Pseudoscalar meson mixing in effective field theory

We show that for any effective field theory of colorless meson fields, the mixing schemes of particle states and decay constants are not only related but also determined exclusively by the kinetic and mass Lagrangian densities. In the general case, these are bilinear in terms of the intrinsic fields and involve nondiagonal kinetic and mass matrices. By applying three consecutive steps this Lagrangian can be reduced to the standard quadratic form in terms of the physical fields. These steps are (i) the diagonalization of the kinetic matrix, (ii) rescaling of the fields, and (iii) the diagonalization of the mass matrix. In such case where the dimensions of the nondiagonal kinetic and mass submatrices are, respectively, $k\ifmmode\times\else\texttimes\fi{}k$ and $n\ifmmode\times\else\texttimes\fi{}n,$ this procedure leads to mixing schemes that involve $[k(k\ensuremath{-}1)/2]+[n(n\ensuremath{-}1)/2]$ angles and k field rescaling parameters. This observation holds true irrespective of the type of particle interactions presumed. The commonly used mixing schemes correspond to a proper choice of the kinetic and mass matrices, and are derived as special cases. In particular, $\ensuremath{\eta}\ensuremath{-}{\ensuremath{\eta}}^{\ensuremath{'}}$ mixing requires one angle, if and only if the kinetic term with the intrinsic fields has a quadratic form.