Hadronic Structure in the Decay $\tau^{-}\to \nu_{\tau}\pi^{-}\pi^{0}\pi^{0}$ and the Sign of the Tau Neutrino Helicity

Based on a sample corresponding to 4.3 million produced tau-pair events, we have studied hadronic dynamics in the decay tau- --> nu_tau pi- pi0 pi0 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) a_1 --> rho pi Born amplitude. From fits to the Dalitz plot and angular observables, we find significant additional contributions from amplitudes for a_1 decay to sigma pi, f_0(1370) pi and f_2(1270) pi, as well as higher dimensional a_1 --> rho pi and rho' pi amplitudes. The squared sigma pi amplitude accounts for ~15% of the total tau- --> nu_tau pi- pi0 pi0 rate in the models considered. 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*10^{-4} and 1.9*10^{-4}, depending on the pi' decay mode. The pi- pi0 pi0 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 a coupling to an a_1 --> K* K amplitude. From a chi^2 fit, 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 --> 3pi 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.