Weak decays of heavy quarks

To investigate the role of real gluons in heavy meson weak decays, we compute the first-order QCD corrections to the total rate for the weak decay of a heavy quark. We find that to this order there are no leading log contributions. Furthermore, the first-order QCD corrections depress the total decay rate, although they provide an enhancement of the nonleptonic rate over the semileptonic rate. We discuss the relevance of our results to the usual picture of QCD enhancements based on short-distance expansions of weak decay amplitudes.