New Determination of the Dalitz-Plot Distribution forτ−Decays

We have measured the $X$ and $Y$ projections of the Dalitz plot of 81000 ${\tau }^{-}$ decays. The decays were observed in a beam of 400-MeV/c $K^{-}\text{'}\mathrm{s}$ in the BNL 30-in. liquid-hydrogen bubble chamber. For the $X$ distribution we find no deviation from phase space. For $Y$ we find a distribution of $\left(\mathrm{phase}\mathrm{space}\right)\times \mathrm{}(1+AY)\mathrm{}$ and have determined for $A$ the values 0.252 ± 0.011 with Coulomb corrections to the distribution, 0.219±0.011 without Coulomb corrections. The results have been obtained using a method which involves measured rather than fitted quantities.