is neutrinos undergoing Cherenkov radiation, emitting one or more particles. We consider the electron-positron pair production in the form ${\color{red}\nu}\to{\color{red}\nu}+{\color{blue}e^-}+{\color{blue}e^+}$. Unconventional kinematical effects appear as modifications of the phase space; nevertheless, Lorentz violation also modifies the neutrino spinors, which in turn alter the matrix element of the process. After propagating a distance $L$, neutrinos will disipate energy by pair production.Then we use the observation of PeV neutrinos to impose that the effective distorsion distance $D(E) =-E/(dE/dx)$ must be greater than $L$, which allows us to constraint the size of the relevant coefficients controlling Lorentz violation. We first consider the conservative approach assuming that Bert & Ernie are atmospheric neutrinos. Then we explore the possibility that these events are of astrophysical origin, in which case the neutrinos would efficiently lose energy falling below the Cherenkov threshold energy. Using this astrophysical Cherenkov threshold we also obtain lower limits (negative values) on possible isotropic modifications of the neutrino dispersion relations.

• Anisotropic Lorentz violation: the high energy of Bert & Ernie allows us to set stringent limits on isotropic Lorentz violation; however, most of the unconventional effects that could arise are direction dependent. For this reason we make use of the 28 high-energy events observed by IceCube, which not only allows us to explore anisotropic effects but also provide a method to set two-sided limits for the SME coefficients.

• Future prospects: we also discuss the ways to determine upper limits on the isotropic SME coefficients. We construct a general upper bound that can be obtained from the no observation of proton decay in the form ${\color{green}p}\to {\color{Brown}n}+{\color{blue}{e^-}}+{\color{red}{\bar\nu_e}}$ and give estimates for upper limits using neutrino time of flight and comment on dispersion of neutrinos from gamma-ray bursts.

Testing relativity with high-energy astrophysical neutrinos.
J. S. Díaz, V. A. Kostelecký, and M. Mewes, Phys. Rev. D 89, 043005 (2014). [arXiv:1308.6344]
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