Lorentz Invariance Violation and IceCube Neutrino Events

The IceCube neutrino spectrum shows a flux which falls of as $E^{-2}$ for sub PeV energies but there are no neutrino events observed above $\sim 3$ PeV. In particular the Glashow resonance expected at 6.3 PeV is not seen. We examine a Planck scale Lorentz violation as a mechanism for explaining the cutoff of observed neutrino energies around a few PeV. By choosing the one free parameter the cutoff in neutrino energy can be chosen to be between 2 and 6.3 PeV. We assume that neutrinos (antineutrinos) have a dispersion relation $E^2=p^2 - (\xi_3/M_{Pl})~p^3$, and find that both $\pi^+$ and $\pi^-$ decays are suppressed at neutrino energies of order of few PeV. We find that the $\mu^-$ decay being a two-neutrino process is enhanced, whereas $\mu^+$ decay is suppressed. The $K^+\rightarrow \pi^0 e^+ \nu_e$ is also suppressed with a cutoff neutrino energy of same order of magnitude, whereas $K^-\rightarrow \pi^0 e^- \bar \nu_e$ is enhanced. The $n \rightarrow p^+ e^- \bar \nu_e$ decay is suppressed (while the $\bar n \rightarrow p^- e^+ \nu_e$ is enhanced). This means that the $\bar \nu_e$ expected from $n$ decay arising from $p+\gamma \rightarrow \Delta \rightarrow \pi^+ n$ reaction will not be seen. This can explain the lack of Glashow resonance events at IceCube. If no Glashow resonance events are seen in the future then the Lorentz violation can be a viable explanation for the IceCube observations at PeV energies.Comment: v2, 16 pages, Version accepted for publication in JHE

Protective effect of Ipomoea aquatica against reserpine induced oxidative stress in brain using mice

Background: The aim of the present study was to investigate the protective potential of alcoholic extract of Ipomoea aquatica extract against haloperidol induced catatonia, reserpine induced hypokinesia and reserpine induced oxidative stress.Methods: The mice were treated with reserpine for three days every other day. It was observed that Ipomoea aquatica MA extract significantly decreased haloperidol induced catatonia at 30, 60, 90 and 120 minutes respectively. The biochemical analysis of brain showed that the treatment with reserpine significantly enhanced peroxidation of lipid and lower levels of superoxide dismutase (SOD), catalase (CAT) and glutathione reductase (GSH), which will be an index for oxidative stress process. Co-administration of extract at (200 mg/kg and 400 mg/kg) significantly lowered the lipid peroxidation and reversed the decrease in brain SOD, CAT and GSH levels.Results: It was observed that the alcoholic extract of Ipomoea aquatica had a protective role against haloperidol induced catatonia, reserpine induced hypokinesia, and reserpine induced oxidative stress.Conclusions: Ipomoea aquatica showed significant activity at the dose of (400 mg/kg)