Analysis of the decay $\tau^- \to \pi^-\pi^- \pi^+v_\tau$ and determination of thea 1(1260) resonance parameters

22 pp. (1993).
Using the ARGUS detector at the DORIS II $e^+e^−$ storage ring we have studied the three-pion hadronic final state in the decay $τ^- → π^-π^-π^+v_τ$. From about 7500 events we conclude that the three-pion system is dominated by the $J^P=1^+$ resonancea1 (1260) decaying preferentially via $ρ^0π^-$. Our data restrict a possible ρπ contribution of three-pion states without intermediate resonances to less than 6% at 95% CL. Fitting a model by Isgur et al. to the data yieldsma1=(1.211±0.007±0.0500.0)GeV/c$^2$ and $Γ$a1=(0.446±0.0021±0.1400.0)GeV/c$^2$. The second errors reflect the model dependence of the result. This is the currently most significant determination of thea1 resonance parameters. The ratio ofS- and D-wave amplitudes for the ρ0π- intermediate state of thea1− decay at the nominala1− mass was found to beD/S=−0.11±0.02. Using thisD/S ratio we update our former measurement of the parity violating asymmetry parameterγ $AV=2gAgV/(g^2_A+g^2_V)$ to 1.25±0.23±0.080.15. The branching ratio of the decay $τ^- → π^-π^-π^+v_τ$ is determined to be Br($τ^- → π^-π^-π^+v_τ$)=(6.8±0.1±0.5)%.