Introduction

The short range fm of exchanges compared to the distances fm at which QCD interactions become strong inspires the hope that QCD perturbation theory may be relevant even in low-energy hadronic weak processes. As usual, however, the development of initial or final hadron states at large distances, where quarks and gluons are nearly on their mass shells, is quite inaccessible by perturbation theory. Only in inclusive measurements on very high invariant mass hadron systems are these effects unimportant. In strange particle decays and to a large extent also T lepton and charmed hadron decays the evolution of the hadron final state at large distances is crucial, and QCD perturbation theory is unable to provide a precise quantitative description: it must be supplemented by estimates of hadronic effects based at best qualitatively on QCD. In inclusive weak decays of heavier (e.g., b) hadrons, the final state hadronic effects should be less important; however, when the decaying hadron contains light quarks, the structure of the initial state cannot be estimated reliably. In applications of QCD to processes involving large momentum transfers (e.g., deep inelastic scattering), ignorance of initial hadron structure may largely be overcome by comparison of results for different values of the large momentum, in which small momentum details are factorized out: this procedure is usually inapplicable in weak decays since the initial hadron is fixed. In the face of these severe difficulties, I do not attempt a precise quantitative analysis of weak decays; rather, I shall consider the basic physical phenomena which appear to be dominant in weak decays, with the hope that their qualitative effects will remain unchanged in an eventual exact treatment. This paper is a review in that it covers a very broad area; many novel points are, however, discussed.

I discuss the several varieties of weak hadronic decays in turn. The simplest is probably the decay of a real boson: if all quark masses are ignored (the chiral symmetry limit), inclusive properties of the hadron final state are the same as would result from decay of a virtual photon with invariant mass . This simplicity is preserved when virtual bosons are produced by a purely leptonic process, such as in heavy lepton decay . The small T mass renders neglect of hadronic effects in decay impossible: nevertheless, the total decay rate is (fortuitously) well approximated by perturbation theory. Decays to single mesons give information on couplings. The same couplings appear in the weak decays of these mesons: for pseudoscalar they measure the violation of chiral symmetry in QCD. Ignorance of structure prevents direct estimation of such decays, except for cases such as . After these leptonic decays, the next major class of weak decays discussed below are the semileptonic ones, of the form , where is a hadron (meson or baryon) and X denotes any hadronic system. Most such decays proceed through a decay of the heavy quark in (although in some meson decays, processes such as , where is a ``spectator'' quark in , may be important, as discussed below). Final state gluon emission and interactions with ``spectator'' quarks from the initial may modify the rate for the complete decay: for charmed meson decays, there is some phenomenological evidence that the modifications to the total rate are small; the lepton energy spectrum is, however, considerably softened. For strange particle decays, the small number of accessible final states make coherent hadronic effects crucial: nevertheless, rates for decays to specific final states may often be estimated by symmetry considerations. The most complicated but most revealing weak decays are the non-leptonic ones. The dominant fundamental mechanisms for such decays are probably (a) , (b) (or and (c) ( are light quarks and denotes a gluon). (Process (a) occurs by diagrams analogous to decay; (b) occurs through or , or channel exchange, depending on the initial charge; (c) occurs through a loop, yielding a (color) charge radius term). In strange particle decays, all three mechanisms may be present. Their relative importance is however probably determined not so much by their intrinsic rates as by the structure of the decaying strange hadrons. A striking phenomenological observation is that non-leptonic strange particle decays are enhanced by a factor of in amplitude over ones, while simple free quark estimates (which necessarily ignore process (c) since it involves a gluon) suggest that they should be comparable. This phenomenon might well be explained if the process (c) dominated these decays (since is pure ): however, no reliable quantitative estimates of its importance are available, but there are some qualitative suggestions that it is insufficient. The isospin structure in processes (a) and (b) depends on the color symmetries of their initial and final states. In the free quark approximation, the and components are of equal strength, but there are indications that gluon exchanges tend to enhance the rates for color channels which give : hadronic effects at large distances may also effect such an enhancement (as suggested by soft pion results in specific cases). In charmed particle decays, measurements of semileptonic branching ratios imply a much smaller enhancement of nonleptonic modes than in strange particle decays. The process (c) is Cabibbo suppressed for c decays, since it leads to final states; the phenomenological suppression of such final states suggests that (c) is indeed unimportant in this case. The observation of a larger hadronic decay width for ; than suggests that process (b) may dominate over (a) in the former case, and be unimportant by virtue of Cabibbo suppression in the latter, leaving (a) dominant. Quantitative estimates of this effect are however difficult. The structure of the decays of and heavier quarks are determined by the forms of their weak couplings. Non-leptonic decays of pseudoscalar mesons containing heavy quarks are probably increasingly dominated by process (a). The presence of light quarks in the lowest-lying such pseudoscalar mesons precludes accurate estimates of their structure. However, weak decays of mesons containing predominantly heavy quarks should be more amenable to reliable estimation: For example, weak parity-violating admixtures into inclusive non-leptonic decays may be calculated with some certainty, and are perhaps not beyond experimental reach at the 0 (1%) level. The possibility of proton decay via in grand unified gauge models has recently received much attention. Modifications to the free quark approximation for this decay rate may occur just as they do for ordinary weak decays; gluon exchange effects may be more important because of the shorter range of the primary interaction (and thus the larger the possible exchanged gluon momenta); nevertheless mundane hadronic effects probably introduce larger uncertainties.

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