Notes on the Kinematic Structure of the Three-Flavor Neutrino Oscillation Framework

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Abstract
These notes present a critique of the standard three-flavor neutrino oscillation framework. The design proposal of the MINOS at Fermilab based on a two-mass eigenstate framework may require serious reconsideration if there is strong mixing between all three flavors of neutrinos. For the LSND and KARMEN neutrino oscillation experiments, the amplitude of neutrino oscillation of the "one mass scale dominance" framework vanishes for certain values of mixing angles as a result of opposite signs of two equal and opposite contributions. Recent astronomical observations leave open the possibility that one of the neutrino mass eigenstates may be nonrelativistic in some instances. Neutrino oscillation phenomenology with a superposition of two relativistic, and one nonrelativistic, mass eigenstates is constructed. It is concluded that if the transition from the nonrelativistic to the relativistic regime happens for energies relevant to the reactor and the LSND neutrino oscillation experiments, then one must consider an ab initio analysis of the existing data.