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 ${\mathcal{L}}^{(0)}+{\mathcal{L}}^{(1)}$. This allows to rely on radiative decays of light mesons ($VP\gamma$ and $P\gamma \gamma$) in order to extract some 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 negligible departure from the Gell-Mann--Okubo mass formula. The mixing angles are ${\theta }_8=-20.40^{\circ }\pm 0.96^{\circ }$ and ${\theta }_0=-0.05^{\circ }\pm 0.99^{\circ }$. We also give the values of all decay constants. It is shown that the common mixing pattern with one mixing angle ${\theta }_P$ is actually quite appropriate and algebraically related to the $\eta /{\eta }^{\prime }$ mixing pattern presently 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 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.

31 pages, 1 figure

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