Study of the Decay ${\mathit{\tau }}^{-}\to 2{\mathit{\pi }}^{-}{\mathit{\pi }}^{+}3{\mathit{\pi }}^0{\nu }_{\tau }$

The decay ${\tau }^{-}\to 2{\pi }^{-}{\pi }^{+}3{\pi }^0{\nu }_{\tau }$ has been studied with the CLEO II detector at the Cornell Electron Storage Ring. The branching fraction is measured to be $(2.85\pm 0.56\pm 0.51)\times {10}^{-4\mathrm{}}$. The result is in good agreement with the isospin expectation but somewhat below the conserved-vector-current prediction. We have searched for resonance substructure in the decay. Within the statistical precision, the decay is saturated by the channels ${\tau }^{-}\to {\pi }^{-}2{\pi }^0\omega {\nu }_{\tau }$, $2{\pi }^{-}{\pi }^{+}\eta {\nu }_{\tau }$, and ${\pi }^{-}2{\pi }^0\eta {\nu }_{\tau }$. This is the first observation of this ω decay mode and the branching fraction is measured to be $({1.89}_{-0.67\mathrm{}}^{+0.74\mathrm{}}\pm 0.40)\times {10}^{-4\mathrm{}}$.