Tau lifetime

The lifetime provides a direct measure of the coupling strength of the to the charged weak current. In the Standard Model, the decay proceeds in perfect analogy to the decay . Assuming universality of the weak coupling and that the neutrino is massless, the lifetime is related to the lifetime[60]. Neglecting corrections of , we have: The statistical precision of the lifetime measurement for a sample of events is given by where is the error in a single decay length measurement, is the beam spread, and ( at =10.5 GeV) is the average distance a travels before decaying. The constants , , and depend on the event topology. For events with the topology, while events have , , and . The first term in the above expression is due to the exponential nature of the decay process. In the second term, with the silicon vertex detector, we expect to be . The third term in the above expression takes into account the finite extent of the beams. To minimize this term, we can either select the events in the vertical plane or use events where both 's decay into three charged tracks (3 3). The measurement using 3 3 events is independent of the beam size () as it is the distance between the 's that is measured.

To date, the lifetime has been measured with a statistical precision of 2%by individual experiments[42]. With the CLEO III sample it should be possible to make several independent measurements of the lifetime each with statistical uncertainty below 1%. For example, using events where one decays into an electron or muon we expect a precision of 0.3%assuming a detection efficiency for this mode of 15%. From a similar analysis using 3 3 decays we expect a lifetime measurement with precision 0.5%assuming a 15%detection efficiency for this mode.

Systematic errors will most likely dominate the measurement of the lifetime. The systematic error in this measurement has several components including charged particle tracking, and uncertainty in the size, composition, and lifetime of the non- events in the sample. With the large data sample and improved tracking due to the silicon vertex detector, we expect that a systematic error below 1%is feasible.