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

Abstract

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

$1/N_c$ approximation and universality of vector mesons

“…If expression (26) is expanded in a series in terms of the square of the mass of the ρ-meson, then such an expansion begins with a term that is completely canceled out by the contribution of the tadpole I tp (m π , Λ π ). Thus, the integral I ρπ contains only a logarithmically divergent (at Λ π → ∞) part.…”

“…A general mathematical framework to deal with axialvector-pseudoscalar mixing in the effective Lagrangians has been developed in [26].…”

Account for axial vector mesons in the $η\toπ^+π^-γ$ and $η' \toπ^+π^-γ$ decays

“…However, in the real world, with small but non-zero bare quark masses, this contribution violates both the U (3) nonet symmetry and the SU (3) flavor symmetry. Thus the PA mixing is an additional source of flavor symmetry breaking in the effective meson Lagrangian [7].…”

Electromagnetic interactions of mesons induced by axial-vector–pseudoscalar mixing

“…Through the study of effective chiral Lagrangians with spin-1 mesons, it has been realized that they possess a cross term a µ ∂ µ π, i.e. the axial-vector a µ and pseudoscalar π fields mix [8][9][10][11][12]. Consequently, one should diagonalize the free part of the Lagrangian by introducing a physical axial-vector field a µ .…”