Shape-function independent relations of charmless inclusive B-decay spectra

A leading-power factorization formula for weight functions relating the B to Xs gamma photon spectrum to arbitrary partial decay rates in B to Xu l nu is derived. These weight functions are independent of the hadronic shape function and allow for the determination of V_{ub} in a model-independent way. We calculate the weight function in renormalization-group improved perturbation theory to complete next-to-next-to leading order at the jet scale mu_i^2 ~ m_b Lambda_{QCD} and to next-to leading order at the hard scale mu_h ~ m_b. First-order power corrections are also included, where a model-dependence enters via the appearance of subleading hadronic shape functions.