Chiral Perturbation Theory for $\tau \to \rho \pi {\nu }_{\tau }$, $\tau \to K^{\ast }\pi {\nu }_{\tau }$, and $\tau \to \omega \pi {\nu }_{\tau }$

Abstract

We use heavy vector meson $SU(2{)}_L\times SU(2{)}_R$ chiral perturbation theory to predict differential decay distributions for $\tau \to \rho \pi {\nu }_{\tau }$ and $\tau \to K^{\ast }\pi {\nu }_{\tau }$ in the kinematic region where $p_V\cdot p_{\pi }/m_V$ (here $V=\rho$ or $K^{\ast }$) is much smaller than the chiral symmetry breaking scale. Using the large number of colors limit we also predict the rate for $\tau \to \omega \pi {\nu }_{\tau }$ in this region (now $V=\omega$). Comparing our prediction with experimental data, we determine one of the coupling constants in the heavy vector meson chiral Lagrangian.

Comments: 14 pages, latex 2e. We include the decay of the tau into the omega, pi minus and the tau neutrino, and extract a value for the coupling constant g2, using experimental data