Hadronic structure in the decay τ^-→ν_τπ^-π ⁰π⁰ and the sign of the tau neutrino helicity

Based on a sample corresponding to 4.3×10⁶ produced τ-pair events, we have studied hadronic dynamics in the decay τ^-→ν_τπ^-π ⁰π⁰ in data recorded by the CLEO II detector operating at the CESR e⁺e^- collider. The decay is dominated by the process τ^-→ν_τa₁^-(1260), with the a₁^- meson decaying to three pions predominantly via the lowest dimensional (mainly S-wave) ρ^-π⁰ Born amplitude. From model-dependent fits to the Dalitz plot and angular observables in bins of 3 π mass, we find significant additional contributions from amplitudes for a₁ decay to σπ, f₀(1370)π, and f₂(1270)π, as well as higher dimensional a₁→ρπ and ρ′ π amplitudes. Notably, the squared σπ amplitude accounts for approximately 15% of the total τ^- →ν_τπ^-π⁰π⁰ rate in the models considered. The data are well described using couplings to these amplitudes that are independent of the 3π mass. These amplitudes also provide a good description for the τ^- →ν_τπ^-π⁰π⁰ Dalitz plot distributions. We have searched for additional contributions from τ^-→ν_τπ′ -(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 π′ decay mode considered. The π^-π⁰π⁰ 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 a₁→K*K amplitude. From a χ² fit using this parametrization, we extract the pole mass and width of the a₁, as well as the magnitude of the K*K coupling. We have also investigated the impact of a possible contribution from the a₁′(1700) meson on this spectrum. Finally, exploiting the parity-violating angular asymmetry in a₁→3π decay, we determine the signed value of the τ neutrino helicity to be h_ντ=-1.02±0.13 (stat)±0.03 (syst+model), confirming the left-handedness of the τ neutrino.