VMD, the WZW Lagrangian and ChPT: The third mixing angle

We show that the Hidden Local Symmetry Model, supplemented with well-knownprocedures for breaking flavor SU(3) and nonet symmetry, provides all theinformation contained in the standard Chiral Perturbation Theory (ChPT)Lagrangian ${\cal L}^{(0)}+{\cal L}^{(1)}$. This allows to rely on radiativedecays of light mesons ($VP\gamma$ and $P \gamma\gamma$) in order to extractsome numerical information of relevance to ChPT: a value for $\Lambda_1=0.20\pm 0.04$, a quark mass ratio of $\simeq 21.2 \pm 2.4$, and a negligibledeparture from the Gell-Mann--Okubo mass formula. The mixing angles are$\theta_8=-20.40^\circ \pm 0.96^\circ$ and $\theta_0=-0.05^\circ \pm0.99^\circ$. We also give the values of all decay constants. It is shown thatthe common mixing pattern with one mixing angle $\theta_P$ is actually quiteappropriate and algebraically related to the $\eta/\eta'$ mixing patternpresently preferred by the ChPT community. For instance the traditional$\theta_P$ is functionally related to the ChPT $\theta_8$ and fulfills$\theta_P \simeq \theta_8/2$. The vanishing of $\theta_0$, supported by alldata on radiative decays, gives a novel relation between mixing angles and theviolation of nonet symmetry in the pseudoscalar sector. Finally, it is shownthat 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 anyneed for additional glueballs.Comment: 31 pages, 1 figur