Propagation of superluminal PeV IceCube neutrinos: A high energy spectral cutoff or new constraints on Lorentz invariance violation

The IceCube observation of cosmic neutrinos with $E_{\nu }>60\mathrm{TeV}$, 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 ${\delta }_{\nu e}={\delta }_{\nu }-{\delta }_e\le 5.2\times 10^{-21}$. 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 ${\delta }_{\nu e}=5.2\times 10^{-21}$, 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 ${\delta }_{\nu }$ being $(0.5\text{to}1.0)\times 10^{-20}$.

Figure 1

Binned number of neutrinos used in our Monte Carlo runs sampled from the star formation rate distribution of Ref. [18].

Figure 2

Mean propagation time before decay as a function of neutrino energy for a threshold energy of 10 PeV.

Figure 3

Calculated neutrino spectra with VPE and redshifting compared with the IceCube data both including a subtraction of atmospheric charm $\nu$’s at the 90% C.L. (cyan) and omitting such a subtraction (black) [5]. Curves from left to right are spectra obtained with rest-frame threshold energies of 1, 2, 4, 10, 20, and 40 PeV. The corresponding values of ${\delta }_{\nu e}$ are given by Eq. (3).