Theory ofτmesonic decays

Abstract

Studies of $\ensuremath{\tau}$ 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 $\ensuremath{\tau}$ lepton: $3\ensuremath{\pi}$, $f(1285)\ensuremath{\pi}$. Both the $\ensuremath{\rho}$ and the ${a}_{1}$ meson contribute to the decay $\ensuremath{\tau}\ensuremath{\rightarrow}{K}^{*}K\ensuremath{\nu}$; it is found that the vector current is dominant. CVC is tested by studying ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$. The branching ratios of $\ensuremath{\tau}\ensuremath{\rightarrow}\ensuremath{\omega}\ensuremath{\pi}\ensuremath{\nu}$ and $K\mathrm{K\ifmmode\bar\else\textasciimacron\fi{}}\ensuremath{\nu}$ are calculated. In terms of a similar mechanism the $\ensuremath{\Delta}s=1$ decay modes of the $\ensuremath{\tau}$ lepton are studied and ${K}_{a}$ dominance is found in $\ensuremath{\tau}\ensuremath{\rightarrow}{K}^{*}\ensuremath{\pi}\ensuremath{\nu}$ and ${K}^{*}\ensuremath{\eta}\ensuremath{\nu}$. The suppression of $\ensuremath{\tau}\ensuremath{\rightarrow}K\ensuremath{\rho}\ensuremath{\nu}$ is revealed. The branching ratio of $\ensuremath{\tau}\ensuremath{\rightarrow}\ensuremath{\eta}K\ensuremath{\nu}$ is computed. As a test of this theory, the form factors of $\ensuremath{\pi}\ensuremath{\rightarrow}e\ensuremath{\gamma}\ensuremath{\nu}$ and $K\ensuremath{\rightarrow}e\ensuremath{\gamma}\ensuremath{\nu}$ are determined. The theoretical results agree with data reasonably well.