Origin of the Weak-Interaction Angle. II

We present a theory of the origin of the weak-interaction angle $\theta$, based on a self-consistency condition linking weak, strong, and electromagnetic symmetry-breaking effects. The value of $\theta$ is related to the observed pattern of breaking of $\mathrm{SU}\left(3\right)\mathrm{}\otimes \mathrm{SU}\left(3\right)\mathrm{}$, and depends upon the value of a new parameter $\xi$, which gives the strength of the weak corrections to strong processes. A characteristic result of the theory is the prediction of a nonelectromagnetic isospin breaking. This solves the $\eta \to 3\pi$ puzzle and accounts for the observed deviation from the Dashen sum rule: ${m_K}^{+2\mathrm{}}-{m_K}^{02}={m_{\pi }}^{+2\mathrm{}}-{m_{\pi }}^{02}$. Although we are not able to give a theoretical evaluation of $\xi$ in a realistic model of weak interactions, a phenomenological determination of $\xi$ is proposed, based on the observed isospin-breaking mass splittings among pseudoscalar mesons. In this way we get the prediction $\theta \approx 0.25$, which is in good agreement with the experimental value.