Semileptonic tau decays, structure functions, kinematics and polarisation

Abstract

The most general angular distribution of two or three meson final states from semileptonic decays $\tau\rightarrow \pi\pi\nu$, $K\pi\nu$, $\pi\pi\pi\nu$, $K\pi\pi\nu$, $K\pi\nu$, $KKK\nu$, $\eta\pi\pi\nu,\,\ldots{}$ of polarized $\tau$ leptons can be characterized by 16 structure functions. Predictions for hadronic matrix elements, based on CVC and chiral Lagrangians and their relations to the structure functions are discussed. Most of them can be determined in currently ongoing high statistics experiments. Emphasis of the kinematical analysis is firstly put on $\tau$ decays in $e^{+}e^{-}$ experiments where the neutrino escapes detection and the $\tau$ rest frame cannot be reconstructed. Subsequently it is shown, how the determination of hadron tracks in double semileptonic events allows to fully reconstruct the $\tau$ kinematics. The implications for the spin analysis are indicated.