2023 Impact factor 4.2
Particles and Fields
Eur. Phys. J. C 17, 593-610
DOI 10.1007/s100520000497

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

M. Benayoun1 - L. DelBuono1 - H.B. O'Connell2

1 LPNHE des Universités Paris VI et VII-IN2P3, Paris, France
2 Stanford Linear Accelerator Center, Stanford University, Stanford CA 94309, USA

Received: 20 June 2000 / Published online: 23 October 2000 - © Springer-Verlag 2000

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) $\rightarrow$ SU(3)$\times$ U(1) satisfies all requirements of the physics of radiative decays without any need for additional glueballs.

Copyright Società Italiana di Fisica, Springer-Verlag 2000