Inclusive B-decay Spectra and Ir Renormalons

B-decay physics is gradually turning into a field of precision phenomenology. Inclusive decay measurements provide some of the most robust tests of the standard model. Classical examples are the rate of B̄ −→ Xsγ decays [1] and constraints on the unitarity triangle through the measurement of Vub from charmless semileptonic decays [2]. The advantage of inclusive measurements over exclusive ones is that the corresponding theoretical predictions are, to large extent, free of hadronic uncertainties. QCD corrections to total decay rates are dominated by short distance scales, of order of the heavy-quark mass m, and are therefore primarily perturbative. Confinement effects appear as power corrections in Λ/m. Moreover, the Operator Product Expansion (OPE) allows one to estimate these power corrections by relating them to specific matrix elements of local operators between B-meson states, which are defined in the infinite–mass limit in the framework of the heavy-quark effective theory (HQET) [3]. These matrix elements can either be computed on the lattice or extracted from experimental data. In reality, however, experiments cannot perform completely inclusive measurements. Precise measurements are restricted to certain kinematic regions where the background is sufficiently low. The experimentally accessible region in B̄ −→ Xsγ is where the photon energy Eγ in the B rest frame is close to its maximal possible value, M/2, (M is the B meson mass),