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 $\Delta (V)=|V_{12}{|}^2-|V_{21}{|}^2$, of $V$ with respect to the main diagonal and the Jarlskog invariant $J(V)=\mathrm{Im}(V_{11}{V}_{12}^{\ast }{V}_{21}^{\ast }{V}_{22})$. These expressions for $\Delta (V)$ and $J(V)$ provide constraints on possible mass matrices from the available data on $V$.

Comments: 5 pages, Latex