Atmospheric Neutrino Predictions and the Influence of Hadron Production

The observation of neutrino flavour transformations of atmospheric neutrinos measured in Super-Kamiokande demands a theoretical explanation. The favoured candidate -- neutrino oscillations -- makes detailed predictions for the energy and path length dependence of the flavour transformations. For this reason, neutrino oscillations is a testable theory, which so far is in excellent agreement with the observations. The detailed comparison between the measured neutrino fluxes at Super-Kamiokande and the expected neutrino flux demands accurate predictions. Such predictions are performed with Monte-Carlo based simulations; the simulation of the Bartol group is used for the analyses in this thesis. Most recently the development of fully three-dimensional (3D) atmospheric neutrino calculations has been a significant theoretical improvement to the predicted neutrino fluxes. Older calculations employed the one-dimensional (1D) approximation; a comparison of these techniques is contained herewith. It is shown that above $3~GeV$ the predictions of the 1D and 3D calculations are in agreement when expressed as a function of neutrino energy or zenith angle; however, a 3D calculation is necessary to correctly calculate the neutrino fluxes as a function of the azimuthal direction. This is shown to be due to the bending of particles in the geo-magnetic field. Atmospheric neutrino predictions are now developed to such an extent that no large approximations (greater than 2\%) exist. Two sources of uncertainty still remain -- the primary cosmic-ray spectrum and hadron production in hadronic interactions. The primary cosmic-ray flux is shown here to introduce around a 7\% uncertainty to the Super-Kamiokande sub-GeV neutrino event sample, increasing with neutrino energy. The systematic uncertainties from hadronic interactions are estimated to be between 20 and 30\%, depending on neutrino energy. The simulation of hadronic interactions remains the largest source of uncertainty in the neutrino flux predictions. Ultimately this is traced to a lack of relevant experimental data; three new experiments will soon provide valuable answers in this area. The HARP experiment is now analysing its data, the construction and operation of the time projection chamber tracking is explained here.