Hadronic structure in the decay tau(-) -> nu(tau)pi(-) pi(0) pi(0) and the sign of the tau neutrino helicity

Based on a sample corresponding to 4.3 x 10(6) produced tau-pair events, we have studied hadronic dynamics in the decay tau(-)--> nu(tau) pi(-) pi(o)pi(o) in data recorded by the CLEO II detector operating at the CESR e(+)e(-) collider. The decay is dominated by the process tau(-)-->nu(tau)a(1)(-)(1260), with the a(1)(-) meson decaying to three pions predominantly via the lowest dimensional (mainly S-wave) rho(-)pi(o) Born amplitude. From model-dependent fits to the Dalitz plot and angular observables in bins of 3 pi mass, we find significant additional contributions from amplitudes for a(1) decay to sigma pi, f(o)(1370) pi, and f(2)(1270) pi, as well as higher dimensional a(1)-->rho pi and rho' pi amplitudes. Notably, the squared sigma pi amplitude accounts for approximately 15% of the total tau(-)-->nu(tau)pi(-)pi(o)pi(o) rate in the models considered. The data are well described using couplings to these amplitudes that are independent of the 3 pi mass. These amplitudes also provide a good description for the tau(-) -->nu(tau)pi(-)pi(+)pi(-) Dalitz plot distributions. We have searched for additional contributions from tau(-)-->nu(tau)pi' -(1300). We place 90% confidence level upper limits on the branching fraction for this channel of between 1.0 x 10(-4) and 1.9 x 10(-4), depending on the pi' decay mode considered. The pi(-)pi(o)pi(o) mass spectrum is parametrized by a Breit-Wigner form with a mass-dependent width which is specified according to the results of the Dalitz plot fits plus an unknown coupling to an a(1)-->K*K amplitude. From a chi(2) fit using this parametrization, we extract the pole mass and width of the a(1), as well as the magnitude of the K*K coupling. We have also investigated the impact of a possible contribution from the a(1)'(1700) meson on this spectrum. Finally, exploiting the parity-violating angular asymmetry in a(1)-->3 pi decay, we determine the signed value of the tau neutrino helicity to be h(nu tau) = - 1.02+/-0.13 (stat) +/- 0.03 (syst + model), confirming the left-handedness of the tau neutrino.