Decay modes and branching ratios

The partial widths for most of the decay modes can be calculated with the present understanding of the Standard Model. The purely leptonic decays can be calculated rigorously, including radiative corrections. Most of the major semileptonic decays with accompanying hadrons can be calculated reliably using experimental data such as and decay constants and the cross section of annihilation into hadrons. Since some of the semileptonic decays cannot be calculated accurately, the total decay width is unknown. It is therefore customary to express the branching ratios normalized to the electron branching ratio . Alternatively, the dependence on can be eliminated by taking the ratio of two branching ratios. This is actually a preferred method of comparing the experimental measurement with the theoretical expectation because many systematic errors cancel in the ratio. In fact, some of the current experiments may be systematics limited after collecting data for a few more years. Since we do not expect any dramatic improvement in the systematic errors in the large data sample expected with the detector under discussion here, comparing the ratio is the only reliable method for the precision test of the prediction. In this section, we discuss the expected precision of the ratios. Also included is a discussion on the sensitivity on the highly suppressed second-class-current decay and the forbidden lepton-number-violating decays.

Tau decays to and In the Standard Model, the purely leptonic decays of the can be calculated rigorously, including the electroweak radiative corrections. This allows a precise test of lepton universality. The branching ratios for the two decays differ by a small phase space factor[62][60], where . The current ratio is [42].

At the present time the most precise measurement of the electronic branching fraction is from CLEO II using a data sample in which both 's decay into electrons[63]. This analysis exploits the power of the CsI calorimeter and charged particle tracking system to reduce the backgrounds from radiative Bhabha and pair events to below 1%. A measurement of using a similar technique is now in progress. Since the momentum of a candidate is required to be greater than 1 GeV/c for proper identification, the same momentum cut must be imposed on the candidates for cancellation of the systematic uncertainties from tracking in /. Based on the CLEO II experience, we expect to obtain some events and a similar number of events from pairs; this corresponds to a statistical precision of 0.28%on the ratio /. The background from other decay modes is expected to be less than a few percent and hadronic backgrounds are expected to be less than 1%, contributing equally to both samples. The overall systematic error in / from the background corrections should be less than 0.1%. The other main source of systematic error is the detection efficiency which has two components: trigger and particle identification. The uncertainties in the and identification efficiency do not cancel in the ratio because of the very different techniques involved. Detection efficiency uncertainty in the ratio could be known to 0.7%and this will dominate the overall precision.

An alternative method would use and events to obtain . This would likely reduce the systematic error due to more complete cancellation of various contributions, especially from trigger effects. We estimate our efficiency for such decay modes to be 15%, giving us some of each type. The statistical uncertainty on / in that case would be 0.22%. With either of these analyses, lepton universality, therefore, can be tested with much improved precision over current measurements.

Tau decays to and The partial widths for the two pseudo-scalar decays, and , can be calculated using the experimental measurements of the and decay constants, and . The ratio of the two partial widths is related by the Cabibbo angle with a phase space correction factor [62][60], Therefore, a precise measurement of the ratio of the branching ratios allows an accurate determination of the Cabibbo angle in decay with high momentum transfer. At present, the ratio is known only to [42].

The CLEO II detector is not well suited for the measurement of this ratio. An accurate measurement of requires good identification at high momenta since the momentum spectrum of the or is relatively flat up to 5 GeV/c and is about 17 . A preliminary study of using one-prong tau decays () finds only 43 events/fb yielding a detection efficiency of 0.45%in CLEO II. The detection efficiency is reduced greatly because a momentum cut of GeV/c is required to obtain a relatively background free sample of decays. Increasing the momentum acceptance of the kaon to 3 GeV/c in CLEO III would increase the efficiency by roughly an order of magnitude.

For a data sample of and improved particle identification at high momentum we expect to identify candidates. Based on our preliminary analysis, the expected background level in the sample is 1%. Assuming a similar detection efficiency for , we expect events. Thus, could be measured with a statistical precision of 1%, a dramatic improvement over the current world average measurement.

Tau decays to and The decays and involve the coupling of the weak vector current to and , respectively. Measurements of the branching ratios allow studies of the hadronic weak current. . The Cabibbo-suppressed decay is related[60] to the Cabibbo-favored decay by where the factor corrects for the differences in the available phase space, and are the coupling strengths of the and to the vector current. The relationship between the two couplings depends on whether the SU(3) symmetry is exact or broken. If SU(3) were exact, then giving On the other hand, for broken SU(3) the Das-Mathur-Okubo[64] sum rules give and the prediction becomes The current world average measurement of the ratio is , which excludes the exact SU(3) symmetry at level[42].

For the measurement of the ratio, , the and candidates can be selected using events where one decays via or . For a data sample of , we expect to collect candidates for a detection efficiency of 15%. Traditionally, the decay is identified with a detached vertex through the decay chain, . Including the branching ratio for the decay chain, the detection efficiency is expected to be 5%. This yields candidates, corresponding to a statistical precision of 0.8%on the ratio of branching ratios. The dominant background in the sample is the 3%feed down from the decay . In the sample, we expect a contamination of 5%from the three-charged-pion decay. The background from the misidentification of as a lepton tag has equal contributions to both samples. We expect an overall systematic error of 0.4%from the uncertainty in the background subtraction. Since the topology of the decay is quite different from that of the , the systematic errors in identification efficiencies do not cancel in the ratio. We expect a systematic uncertainty of 1.6%on the ratio of these efficiencies. This yields an overall precision on the ratio of 1.8%, allowing a sensitive test of the Das-Mathur-Okubo sum rules.

An independent method of measuring the ratio is to use the other decay channel . A preliminary analysis using CLEO II data where the is required to have GeV/c yields 18 candidates per fb with about 20%background. The overall detection efficiency for this process is only 0.23%and is dominated by the limited momentum range of particle identification. Extending the identification up to 3 GeV/c would increase the detection efficiency for this mode by a factor of 15. A similar gain in the purity of the sample is expected with improved particle identification. Thus, for a 30 fb data set, we expect 4500 events providing a measurement of with a statistical precision of 1.5%and with much lower systematics than the previous method.

Tau decays with mesons CLEO has recently observed the first example of decays with an meson in the final state, [65]. The branching ratio for the decay has been calculated using the measured cross section for together with the CVC hypothesis. Using the cross sections measured at Novosibirsk and DCI, Gilman predicts[66] the branching ratio to be %. This is in good agreement with the CLEO II measurement of ()%.

There is no firm theoretical prediction on the branching ratio for the decay . However, the branching ratio is related to that for the decay by isospin invariance: .

The decay is allowed in the Standard Model but is suppressed. The branching ratio has been estimated using a Chiral Effective Lagrangian by A. Pich[67], There are other decay modes such as and which are predicted to have very small branching ratios.

To study the above decays requires large data samples and these can only be observed and studied at a facility with CESR Phase 3 levels of luminosity and a detector comparable to CLEO III.

Second-class-current decay The decay is of particular interest in the Standard Model of electroweak interactions as it is an example of a decay via a second class current. Weak currents are classified according to their parity as shown in Table .

Since the final state contains two pseudoscalars, the decay must proceed by a vector current, but the parity of the is , hence this proceeds through a second class current. Second class currents are strongly suppressed due to isospin symmetry in the Standard Model and a branching ratio of order is expected. Observation of a sizable branching fraction could indicate the existence of second class currents or some other new interaction. The current upper limit on this branching ratio is at the 95%confidence level[65] and could approach for CLEO II, but will likely be limited by background from given the poor CLEO II separation.

The simplicity of the decay process provides a clean laboratory for the search[68]. The candidates for the decay can be selected with a lepton tag. A tag with no accompanying photon may also be possible. The meson is required to decay into the final state. The other decay channel, , is not usable because of the large background from the unsuppressed decay . The dominant backgrounds are expected to be due to the following decay modes:

• , where one of the photons from the decay is lost and the other photon is combined with initial state radiation or a fake photon created by the crystal clustering algorithm due to shower fluctuation or noise.
• , where one photon from each decay is lost because the photon is very soft or merged with another photon.
• , with the misidentified as a .

Forbidden decays The search for decays forbidden by the Standard Model has long been a tradition of particle physics. In recent years the immense interest in models that go beyond the Standard Model, such as compositeness, technicolor, lepto-quark, and new horizontal gauge bosons, has intensified interest in these kinds of searches[69].

The traditional hunting ground, such as or decay, has a limited number of decay channels because of the limited phase space. The lepton is an ideal laboratory for the search of the decay of a third generation lepton into first or second generation leptons or hadrons. The large lepton mass allows the decay into a number of purely leptonic final states such as and or semileptonic final states such as and . In several interesting models the rate for a lepton number violating decay involving a is many orders of magnitude larger than a similar decay involving a muon due to the large mass of the . For example, in a superstring model decays are enhanced by over muon decays leading to the prediction that . In a model with a charged Higgs, decays are enhanced by leading to the prediction that .

To date the most sensitive search for lepton number violating decays has been carried out by the CLEO II experiment. Here a 95%confidence limit of has been set for the decay [70]. Other experiments have set limits on similar decays which are in the range of to [42]. Since almost all of these searches have been limited by statistics (e.g., the CLEO II result on ), we expect to reach the sensitivity of for most channels with a sample of 30 fb.