Three neutrino oscillations applied to solar and long baseline experiments
Creators: name: Hayward, Scott Kelly
Publisher: name: University of British Columbia
Year: 2009

description: Details of the Standard Solar Model and experiments measuring neutrinos produced inside the sun and in the upper atmosphere are reviewed. Inconsistencies between theoretical calculations and experimental measurements are discussed, establishing the need for new physics beyond the Standard Model of Particle Physics. Neutrino oscillations are introduced as a viable solution and the phenomenology in the two flavour case is reviewed. Calculations of neutrino oscillations at long baseline experiments are performed using realistic spectra and source/detector combinations. Both vacuum and matter enhanced oscillations of solar neutrinos are computed to account for the solar neutrino data, and allowed regions of parameter space are found. New analytical results are presented which determine the three family hamiltonian in matter. Oscillation probabilities in vacuum are calculated, and methods to account for matter effects are outlined. A numerical treatment to determine the CKM parameters in matter is shown to be identical to existing analytical results in the literature. Computer codes developed to calculate long baseline neutrino oscillation experiments through the earth's variable density are discussed. Several techniques used in a second set of programs written to determine solar neutrino survival probabilities in the three neutrino case are also reviewed. Symmetries between four different mass hierarchies which have two well-separated mass scales are studied. A two-fold degeneracy noted in the literature is shown to be inherent in experiments which only measure muon neutrino oscillations, and an expression relating the two sets of CKM parameters is calculated. Detailed computations illustrate how long baseline experiments can determine the CKM parameters. First order matter effects are included and numerical work shows where matter effects are likely to break some of the symmetries. The phenomenon of CP violation in both vacuum and matter is studied in the three neutrino scenario. Existing work on first order matter and CP corrections to oscillation probabilities at long baseline experiments is extended to second order. It is argued that since CP effects are very likely to be smaller than matter, second order corrections are necessary. In detailed calculations, second order effects are clearly apparent. At high energies the approximation breaks down, but numerical results yield accurate answers allowing further study. Several strategies to isolate CP violation from competing matter effects are suggested, including tuning the neutrino beam energy and a novel approach which combines data sets from accelerator and reactor based experiments. Finally, new analytical work is presented showing that CP violation may modify the ratio of µ-type to e-type neutrinos in the atmospheric flux. The magnitude of the effect is estimated and found to be significant. New techniques allow solar neutrino survival probabilities to be calculated including three mixing angles and two mass scales. A preliminary survey is performed assuming one relevant mass scale but including the three angular parameters. A distinct three neutrino solution is found by allowing the large neutrino mass squared difference to drop somewhat below the atmospheric neutrino data's best fit solution of 3 x 10-4 eV². Then the high energy tail of the 8B neutrino flux is converted to vT by a second resonance in the sun, leaving unique spectral characteristics to differentiate it from two neutrino models. [Scientific formulae used in this abstract could not be reproduced.]