Implications of atmospheric neutrino data

Abstract

A new quantitative and numerically efficient model of the most recent, more finely binned in energy, Super Kamiokande experiment is developed. By reproducing an analysis of this data performed by the experimentalist, including the restrictions of the atmospheric data on $ heta_{13}$, we are assured of the accuracy of the model. We combine this model, with models of the K2K, MINOS, and CHOOZ experiments, to perform an analysis in which we utilize the full three neutrino oscillation probabilities and a full three neutrino treatment of the Earth MSW effect. We find that the SK atmospheric data provides the best bound of $ heta_{13}$ from above while CHOOZ continues to provide the best lower bound on negative $ heta_{13}$. This comes about because of the importance of linear and higher terms in $ heta_{13}$, because in the region $L/E_ ugtrsim 10^4$ km/GeV the subdominant expansion is not convergent and linear and higher terms in $ heta_{13}$ become relatively more important, and because the atmospheric data reaches into this region. We show that the Earth MSW effect plays an important role in causing this effect. We find a best fit value $ heta_{13}=-0.07^{+0.18}_{-0.11}$, assuming no CP violation.