Theory of charmless inclusive B decays and the extraction of Vub -: art. no. 073006

We present state-of-the-art theoretical expressions for the triple differential (B) over bar -> X(u)l(-)nu decay rate and for the (B) over bar -> 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) over bar -> X(s)gamma photon spectrum. This eliminates the dominant theoretical uncertainties from predictions for (B) over bar -> X(u)l(-)(nu) over bar 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) over bar -> X(u)l(-)(nu) over bar 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 leptonic invariant mass.