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

TL;DR

This paper demonstrates that the Hidden Local Symmetry Model, combined with symmetry-breaking procedures, encapsulates the Chiral Perturbation Theory Lagrangian, enabling extraction of key parameters from light meson radiative decays and clarifying pseudoscalar mixing angles.

Contribution

It shows the Hidden Local Symmetry Model reproduces ChPT Lagrangian and relates mixing angles, providing a unified framework for analyzing light meson decays and pseudoscalar mixing.

Findings

Determined key parameters like =0.20 1.04 and quark mass ratio 1.2 2.4.

Found the mixing angle  0.400.96 and  .050.99 degrees.

Established the relation  .050.99 degrees and the validity of the one-angle mixing pattern.

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.