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

Based on a sample corresponding to $4.3\\ifmmode\\times\\else\\texttimes\\fi{}{10}^{6}$ produced $\\ensuremath{\\tau}$-pair events, we have studied hadronic dynamics in the decay ${\\ensuremath{\\tau}}^{\\ensuremath{-}}\\ensuremath{\\rightarrow}{\\ensuremath{\\nu}}_{\\ensuremath{\\tau}}{\\ensuremath{\\pi}}^{\\ensuremath{-}}{\\ensuremath{\\pi}}^{0}{\\ensuremath{\\pi}}^{0}$ in data recorded by the CLEO II detector operating at the CESR ${e}^{+}{e}^{\\ensuremath{-}}$ collider. The decay is dominated by the process ${\\ensuremath{\\tau}}^{\\ensuremath{-}}\\ensuremath{\\rightarrow}{\\ensuremath{\\nu}}_{\\ensuremath{\\tau}}{a}_{1}^{\\ensuremath{-}}(1260),$ with the ${a}_{1}^{\\ensuremath{-}}$ meson decaying to three pions predominantly via the lowest dimensional (mainly S-wave) ${\\ensuremath{\\rho}}^{\\ensuremath{-}}{\\ensuremath{\\pi}}^{0}$ Born amplitude. From model-dependent fits to the Dalitz plot and angular observables in bins of $3\\ensuremath{\\pi}$ mass, we find significant additional contributions from amplitudes for ${a}_{1}$ decay to $\\ensuremath{\\sigma}\\ensuremath{\\pi},$ ${f}_{0}(1370)\\ensuremath{\\pi},$ and ${f}_{2}(1270)\\ensuremath{\\pi},$ as well as higher dimensional ${a}_{1}\\ensuremath{\\rightarrow}\\ensuremath{\\rho}\\ensuremath{\\pi}$ and ${\\ensuremath{\\rho}}^{\\ensuremath{'}}\\ensuremath{\\pi}$ amplitudes. Notably, the squared $\\ensuremath{\\sigma}\\ensuremath{\\pi}$ amplitude accounts for approximately 15% of the total ${\\ensuremath{\\tau}}^{\\ensuremath{-}}\\ensuremath{\\rightarrow}{\\ensuremath{\\nu}}_{\\ensuremath{\\tau}}{\\ensuremath{\\pi}}^{\\ensuremath{-}}{\\ensuremath{\\pi}}^{0}{\\ensuremath{\\pi}}^{0}$ rate in the models considered. The data are well described using couplings to these amplitudes that are independent of the $3\\ensuremath{\\pi}$ mass. These amplitudes also provide a good description for the ${\\ensuremath{\\tau}}^{\\ensuremath{-}}\\ensuremath{\\rightarrow}{\\ensuremath{\\nu}}_{\\ensuremath{\\tau}}{\\ensuremath{\\pi}}^{\\ensuremath{-}}{\\ensuremath{\\pi}}^{+}{\\ensuremath{\\pi}}^{\\ensuremath{-}}$ Dalitz plot distributions. We have searched for additional contributions from ${\\ensuremath{\\tau}}^{\\ensuremath{-}}\\ensuremath{\\rightarrow}{\\ensuremath{\\nu}}_{\\ensuremath{\\tau}}{\\ensuremath{\\pi}}^{\\ensuremath{'}}\\ensuremath{-}(1300).$ We place $90%$ confidence level upper limits on the branching fraction for this channel of between $1.0\\ifmmode\\times\\else\\texttimes\\fi{}{10}^{\\ensuremath{-}4}$ and $1.9\\ifmmode\\times\\else\\texttimes\\fi{}{10}^{\\ensuremath{-}4},$ depending on the ${\\ensuremath{\\pi}}^{\\ensuremath{'}}$ decay mode considered. The ${\\ensuremath{\\pi}}^{\\ensuremath{-}}{\\ensuremath{\\pi}}^{0}{\\ensuremath{\\pi}}^{0}$ 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 ${a}_{1}\\ensuremath{\\rightarrow}{K}^{*}K$ amplitude. From a ${\\ensuremath{\\chi}}^{2}$ 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 ${a}_{1}^{\\ensuremath{'}}(1700)$ meson on this spectrum. Finally, exploiting the parity-violating angular asymmetry in ${a}_{1}\\ensuremath{\\rightarrow}3\\ensuremath{\\pi}$ decay, we determine the signed value of the $\\ensuremath{\\tau}$ neutrino helicity to be ${h}_{{\\ensuremath{\\nu}}_{\\ensuremath{\\tau}}}=\\ensuremath{-}1.02\\ifmmode\\pm\\else\\textpm\\fi{}0.13 (\\mathrm{stat})\\ifmmode\\pm\\else\\textpm\\fi{}0.03 (\\mathrm{s}\\mathrm{y}\\mathrm{s}\\mathrm{t}+\\mathrm{m}\\mathrm{o}\\mathrm{d}\\mathrm{e}\\mathrm{l}),$ confirming the left-handedness of the $\\ensuremath{\\tau}$ neutrino.