Dartmouth Events

Abstract:  Neutrinos are elusive elementary particles that provide a unique probe beyond the Standard Model of elementary particle physics. Under this theoretical framework, neutrinos are predicted to be massless, left-handed, and to conserve their leptonic flavor charge. Recent experimental developments have suggested that none of these predictions may be true; at least two of the three neutrinos are known to be massive, implicitly suggesting that right-handed neutrinos might exist, and they are also known to oscillate between different flavors. Of specific interest are time-of-flight experiments involving the muonic neutrino, which measure velocity in an attempt to discern the neutrino's absolute mass. These experiments have recorded velocities that have been well consistent with the speed of light, yet their mean values have suspiciously often been superluminal, albeit at a small statistical significance. To scrutinize this result, in this thesis, a framework is presented to treat the neutrino wavefunction as a sum of uncertainty-based Gaussian wave packets. This methodology is then used to describe the nature of the quantum mechanical interactions between the particle and the detector. It is argued here that the median position of the resulting probability density function, as opposed to the mean, is where the detector should fire on average. As such, using the mean position may not yield an accurate inference of the neutrino's speed. Several factors that may contribute to skewness, including mixing parameters and mass spectra, are explored before extending this analysis to real experiments. Monte Carlo techniques are then used to simulate time-of-flight measurements for the MINOS experiment before comparing the results to the T2K experiment.