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

Based on a sample corresponding to 4.3x10{sup 6} produced {tau}-pair events, we have studied hadronic dynamics in the decay {tau}{sup -}{yields}{nu}{sub {tau}}{pi}{sup -}{pi}{sup 0}{pi}{sup 0} in data recorded by the CLEO II detector operating at the CESR e{sup +}e{sup -} collider. The decay is dominated by the process {tau}{sup -}{yields}{nu}{sub {tau}}a{sub 1}{sup -}(1260), with the a{sub 1}{sup -} meson decaying to three pions predominantly via the lowest dimensional (mainly S-wave) {rho}{sup -}{pi}{sup 0} 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{sub 1} decay to {sigma}{pi}, f{sub 0}(1370){pi}, and f{sub 2}(1270){pi}, as well as higher dimensional a{sub 1}{yields}{rho}{pi} and {rho}{sup '}{pi} amplitudes. Notably, the squared {sigma}{pi} amplitude accounts for approximately 15% of the total {tau}{sup -}{yields}{nu}{sub {tau}}{pi}{sup -}{pi}{sup 0}{pi}{sup 0} 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}{sup -}{yields}{nu}{sub {tau}}{pi}{sup -}{pi}{sup +}{pi}{sup -} Dalitz plot distributions. We have searched for additional contributions from {tau}{sup -}{yields}{nu}{sub {tau}}{pi}{sup '}-(1300). We place 90% confidence level upper limits on the branching fraction formore » this channel of between 1.0x10{sup -4} and 1.9x10{sup -4}, depending on the {pi}{sup '} decay mode considered. The {pi}{sup -}{pi}{sup 0}{pi}{sup 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{sub 1}{yields}K{sup *}K amplitude. From a {chi}{sup 2} fit using this parametrization, we extract the pole mass and width of the a{sub 1}, as well as the magnitude of the K{sup *}K coupling. We have also investigated the impact of a possible contribution from the a{sub 1}{sup '}(1700) meson on this spectrum. Finally, exploiting the parity-violating angular asymmetry in a{sub 1}{yields}3{pi} decay, we determine the signed value of the {tau} neutrino helicity to be h{sub {nu}}{sub {tau}}=-1.02{+-}0.13 (stat){+-}0.03 (syst+model), confirming the left-handedness of the {tau} neutrino. (c) 1999 The American Physical Society.« less