Decays

The decay of an ``isolated'' with large invariant mass is similar to that of a virtual photon with the same mass; the latter case is discussed in Ref. [2]. The decay is initiated by the production of a pair. The possibility of final state interactions allows these quarks to be produced with a spectrum of invariant masses extending up to the kinematic limit . Very large quark invariant masses are dissipated by radiation of a cascade of gluons at short distances, as described by perturbation theory. However, for parton invariant masses below a critical , this perturbative description becomes inadequate, and one must resort to a largely phenomenological model for the final formation of hadrons.

At present, the only available source of ``isolated'' is heavy leptons decay , in which the has an invariant mass spectrum (with , and assuming the observed coupling): the decays of thus produced are therefore dominated by the region of low parton invariant masses, inaccessible to perturbation theory. In the free quark approximation (presumably valid as ) the diagram of Fig. 1 for T decay implies a leptonic branching ratio (recall the three possible colors of a quark pair). Perturbative gluon exchanges between the final quarks modify this to (2). Ignoring quark masses, the complete leptonic branching ratio may be estimated using the relation of weak and electromagnetic currents mentioned above by integration of the observed isovector decay rate (this isospin component is identified by even numbers of final ) over the invariant mass spectrum produced in decay, suggesting an suppression relative to the free quark result [3]. (For , this estimate fortuitously agrees with the perturbative result.) Experimental measurements are as yet of insufficient precision to test the estimate (e.g., Ref. [4]).

[ Figure 1 ] Schematic diagram for semileptonic decay of a heavy lepton.

In addition to their total rate, other inclusive features of decays may be considered. The angular distribution of final state hadronic energy could be calculated at high by QCD perturbation theory, but in decays is dominated by hadronic effects, leaving no trace of two quark jets. For any serious application of QCD perturbation theory to be possible, it is essential that the final formation of hadrons is sensitive only to the local structure of the parton state, and not on its global properties or details of its production (for further discussion on this point, see Ref. [2]). The approximate agreement between multiplicities measured in decays and in related decays supports this belief.

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