Particle oscillations

Abstract

The formalism of neutrino oscillation has complicate issues. For instance, neutrinos always move ultrarelativistically in actual experimental conditions and the oscillation occurs among the three flavors. In this chapter, before going into the detail of the neutrino oscillation, we will understand the oscillations of simple cases of two flavor particles at rest. First, the Schrödinger equation of two flavor particles is understood as a differential equation that defines the time development of the basis states due to flavor-transition amplitudes. The time-dependent wave functions are derived as general solutions to the Schrödinger equation. The wave functions for mass eigenstates and flavor eigenstates are obtained by choosing initial conditions in the general wave function. The probability of the flavor oscillation is calculated from the wave function which started from a specific flavor state at time t = 0. The oscillation phenomena are also described as the interference between the diagrams which have the same initial flavor states and the same final flavor states but different intermediate mass eigenstates. In the course of these considerations, the relation among the mass, the mixing and the flavor oscillation becomes clear.