Proposal of a Simple Method to Estimate Neutrino Oscillation Probability and CP Violation in Matter

Abstract

We study neutrino oscillation within the framework of three generations in matter. We propose a simple method to approximate the coefficients A, B and C which do not depend on the CP phase \delta in the oscillation probability P(\nu_e \to \nu_{\mu})=A\cos \delta + B\sin \delta +C. An advantage of our method is that an approximate formula of the coefficients A, B and C in arbitrary matter {\it without the usual first order perturbative calculations} of the small parameter \Delta m_{21}^2/\Delta m_{31}^2 or \sin \theta_{13} can be derived. Furthermore we show that all the approximate formulas for low, intermediate and high energy regions given by other authors in constant matter can be easily derived from our formula. It means that our formula is applicable over a wide energy region.