Hadronic structure in the decayτ−→ντπ−π0π0and the sign of the tau neutrino helicity

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Abstract

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.

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