QCD tests from r decay

The inclusive semi-leptonic decay rate of the r lepton could provide an important testing ground for QCD if and when a r factory is constructed. The simplest quantity to look at is the ratio 

On the other hand, from the data on the branching fraction BRe for a T to decay into an electron (or into a muon, BR = 0.973BRe) we have (see Table 14.1) 

Since the accuracy of both measurements should increase considerably in the near future, let us briefly discuss the corrections expected to the naive prediction (4.3.4). These come from contributions such as (i) electroweak, (ii) perturbative QCD and (iii) non-perturbative QCD. 

The electroweak corrections are small but are not negligible as they are proportional to ln(M /mT). The estimate (Marciano and Sirlin, 1988) 

QCD perturbative corrections are in principle calculable by treating the reactions as the decay into ud (or us) plus gluons and additional qq pairs, as if the latter were free particles. This gives (Narison and Pich, 1988 Braaten, 1989a) 

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