Theory of Charmless Inclusive B Decays and the Extraction of V_{ub}

Details Theory of Charmless Inclusive B Decays and the Extraction of V_{ub} Theory of Charmless Inclusive B Decays and the Extraction of V_{ub}

2005-04-11

arxiv.org/abs/hep-ph/0504071v3

Phys.Rev.D72:073006,2005

Physics

High Energy Physics

High Energy Physics - Phenomenology

45 pages, 4 figures; several minor revisions, more systematic treatment of subleading shape-function effects, numerical result

Scientific paper

10.1103/PhysRevD.72.073006

We present ``state-of-the-art'' theoretical expressions for the triple differential B->X_u l^- nu decay rate and for the B->X_s gamma photon spectrum, which incorporate all known contributions and smoothly interpolate between the ``shape-function region'' of large hadronic energy and small invariant mass, and the ``OPE region'' in which all hadronic kinematical variables scale with M_B. The differential rates are given in a form which has no explicit reference to the mass of the b quark, avoiding the associated uncertainties. Dependence on m_b enters indirectly through the properties of the leading shape function, which can be determined by fitting the B->X_s gamma photon spectrum. This eliminates the dominant theoretical uncertainties from predictions for B->X_u l^- nu decay distributions, allowing for a precise determination of |V_{ub}|. In the shape-function region, short-distance and long-distance contributions are factorized at next-to-leading order in renormalization-group improved perturbation theory. Higher-order power corrections include effects from subleading shape functions where they are known. When integrated over sufficiently large portions in phase space, our results reduce to standard OPE expressions up to yet unknown O(alpha_s^2) terms. Predictions are presented for partial B->X_u l^- nu decay rates with various experimental cuts. An elaborate error analysis is performed that contains all significant theoretical uncertainties, including weak annihilation effects. We suggest that the latter can be eliminated by imposing a cut on high lepton invariant mass.

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