Application of Current Algebra in Three Pseudoscalar Meson Decays of $τ$ Lepton

Abstract

The decays of $τ\to 3πν$ and $τ\to πK^{*} ν, Kρν$ 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 $τ$ 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 $3π$ spectrum, we determine the $A_1$ parameters, $m_A=1.24\pm 0.02 GeV$, $Γ_A=0.43\pm 0.02$ GeV; the hard current algebra calculation yields a $3π$ branching ratio of $19 \pm 3 \%$.