Measurement of the hadronic decay current in τ−→π−−+vτ

The decay τ−→π−−+vτ has been studied using data collected with the OPAL detector at LEP during 1992 and 1993. The hadronic structure functions for this decay are measured model independently assuming G-parity invariance and neglecting scalar currents. Simultaneously the parity violating asymmetry parameter is determined to be$$\gamma VA = 1.08 _{ - 0.41 - 0.25}^{ + 0.46 + 0.14} $$, consistent with the Standard Model prediction of γVA=1 for left-handed tau neutrinos. Models of Kühn and Santamaria and of Isgur et al. are used to fit distributions of the invariant 3π mass as well as 2π mass projections of the Dalitz plot. The model dependent mass and width of thea1 resonance are measured to be$$m_{a_1 } = 1.266 \pm 0.014_{ - 0.002}^{ + 0.012} $$ GeV and$$\Gamma _{a_1 } = 0.610 \pm 0.049_{ - 0.019}^{ + 0.053} $$ GeV for the Kühn and Santamaria model and$$m_{a_1 } = 1.202 \pm 0.009_{ - 0.001}^{ + 0.009} $$ GeV and$$\Gamma _{a_1 } = 0.422 \pm 0.023_{ - 0.004}^{ + 0.033} $$ GeV for the Isgur et al. model. The model dependent values obtained for the parity violating asymmetry parameter are γVA=0.87±0.27−0.06+0.05 for the Kühn and Santamaria model and γVA=1.10±0.31−0.14+0.13 for the Isgur et al. model. Within the Isgur et al. model the ratio of theS-andD-wave amplitudes is measured to beD/S=−0.09±0.03±0.01.