We report the results of a study of the three-prong decay mode of the $\tau$ in data taken with the DELCO detector at the SLAC $e^{+}{e}^{-}$ storage ring PEP. We determine the total three-prong branching ratio to be $B\left(3\right)=(12.1\mathrm{}\pm 0.5\pm 1.2)\%$ and the exclusive branching ratios $B(\tau \to {\pi }^{+}{\pi }^{-}{\pi }^{\pm }\nu )=(5.0\mathrm{}\pm 0.1)\%$ and $B(\tau \to {\pi }^{+}{\pi }^{-}{\pi }^{\pm }{\pi }^0\nu )=(6.0\mathrm{}\pm 1.2)\%$, respectively. The data with three charged pions allow for the determination of the mass and width of the $A_1$ resonance as $M_{A_1}=1056\mathrm{}\pm 20\pm 15$ MeV and ${\Gamma }_{A_1}={476}_{-120\mathrm{}}^{+132\mathrm{}}\pm 54$ MeV.

• Received 23 December 1985

DOI:https://doi.org/10.1103/PhysRevLett.56.2132