Massive neutrinos, Lorentz invariance dominated standard model and the phenomenological approach to neutrino oscillations

Abstract

For the electroweak interactions, the massive neutrino perturbative kinematical procedure is developed in the massive neutrino Fock space. This yields the dominant Lorentz invariant Standard Model mass-less flavor neutrino cross-sections as well as the neutrino oscillation cross-sections some of which are Lorentz invariance and flavor conservation violating. But all these oscillating cross-sections being proportional to the squares of neutrino masses are practically unobservable in the laboratory; however, they are consistent with the original Pontecorvo neutrino oscillating transition probability expression at short time (baseline), as presented by Dvornikov. Then, by mimicking the time dependence of the original Pontecorvo neutrino oscillating transition probability, one can formulate the dimensionless neutrino intensity-probability I, by phenomenological extrapolating the time t, or, equivalently the baseline distance L away from the collision point for the oscillating differential cross-section. For the incoming neutrino of 10MeV in energy and neutrino masses from Fritzsch analysis with the neutrino mixing matrix of Harrison, Perkins and Scott, the baseline distances at the first two maxima of the neutrino intensity are L=281km and L=9279km . The intensity I at the first maximum conserves the flavor, while at the second maximum; the intensities violate the flavor, respectively, in the final and initial state. At the end some details are given as to how these neutrino oscillations away from the collision point one should be able to verify experimentally.