Vector-Meson Mixing and Broken Nonet Symmetry

Vector-meson mixing is investigated using a simple ansatz for the vector-meson nonet propagator. The first and the modified second spectral-function sum rules of Weinberg are tested using this ansatz. As a consequence it is found that the first sum rules possess a higher symmetry than is usually assumed. The modifications to the second sum rules are found to be incorrect in certain cases. In addition the $\omega -\phi$ mixing angle is estimated and found to be close to the ideal value. The quantity $\frac{f_{\kappa }}{f_{\pi }}$ is calculated and used to test the validity of a conjectured modified second sum rule. Finally two independent methods are used to estimate $\Delta \mathrm{}\left(0\right)=\frac{1}{2}f_{\kappa }^{}{}_{}{}^{2}m_{\kappa }^{}{}_{}{}^2$. Agreement is found between the methods, but the result is found to be larger by a factor of 2 than the usually accepted "standard value."