Measurement of the Branching Fraction for $\tau \to \rho \nu$

This Letter presents a measurement of the decay ${\tau }^{-}\to {\rho }^{-}{\nu }_{\tau }$ using data obtained with the Mark II detector at SPEAR. In the center-of-mass energy region $4.5<~E_{\mathrm{c}.\mathrm{m}.\mathrm{}}<~6.0$ GeV 85 events are observed in which a charged $\rho$ was found in coincidence with either an electron or a muon. It was determined that $B({\tau }^{-}\to {\rho }^{-}{\nu }_{\tau })=(20.5\mathrm{}\pm 4.1)\%$ and the ratio $\frac{B({\tau }^{-}\to {\rho }^{-}{\nu }_{\tau })}{B({\tau }^{-}\to e^{-}{\nu }_{\tau }{\overline{\nu }}_e)}=1.11\mathrm{}\pm 0.23$.