Theory ofτmesonic decays

Studies of $\tau$ mesonic decays are presented. A mechanism for the axial-vector current at low energies is proposed. The VMD is used to treat the vector current. All the meson vertices of both normal parity and abnormal parity (Wess-Zumino-Witten anomaly) are obtained from an effective chiral theory of mesons. $a_1$ dominance is found in the decay modes of the $\tau$ lepton: $3\pi$, $f\left(1285\right)\mathrm{}\pi$. Both the $\rho$ and the $a_1$ meson contribute to the decay $\tau \to K^{*}K\nu$; it is found that the vector current is dominant. CVC is tested by studying $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}$. The branching ratios of $\tau \to \omega \pi \nu$ and $K\mathrm{K¯}\nu$ are calculated. In terms of a similar mechanism the $\Delta s=1\mathrm{}$ decay modes of the $\tau$ lepton are studied and $K_a$ dominance is found in $\tau \to K^{*}\pi \nu$ and $K^{*}\eta \nu$. The suppression of $\tau \to K\rho \nu$ is revealed. The branching ratio of $\tau \to \eta K\nu$ is computed. As a test of this theory, the form factors of $\pi \to e\gamma \nu$ and $K\to e\gamma \nu$ are determined. The theoretical results agree with data reasonably well.