The decay τ→3πν_τ and characteristics ofa ₁ meson

Abstract

The phenomenological meson Lagrangian based on the four-quark interactions of the scalar, pseudoscalar, vector and axial-vector types is used for description of the decay τ⁻→π⁺π⁻π⁻ v _τ. The structure of the main hadronic vertexa ⁻₁ ρπ is discussed. The expression for the axial hadronic currentJ ^μ(a ₁→3π) is obtained. The low-energy limit of this current is analysed. Spectral functions for the main channel of the given process are calculated. The fitting of the experimental data leads to the following values of thea ₁ parameters:

$$\begin{gathered} m_{a_1 } = 1242 \pm 37MeV,\Gamma _{a_1 } = 465_{ - 143}^{ + 228} MeV\left( {DELCO} \right); \hfill \\ \hfill \\ m_{a_1 } = 1260 \pm 14MeV,\Gamma _{a_1 } = 298_{ - 34}^{ + 40} MeV\left( {MARK II} \right); \hfill \\ \hfill \\ m_{a_1 } = 1250 \pm 9MeV,\Gamma _{a_1 } = 488 \pm 32MeV\left( {ARGUS} \right). \hfill \\ \end{gathered} $$