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 $τ\rightarrow ρπν_τ$ and $τ\rightarrow K^* πν_τ$ in the kinematic region where $p_V \cdot p_π/m_V$ (here $V = ρ$ or $K^*$) is much smaller than the chiral symmetry breaking scale. Using the large number of colors limit we also predict the rate for $τ\rightarrow ωπν_τ$ in this region (now $V = ω$). Comparing our prediction with experimental data, we determine one of the coupling constants in the heavy vector meson chiral Lagrangian.