Extended partially conserved axial-vector current hypothesis and model-dependent results

The corrections to Goldberger-Treiman relations for $\Delta S=0\mathrm{}$ and $\left|\Delta S\right|=1\mathrm{} \beta$ decays (${\Delta }_{\pi }$ and ${\Delta }_K$, respectively) are estimated from a Veneziano-type model for three-point functions. The effect of unitarizing the model is also discussed, and it turns out that ${\Delta }_{\pi }$ and ${\Delta }_K$ are almost insensitive to a variation in the widths of the pseudoscalar-meson daughters. Moreover, the predictions for ${\Delta }_{\pi }$ and ${\Delta }_K$ are in close agreement with experiment. Finally, on-mass-shell extrapolation factors for chiral anomalies in $\eta \to \gamma \gamma$ and $\eta \to {\pi }^{+}{\pi }^{-}\gamma$ are also derived, and agreement with experiment is found without the need for invoking $\eta -{\eta }^{\prime }$ mixing. In summary, the model discussed here seems to be a suitable implementation of the recently proposed extended partially conserved axial-vector current hypothesis.