1-3 events: The decay length method (DL) described below uses only events with a 1-3 topology. Any pair of oppositely charged tracks which are consistent with originating from a photon conversion  are excluded. An event is then required to have exactly three tracks which form a common vertex in one hemisphere, and a single charged track in the opposite hemisphere. Each of the three tracks must have at least 25 hits in the CDC and at least one hit in the VXD, and the per degree of freedom of the track fit must be less than 5 for two of the tracks and less than 15 for the third. The probability for the vertex fit must be at least 0.02%. This results in a final sample of 257 events.
1-1 events: For the two methods employing impact parameters, only events with a 1-1 topology are used (here photon conversions are also removed). For the direct impact parameter (IP) method, at least one track in each event must have: a momentum greater than 3 GeV/c and less than 40 GeV/c, at least 40 CDC hits and at least one hit in the VXD, a polar angle in the range , a per degree of freedom for the track fit less than 5.0, and a distance of closest approach to the interaction point along the beam direction less than 2.5 mm. For the impact parameter difference (IPD) method, both tracks in each event must satisfy these criteria. For both methods the tracks must have opposite charge, each event must have a two-prong invariant mass of at least 8 GeV/c, the angle between the two tracks must be at least 2.8 rad, and the missing momentum in the event must satisfy These criteria result in a sample of 1556 tracks (from 912 events) for the IP method, and 642 events for the IPD method.
The main contamination for 1-3 events is from multihadron events, whereas for events in the 1-1 topology the primary backgrounds are Bhabha scattering, two-photon interactions, and muon-pair final states. Table i summarizes the background fractions in the final event samples used in each of the three tau lifetime measurements.
A few track and event quantities are plotted in Fig. 1 and Fig. 2 for tau-pair events in the 1-3 and 1-1 topologies, respectively. In all plots, the dots represent data and the histograms Monte Carlo. The three-prong momentum and invariant mass for 1-3 events are shown in Fig. 1(a) and 1(b), respectively. Figure 1(c) shows the largest opening angle between the three-prong momentum direction and one of the three tracks, while in Fig. 1(d) is plotted the probability of the three-prong vertex fit. The distributions in Fig. 2 for 1-1 events represent (a) the track momentum, (b) the track fit per degree of freedom, (c) the invariant mass of the two tracks and (d) their acolinearity. Good agreement is seen in all the distributions, indicating sufficient accuracy in the Monte Carlo simulation of the data.