Analysis of the decay τ^- →π^-π^-π⁺v_τ and determination of the a₁(1260) resonance parameters

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⁺ resonance a₁ (1260) decaying preferentially via ρ⁰π^-. 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 yields {Mathematical expression} and {Mathematical expression}. The second errors reflect the model dependence of the result. This is the currently most significant determination of the a₁ resonance parameters. The ratio of S- and D-wave amplitudes for the ρ⁰π^- intermediate state of the a₁^- decay at the nominal a₁^- mass was found to be D/S=-0.11±0.02. Using this D/S ratio we update our former measurement of the parity violating asymmetry parameter {Mathematical expression} to 1.25±0.23±_0.08^0.15. 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)%.