Rare decays

Precision measurement of Thus far the only evidence for the transition has been in the observation of leptons with momenta above that allowed for transitions. Recent measurements from CLEO II show somewhat smaller signals than reported originally[11]. Figure shows the CLEO II signal and Table provides a summary of recent measurements. The extracted values of are based on the Altarelli model[12], with the results of different models differing by more than 50%.

CLEO has searched for evidence of the exclusive semileptonic reactions , for which ARGUS has claimed an observation[15]. CLEO does not observe these final states and quotes an upper limit at the 90%confidence level[16]. The range of values reflects differences in theoretical models (see Fig. ). With twenty times the statistics expected from the CESR upgrade and the addition of background reduction supplied by particle identification and vertex detection, we should be able to measure the branching ratios, but probably not the form-factors.

Theoretical input on these crucial decay parameters may be obtained from applying HQET to the corresponding charm decays , which CLEO III can measure, and possibly from studies of .

Measurement of ``penguin'' processes Radiative decays can occur only via the ``penguin'' diagrams shown in Fig. . The simplest such decay is , since the decay is forbidden by angular momentum conservation. CLEO has recently made the first observation of this process[1]. The data are shown in Fig. and the measured branching ratio is .

There are also hadronic penguins. The diagrams for these processes can be obtained by replacing the photon with a gluon. Examples of such processes are and the Cabibbo-suppressed decay [17]. Interference between the rare ``penguin'' processes and the transitions may provide a means of seeing CP violation in decays. CLEO has recently shown evidence that these processes do exist[18].

The Standard Model requires penguins to explain decay and predicts decays that occur only via penguins to have branching ratios in the range. The inclusive branching ratio is predicted to be [19]. The shape of the inclusive hadronic mass spectrum[20] (see Fig. ) and exclusive branching ratios[21] (see Table ) have also been calculated. Measuring the branching ratios for explicit channels determines values of the form-factors at =0. These are intimately related to the form-factors in exclusive semileptonic decays and thus may be useful in pinning them down.

Another exciting possibility is to determine the length of one side of the CKM triangle by measuring the penguin process . This, when combined with , could be used to determine the ratio . Clearly, charged hadron identification is essential to distinguish the from the and it also very useful in reducing backgrounds in all of the rare decay channels.

As an illustration of the sensitivity of the penguin process to high mass objects beyond the Standard Model we show in Fig. the implications for the two Higgs doublet model. In such a model a charged Higgs boson can substitute for the in the loop. The figure shows the region in the space of mass versus ratio of vacuum expectation values that is consistent with the CLEO II limits on branching ratio. Masses less than 250 GeV/c are excluded for this model.

Another example is the search for a supersymmetric squark. Figure shows the region in the squark mass versus Higgs mass space[26] excluded by the CLEO II limits. Only the range is excluded.

Higher luminosity will increase the sensitivity to more loop decays and will allow a more precise comparison with Standard Model predictions, thus improving our sensitivity to high mass extensions or violations of the Model. This opens a window to new physics that is competitive with the much more expensive approach of building higher energy colliders.

The recent CLEO II observation of the sum of and mentioned above [2] is consistent with a loop decay branching ratio, . With the CESR/CLEO upgrade this measurement will improve as a result of the increased luminosity and the new high momentum particle identification system. Also we can expect many other loop decay modes to show up. Table shows some of the theoretical predictions.

Decays to baryon-antibaryon pairs The can decay to baryons and, therefore, offers a unique opportunity to study the dynamics of baryon pair creation in a reaction where at least the initial state and the initial coupling are well defined. Even at the most fundamental level we are completely ignorant of the production mechanism. For example, does it proceed through diquark-antidiquark pairs? There are data from CLEO and ARGUS on inclusive proton, , and yields in decay [27] but because of the low efficiencies for reconstructing exclusive decays of mesons and charmed baryons, a definitive study must await the larger data samples from the upgraded CESR.

Purely leptonic decays In the Standard Model the purely leptonic decay of the into a lepton and a neutrino should proceed as in pion decay, through the annihilation of the and quarks into a , materializing as . The rate is proportional to and to the bound-state overlap factor . Once is known, a measurement can give us an experimental value for , which comes into calculations of mixing, CP violation, and other weak processes involving the interaction between the quarks in the meson. Theoretical predictions for from QCD sum rules[28] and lattice calculations[29] cover the range from 105 to 187 MeV.

The leptonic decay rate is also sensitive to new physics; for example, the mass and coupling of a possible technipion can be limited [30] by Since the rate should be proportional to the square of the lepton mass, the most copious mode is , which however is identifiable only in tagged events, because of the missing neutrinos. The much smaller branching ratio for , about , might be measurable without tagging, since the muons will be nearly monoenergetic near the threshold. Very high luminosities may be required, however, since a branching ratio of yields only about one event per 10 fb at the . Non-Standard Model enhancements, however, could give a much larger event rate.

Forbidden dilepton decays Certain decays are strictly forbidden in the Standard Model, for example, those that violate an accepted conservation law. Still other decays may be allowed but at an undetectably low branching ratio. In the cases in which the particular final state is easily recognizable experimentally and not obscured by backgrounds, the search for such modes can expose weaknesses in the model. Typical examples are and , which are forbidden by the absence of transitions between lepton families in the Standard Model. If there were a ``horizontal gauge boson'' that would allow , the branching ratio for would be[31] The present CLEO[32] upper limit of , limited only by the size of the available event sample, implies a lower limit on the mass of the horizontal gauge boson of 8 TeV. The mass sensitivity increases as the fourth root of the number of decays searched.

The decays and violate the Standard Model GIM suppression of flavor changing neutral currents, but are allowed through loop diagrams at the level of and respectively[33]. The CLEO upper limits, for both[32], can be improved simply by searching larger data samples.