Physical Implications of Neutrino Mixing Angles and CP-Violating Phase

The origin of the asymmetry between matter and antimatter in the universe remains a great mystery. In 1998, neutrino oscillations, neutrino flavor changes over the journey from the sun to the earth's surface, were observed in atmospheric neutrinos, shattering assumptions that neutrinos were massless and indicating a possible violation of change and parity symmetry (CP-symmetry) in the neutrino sector. If neutrinos violate CP-symmetry, leptogenesis is possible, hypothetically generating leptons in greater quantities than antileptons, potentially explaining the asymmetry between matter and antimatter, which makes existence possible.

By deriving the neutrino mixing matrix and expanding it in terms of small deviations about the Tri-bimaximal mixing pattern to the third order, it has been shown that slight variations in these parameters can significantly affect flavor transition probabilities and the possibility of leptogenesis. I examined the dependence of each transition probability on each mixing angle, Dirac CP-violating phase, and mass ordering, identifying the electron to muon and tau to electron flavor channels as the most sensitive to such variations. I also calculated leptogenesis in terms of the Dirac CP-violating phase for a model derived from the double tetrahedral T' group theory, finding it to be nonzero with flavor effects included. These results may guide future experiments and model building in hopes of observing CP-violation and explaining the observed matter-antimatter asymmetry.

Written under the mentorship of Dr. Mu-Chun Chen at UC Irvine, the following paper outlines my research, primarily conducted in Mathematica, as well as C++.

Solar Neutrino Visualization

The image to the right is a visualization of neutrino flavor states over their journey from the sun to the earth's surface. It is generated using experimentally determined flavor and energy distributions at the sun's surface to track flavor transition probabilities over time according to their quantum mechanical wave functions. I have simulated measurements throughout the course of the journey, so that each plotted point represents the most likely flavor state observed in a single measurement taken at its location. In other words, previously plotted points are not considered in determine the flavor at each new point.

This visualization was created in C++ using the third-order expansion of the Tri-bimaximal neutrino mixing matrix and experiementally bound mass values. The code was subsequently transformed for use in the generation of movement for the dance piece Sankhara.