Measurement of the $\tau$ Lepton Lifetime with the Three-dimensional Impact Parameter Method

A new method is presented for the measurement of the mean $\tau$ lepton lifetime using events in which $\tau$'s are pair-produced and both $\tau$'s decay to hadrons and $\nu_\tau$. Based on the correlation between the two $\tau$'s produced at a symmetric $e^+ e^-$ collider, the 3DIP method relies on the three-dimensional information from a double-sided vertex detector and on kinematic constraints for the precise measurement of the $\tau$ decay angles. Using the data collected from 1992 to 1994 with the ALEPH detector at LEP, a $\tau$ lifetime of $288.0 \pm 3.1 \pm 1.3 $\fs is obtained from the sample in which both $\tau$'s decay to one charged track, and $292.8 \pm 5.6 \pm 3.0 $\fs from the sample in which one $\tau$ decays to one prong and the other to three prongs. The results show small statistical correlations with those derived from other methods. When combined with the previously published ALEPH measurements, the resulting $\tau$ lifetime is $291.2 \pm 2.0 \pm 1.2 $\fs .