Corrections to mass scale predictions in SO(10) GUT with higher dimensional operators

We calculate the two loop contribution to the predictions of the mass scales in an SO(10) grand unified theory. We consider the modified unification scale boundary conditions due to the non-renormalizable higher dimensional terms arising from quantum gravity or spontaneous compactification of extra dimensions in Kaluza-Klein type theory. We find the range of these couplings which allows left-right symmetry to survive till very low energy (as low as $\sim$ TeV) and still be compatible with the latest values of $\sin^2 \theta_W$ and $\alpha_s$ derived from LEP. We consider both the situation when the left-right parity is broken and conserved.We consider both supersymmetric and non-supersymmertic versions of the SO(10) theory.Taking the D-conserved non-susy case as an example we calculate the effects of moderate threshold uncertainties at the heavy scale, due to the unknown higgs masses,on the gravity induced couplings.Comment: 18 pages with three figures available on request([email protected]),UH-511-780-9

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