High-Energy Neutrino Flavor State Transition Probabilities

We analytically determine neutrino transitional probabilities and abundance ratios at various distances from the source of creation in several astrophysical contexts, including the Sun, supernovae and cosmic rays. In doing so, we determine the probability of a higher-order transition state from $\nu_\tau\rightarrow\nu_\lambda$, where $\nu_\lambda$ represents a more massive generation than Standard Model neutrinos. We first calculate an approximate cross-section for high-energy neutrinos which allows us to formulate comparisons for the oscillation distances of solar, supernova and higher-energy cosmic ray neutrinos. The flavor distributions of the resulting neutrino populations from each source detected at Earth are then compared via fractional density charts.