Structure functions in the decay ${\tau }^{\mp }\to {\pi }^{\mp }{\pi }^0{\pi }^0{\nu }_{\tau }$

Using the CLEO II detector operating at the Cornell Electron Storage Ring (CESR) $e^{+}{e}^{-}$ collider, we have measured the structure functions in the decay ${\tau }^{\mp }\to {\pi }^{\mp }{\pi }^0{\pi }^0{\nu }_{\tau },$ based on a sample corresponding to $4\times {10}^6$ produced $\tau$-pair events. We determine the integrated structure functions, which depend only on the three pion invariant mass, as well as the structure functions differential in the Dalitz plot variables. We extract model independent limits on non-axial-vector contributions from the measured structure functions as less than $16.6\%$ of the total branching fraction, at the $95\%$ confidence level. Separating the non-axial-vector contributions into scalar and vector contributions, we measure that scalars (vectors) contribute with less than 9.4% (7.3%) to the total branching fraction, at the 95% confidence level.