A general framework to diagonalize vector-scalar and axial-vector-pseudoscalar transitions in the effective meson Lagrangian

A new mathematical framework for the diagonalization of the nondiagonal vector-scalar and axial-vector-pseudoscalar mixing in the effective meson Lagrangian is described. This procedure has unexpected connections with the Hadamard product of n×n matrices describing the couplings, masses, and fields involved. The approach is argued to be much more efficient as compared with the standard methods employed in the literature. The difference is especially noticeable if the chiral and flavor symmetry is broken explicitly. The paper ends with an illustrative application to the chiral model with broken U(3)L×U(3)R symmetry.