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 theo
retical 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.
In this essay we extend the standard discussion of neutrino oscillations to astrophysical neutrinos propagating through expanding space. This extension introduces a new cosmological parameter $I$ into the oscillation phase. The new parameter records
cosmic history in much the same manner as the redshift z or the apparent luminosity D_L. Measuring $I$ through neutrino oscillations could help determine cosmological parameters and discriminate among different cosmologies.
Current experimental data on neutrino mixing are very well described by TriBiMaximal mixing. Accordingly, any phenomenological parametrization of the MNSP matrix must build upon TriBiMaximal mixing. We propose one particularly natural parametrization
, which we call TriMinimal. The three small deviations of the PDG angles from their TriBiMaximal values, and the PDG phase, parametrize the TriMinimal mixing matrix. As an important example of the utility of this new parametrization, we present the simple resulting expressions for the flavor-mixing probabilities of atmospheric and astrophysical neutrinos. As no foreseeable experiment will be sensitive to more than second order in the small parameters, we expand these flavor probabilities to second order.
We consider the neutrino (and antineutrino) flavors arriving at Earth for neutrinos produced in the annihilation of weakly interacting massive particles (WIMPs) in the Suns core. Solar-matter effects on the flavor propagation of the resulting $agt$ G
eV neutrinos are studied analytically within a density-matrix formalism. Matter effects, including mass-state level-crossings, influence the flavor fluxes considerably. The exposition herein is somewhat pedagogical, in that it starts with adiabatic evolution of single flavors from the Suns center, with $theta_{13}$ set to zero, and progresses to fully realistic processing of the flavor ratios expected in WIMP decay, from the Suns core to the Earth. In the fully realistic calculation, non-adiabatic level-crossing is included, as are possible nonzero values for $theta_{13}$ and the CP-violating phase $delta$. Due to resonance enhancement in matter, nonzero values of $theta_{13}$ even smaller than a degree can noticeably affect flavor propagation. Both normal and inverted neutrino-mass hierarchies are considered. Our main conclusion is that measuring flavor ratios (in addition to energy spectra) of $agt$ GeV solar neutrinos can provide discrinination between WIMP models. In particular, we demonstrate the flavor differences at Earth for neutrinos from the two main classes of WIMP final states, namely $W^+ W^-$ and 95% $b bar{b}$ + 5% $tau^+tau^-$. Conversely, if WIMP properties were to be learned from production in future accelerators, then the flavor ratios of $agt$ GeV solar neutrinos might be useful for inferring $theta_{13}$ and the mass hierarchy.
