Theoretical Update of the Semileptonic Branching Ratio of B Mesons

We reconsider the prediction of the semileptonic branching ratio of B mesons, using the recent calculation [1] of the radiative corrections with account for finite quark masses in nonleptonic decays and taking into account 1/mb corrections. For the semileptonic branching ratio we obtain BSL = (11.8±1.6)% using pole quark masses and BSL = (11.0± 1.9)% using running MS quark masses. The uncertainty is dominated by unknown higher order perturbative corrections. We conclude that the present accuracy of the theoretical analysis does not allow to state a significant disagreement with the experimental results. However, our re-analysis of the decay b → ccs yields an increase of (35±11)% due to nextto-leading order corrections including mass dependent terms, which further emphasizes the problem of the average charm quark content of the final states in B decays. Submitted to Phys. Lett. B Address after September 1994: CERN, Theory Division, CH–1211 Genève 23, Switzerland. On leave of absence from St. Petersburg Nuclear Physics Institute, 188350 Gatchina, Russia. 1. The theoretical description of inclusive weak decays of heavy hadrons has made considerable progress over the recent years, see [2] for a review. It could be shown that in the limit of infinite heavy quarks the decay rate coincides with that of the corresponding free quark decay; corrections to that limit are of nonperturbative origin and suppressed by at least two powers in the heavy quark mass [3]. Today there is increasing confidence that QCD predictions of heavy particle decays rest on a firm theoretical foundation. In view of these apparent advances and with the availability of new and more precise data on the semileptonic branching ratio BSL of the B meson [4], the long felt discrepancy between its measured and its predicted value becomes more and more baffling [5, 6]. Over the last years, the main efforts were concentrated on the determination of the size of nonperturbative power-suppressed corrections to the free quark decay, which, however, turned out to be small, of natural size ∼ 1GeV2/mb ∼ 5%, and cannot explain the experimental value of BSL. Thus, it seems timely to place more emphasis on perturbative radiative corrections to the free quark decay, which since the well-known analysis by Altarelli and Petrarca [7] have not been receiving proper attention in the literature. In this letter we update the theoretical prediction of the semileptonic branching ratio of B mesons using a recent calculation [1] of the charm quark mass dependence of radiative corrections to nonleptonic decays. In addition we re-analyze the decay rate Γ(b → ccs), taking into account the quark mass dependence of radiative corrections and the contributions of penguins. The semileptonic branching ratio is then evaluated using both pole masses and running quark masses. The latter procedure was advocated in [8] on the evidence of the cancellation of renormalon singularities [9]. Finally, we discuss shortly the problem of fixing a proper renormalization scale in heavy quark decays. 2. The semileptonic branching ratio of B mesons is defined by BSL ≡ Γ(B → Xeν)