Application of Current Algebra in Three Pseudoscalar Meson Decays of $\tau$ Lepton

The decays of $\tau \to 3\pi \nu$ and $\tau \to \pi K^{*} \nu, K\rho \nu$ are calculated using the hard pion and kaon current algebra and assuming the Axial-Vector meson dominance of the hadronic axial currents. Using the experimental data on their masses and widths, the $\tau$ decay branching ratios into these channels are calculated and found to be in a reasonable agreement with the experimental data. In particular, using the available Aleph data on the $3\pi$ spectrum, we determine the $A_1$ parameters, $m_A=1.24\pm 0.02 GeV$, $\Gamma _A=0.43\pm 0.02$ GeV; the hard current algebra calculation yields a $3\pi$ branching ratio of $19 \pm 3 \%$.