Constraints on mass matrices due to measured property of the mixing matrix

Abstract

It is shown that two specific properties of the unitary matrix V can be expressed directly in terms of the matrix elements and eigenvalues of the hermitian matrix M which is diagonalized by V. These are the asymmetry Δ(V) = |V₁₂|²-|V₂₁|², of V with respect to the main diagonal and the Jarlskog invariant J(V ) = Im(V₁₁V ^∗₁₂V ∗₂₁V₂₂). These expressions for Δ(V ) and J(V ) provide constraints on possible mass matrices from the available data on V.