Inclusive semileptonic B decays

In the framework of the Standard Model, the quark sector is characterised by a rich pattern of flavourchanging transitions, described by the CabibboKobayashi-Maskawa (CKM) matrix. The quark transitions B → Xclν and B → Xulν provide a way for determining these CKM matrix elements. This report reviews the experimental measurements used to extract the quark mixing parameters |Vcb| and |Vub| from the inclusive branching fractions of semileptonic b-hadron decays Br(B → Xlν). At present, the values of |Vqb| obtained from inclusive semileptonics decays are more precise than the corresponding exclusive determinations. All theoretical approaches used to extract |Vqb| exploit the fact that the mass of the b quark is large compared to the scale ΛQCD that determines lowenergy hadronic physics. The basis for precise calculations is the expansion in powers of ΛQCD/mb , where effective-field-theory methods are used to separate non-perturbative from perturbative contributions. Several studies have shown that the spectator model decay rate is the leading term in a well-defined expansion controlled by the parameter ΛQCD/mb. Nonperturbative corrections to this leading approximation arise only to order 1/m2b. The key issue in this approach is the ability to separate non-perturbative corrections, that can be expressed as a series in powers of 1/mb, and perturbative corrections, expressed in powers of αs. There are different methods [4] [5] [2] [3] [6] [17] to handle the energy scale μ used to separate long-distance from short-distance physics and they are discussed in the theory part of these proceedings. The coefficients of the 1/mb power terms are expectation values of operators that include nonperturbative physics. In this framework, non-perturbative corrections are parameterized by quark masses and matrix elements of higher dimensional operators that at present are poorly known. The experimental accuracy already achieved, and the one expected from the large data sets recorded by the B-factories, make the ensuing theory uncertainty a major limiting factor. The extraction of the non-perturbative parameters, describing the heavy quark masses, kinetic energy of the b quark and the 1/m3b corrections, directly from the data has therefore become a key issue. Recently, a lot of progress has been made on the use of the moments of energy and mass spectra in B → Xclν̄ and B →→ Xsγ for performing these determinations.