# Three Flavor Neutrino Oscillations in Matter: Flavor Diagonal Potentials, the Adiabatic Basis and the CP phase - High Energy Physics - Phenomenology

Three Flavor Neutrino Oscillations in Matter: Flavor Diagonal Potentials, the Adiabatic Basis and the CP phase - High Energy Physics - Phenomenology - Download this document for free, or read online. Document in PDF available to download.

Abstract: We discuss the three neutrino flavor evolution problem with general,flavor-diagonal, matter potentials and a fully parameterized mixing matrix thatincludes CP violation, and derive expressions for the eigenvalues, mixingangles and phases. We demonstrate that, in the limit that the mu and taupotentials are equal, the eigenvalues and matter mixing angles theta 12 andtheta 13 are independent of the CP phase, although theta 23 does have CPdependence. Since we are interested in developing a framework that can be usedfor S matrix calculations of neutrino flavor transformation, it is useful towork in a basis that contains only off-diagonal entries in the Hamiltonian. Wederive the -non-adiabaticity- parameters that appear in the Hamiltonian in thisbasis. We then introduce the neutrino S matrix, derive its evolution equationand the integral solution. We find that this new Hamiltonian, and therefore theS matrix, in the limit that the mu and tau neutrino potentials are the same, isindependent of both theta 23 and the CP violating phase. In this limit, any CPviolation in the flavor basis can only be introduced via the rotation matrices,and so effects which derive from the CP phase are then straightforward todetermine. We show explicitly that the electron neutrino and electronantineutrino survival probability is independent of the CP phase in this limit.Conversely, if the CP phase is nonzero and mu and tau matter potentials are notequal, then the electron neutrino survival probability cannot be independent ofthe CP phase.

Author: ** James P. Kneller, Gail C. McLaughlin**

Source: https://arxiv.org/