# 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 ($VP\gamma$ 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 $\eta/\eta'$ 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.
Document type :
Journal articles

http://hal.in2p3.fr/in2p3-00195758
Contributor : Dominique Girod <>
Submitted on : Tuesday, December 11, 2007 - 2:25:05 PM
Last modification on : Friday, April 10, 2020 - 5:04:17 PM

### Citation

M. Benayoun, L. del Buono, H. B. O'Connell. VMD, the WZW Lagrangian and ChPT: The Third Mixing Angle. European Physical Journal C: Particles and Fields, Springer Verlag (Germany), 2000, 17, pp.593-610. ⟨10.1007/s100520000497⟩. ⟨in2p3-00195758⟩

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