Matter effects on neutrino oscillations

2013 Spring.Includes bibliographical references.An introduction to neutrino oscillations in vacuum is presented, followed by a survey of various techniques for obtaining either exact or approximate expressions for νμ→ νe oscillations in matter. The method developed by Arafune, Koike, and Sato uses a perturbative analysis to find an approximation for the evolution operator. The method used by Freund yields an approximate oscillation probability by diagonalizing the Hamiltonian, finding the eigenvalues and eigenvectors, and then using those to find modified mixing angles with the matter effect taken into account. The method devised by Mann, Kafka, Schneps, and Altinok produces an exact expression for the oscillation by determining explicitly the evolution operator. These methods are compared to each other using the T2K, MINOS, NOνA, and LBNE parameters