Theory of Semi– and Nonleptonic Decays of Heavy Mesons

I review some of the recent developments in the theoretical description of weak inclusive decays of heavy mesons. The topics cover the value of |Vcb| as extracted from semileptonic inclusive decays and a short discussion of the theoretical errors. I also present the results of a recent calculation of next–to–leading order corrections to nonleptonic inclusive B decays which allows an improved prediction of the semileptonic branching ratio of B mesons. 1 Outline of Theoretical Foundations During the recent two years, the theoretical description of inclusive decays of heavy hadrons has experienced considerable progress. For quark masses mQ ≫ ΛQCD, the well–known short–distance expansion technique yields an expansion in inverse powers of the heavy quark mass, the so–called heavy quark expansion (HQE) [1]. The starting point for the HQE of, e.g., the decay rate of a B meson into a final state X is its representation as imaginary part of the relevant forward–scattering amplitude: Γ(B → X) = 1 mB Im i ∫ dx 〈B|TLW (x)LW (0)|B〉. (1) Here LW is the effective weak Lagrangian mediating the decay B → X. As shown in [1], for a very heavy b quark mass mb, a short distance expansion of Eq. (1) yields: Γ(B → X) = GFm 5 b 192π3 |CKM| { C (X) 0 (αs(μ)) 〈B|b̄b|B〉 2mB + C (X) 2 (αs(μ)) 1 mb 〈B|b̄gsσμνF b|B〉 2mB +O (