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Register a new userPropagation of Superluminal PeV IceCube Neutrinos: A High Energy Spectral Cutoff or New Constraints on Lorentz Invariance Violation
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The IceCube observation of cosmic neutrinos with $E_{ u} > 60$ TeV, most of which are likely of extragalactic origin, allows one to severely constrain Lorentz invariance violation (LIV) in the neutrino sector, allowing for the possible existence of superluminal neutrinos. The subsequent neutrino energy loss by vacuum $e^+e^-$ pair emission (VPE) is strongly dependent on the strength of LIV. In this paper we explore the physics and cosmology of superluminal neutrino propagation. We consider a conservative scenario for the redshift distribution of neutrino sources. Then by propagating a generic neutrino spectrum, using Monte Carlo techniques to take account of energy losses from both VPE and redshifting, we obtain the best present constraints on LIV parameters involving neutrinos. We find that $delta_{ u e} = delta_{ u} - delta_e le 5.2 times 10^{-21}$. Taking $delta_e le 5 times 10^{-21}$, we then obtain an upper limit on the superluminal velocity fraction for neutrinos alone of $1.0 times 10^{-20}$. Interestingly, by taking $delta_{ u e} = 5.2 times 10^{-21}$, we obtain a cutoff in the predicted neutrino spectrum above 2 PeV that is consistent with the lack of observed neutrinos at those energies, and particularly at the Glashow resonance energy of 6.3 PeV. Thus, such a cutoff could be the result of neutrinos being slightly superluminal, with $delta_{ u}$ being $(0.5 {rm to} 1.0) times 10^{-20}$.
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It has been speculated that Lorentz-invariance violation (LIV) might be generated by quantum-gravity (QG) effects. As a consequence, particles may not travel at the universal speed of light. In particular, superluminal extragalactic neutrinos would rapidly lose energy via the bremssthralung of electron-positron pairs (nu -> nu e+ e-), damping their initial energy into electromagnetic cascades, a figure constrained by Fermi-LAT data. We show that the two cascade neutrino events with energies around 1 PeV recently detected by IceCube -if attributed to extragalactic diffuse events, as it appears likely- can place the strongest bound on LIV in the neutrino sector, namely delta =(v^2-1) < O(10^(-18)), corresponding to a QG scale M_QG ~ 10^5 M_Pl (M_QG >~ 10^(-4) M_Pl) for a linear (quadratic) LIV, at least for models inducing superluminal neutrino effects (delta > 0).
A full energy and flavor-dependent analysis of the three-year high-energy IceCube neutrino events is presented. By means of multidimensional fits, we derive the current preferred values of the high-energy neutrino flavor ratios, the normalization and spectral index of the astrophysical fluxes, and the expected atmospheric background events, including a prompt component. A crucial assumption resides on the choice of the energy interval used for the analyses, which significantly biases the results. When restricting ourselves to the ~30 TeV - 3 PeV energy range, which contains all the observed IceCube events, we find that the inclusion of the spectral information improves the fit to the canonical flavor composition at Earth, (1:1:1), with respect to a single-energy bin analysis. Increasing both the minimum and the maximum deposited energies has dramatic effects on the reconstructed flavor ratios as well as on the spectral index. Imposing a higher threshold of 60 TeV yields a slightly harder spectrum by allowing a larger muon neutrino component, since above this energy most atmospheric tracklike events are effectively removed. Extending the high-energy cutoff to fully cover the Glashow resonance region leads to a softer spectrum and a preference for tau neutrino dominance, as none of the expected electron antineutrino induced showers have been observed so far. The lack of showers at energies above 2 PeV may point to a broken power-law neutrino spectrum. Future data may confirm or falsify whether or not the recently discovered high-energy neutrino fluxes and the long-standing detected cosmic rays have a common origin.
We report constraints on the sources of ultra-high-energy cosmic ray (UHECR) above $10^{9}$ GeV, based on an analysis of seven years of IceCube data. This analysis efficiently selects very high energy neutrino-induced events which have deposited energies from $sim 10^6$ GeV to above $10^{11}$ GeV. Two neutrino-induced events with an estimated deposited energy of $(2.6 pm 0.3) times 10^6$ GeV, the highest neutrino energies observed so far, and $(7.7 pm 2.0) times 10^5$ GeV were detected. The atmospheric background-only hypothesis of detecting these events is rejected at 3.6$sigma$. The hypothesis that the observed events are of cosmogenic origin is also rejected at $>$99% CL because of the limited deposited energy and the non-observation of events at higher energy, while their observation is consistent with an astrophysical origin. Our limits on cosmogenic neutrino fluxes disfavor the UHECR sources having cosmological evolution stronger than the star formation rate, e.g., active galactic nuclei and $gamma$-ray bursts, assuming proton-dominated UHECRs. Constraints on UHECR sources including mixed and heavy UHECR compositions are obtained for models of neutrino production within UHECR sources. Our limit disfavors a significant part of parameter space for active galactic nuclei and new-born pulsar models.
We report on the observation of two neutrino-induced events which have an estimated deposited energy in the IceCube detector of 1.04 $pm$ 0.16 and 1.14 $pm$ 0.17 PeV, respectively, the highest neutrino energies observed so far. These events are consistent with fully contained particle showers induced by neutral-current $ u_{e,mu,tau}$ ($bar u_{e,mu,tau}$) or charged-current $ u_{e}$ ($bar u_{e}$) interactions within the IceCube detector. The events were discovered in a search for ultra-high energy neutrinos using data corresponding to 615.9 days effective livetime. The expected number of atmospheric background is $0.082 pm 0.004 text{(stat)}^{+0.041}_{-0.057} text{(syst)}$. The probability to observe two or more candidate events under the atmospheric background-only hypothesis is $2.9times10^{-3}$ ($2.8sigma$) taking into account the uncertainty on the expected number of background events. These two events could be a first indication of an astrophysical neutrino flux, the moderate significance, however, does not permit a definitive conclusion at this time.
We present a relationship, E_ u^{max} = m_{ u} M_{Planck}/M_{weak}, among the highest observed neutrino energy (~PeV) and the neutrino mass, the weak scale, and the Planck energy. We then discuss some tests of this relationship, and present some theoretical constructs which motivate the relationship. It is possible that all massive particles are subject to maximum energies given by similar relationships, although only the neutrino seems able to offer interesting phenomenology. We discuss implications which include no neutrino detections at energies greater than PeV, and changes in expectations for the highest energy cosmic rays. A virtue of this hypothesis is that it is easily invalidated should neutrinos be observed with energies much great than the PeV scale. An almost inescapable implication is that Lorentz Invariance is a low energy principle, yet it appears that violation may be only observable in high-energy astrophysical neutrinos.
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