Chiral Perturbation Theory for $τ\to ρπν_τ$, $τ\to K^* πν_τ$, and $τ\to ωπν_τ$

We use heavy vector meson $SU(2)_L \times SU(2)_R$ chiral perturbation theory to predict differential decay distributions for $\tau \rightarrow \rho \pi \nu_\tau$ and $\tau \rightarrow K^* \pi \nu_\tau$ in the kinematic region where $p_V \cdot p_\pi/m_V$ (here $V = \rho$ or $K^*$) is much smaller than the chiral symmetry breaking scale. Using the large number of colors limit we also predict the rate for $\tau \rightarrow \omega \pi \nu_\tau$ 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.