VMD, the WZW Lagrangian and ChPT: The Third Mixing Angle

Abstract

We show that the Hidden Local Symmetry Model, supplemented with well-known procedures for breaking flavor SU(3) and nonet symmetry, provides all the information contained in the standard Chiral Perturbation Theory (ChPT) Lagrangian ${\cal L}^{(0)}+{\cal L}^{(1)}$. This allows to rely on radiative decays of light mesons ($VPγ$ and $P γγ$) in order to extract some numerical information of relevance to ChPT: a value for $Λ_1=0.20 \pm 0.04$, a quark mass ratio of $\simeq 21.2 \pm 2.4$, and a negligible departure from the Gell-Mann--Okubo mass formula. The mixing angles are $θ_8=-20.40^\circ \pm 0.96^\circ$ and $θ_0=-0.05^\circ \pm 0.99^\circ$. We also give the values of all decay constants. It is shown that the common mixing pattern with one mixing angle $θ_P$ is actually quite appropriate and algebraically related to the $η/η'$ mixing pattern presently preferred by the ChPT community. For instance the traditional $θ_P$ is functionally related to the ChPT $θ_8$ and fulfills $θ_P \simeq θ_8/2$. The vanishing of $θ_0$, supported by all data on radiative decays, gives a novel relation between mixing angles and the violation of nonet symmetry in the pseudoscalar sector. Finally, it is shown that the interplay of nonet symmetry breaking through U(3) $\ra$ SU(3)$\times$ U(1) satisfies all requirements of the physics of radiative decays without any need for additional glueballs.