Measurements of tau lepton decays provide a unique test of lepton universality. Assuming the tau to have the same coupling to the W-boson as the muon and electron, the tau mass , the tau lifetime , and the branching fraction are related as follows: where and are the mass and lifetime of the muon. Currently the precision of this test is limited by measurements of the lifetime and the electronic branching ratio of the tau.
The Stanford Linear Collider (SLC) and the SLC Large Detector (SLD) provide an excellent facility for measuring the tau lifetime. Decays of tau pairs produced at the mass peak are highly boosted and collimated, and are relatively easy to distinguish from other final states. In addition, the SLC is characterized by a very small and stable luminous region, while the SLD with its CCD pixel vertex detector has the capability of measuring three-dimensional space points with high resolution close to the interaction point. The combination of these features substantially reduces the uncertainty in the determination of both the production and decay points of the tau, allowing for precise measurements with a relatively small sample of events.
The results reported here are based on a sample of 1671 tau-pair candidates collected by SLD in 1992 and 1993. Three different techniques are used to determine the tau lifetime. In the first method, which uses tau-pair events in the 1 vs. 3 topology, the tau lifetime is extracted directly by measuring the decay length of the tau on the three-prong side of the event. The other two methods employ events in which both taus decay to a one-prong. In the impact parameter method, the tau lifetime is inferred from the distribution of impact parameters of the charged tracks, while in the impact parameter difference method, it is extracted from the correlation between the impact parameters and acoplanarity of the two tracks in the event. The decay length method gives a direct measurement of the tau lifetime, with relatively small backgrounds. The impact parameter and impact parameter difference techniques benefit from the large one-prong branching fraction of the tau, and are independent of the decay length method.