Perturbative corrections to the determination of Vub from the P+spectrum in B ->Xu l nu bar

We investigate the relation between the E spectrum in B → Xsγ decay and the P+ spectrum in semileptonic B → Xu(ell)(bar ν) decay (P+ is the hadronic energy minus the absolute value of the hadronic three-momentum), which provides in principle the theoretically simplest determination of |Vub| from any of the ''shape function regions'' of B → Xu(ell)(bar ν) spectra. We calculate analytically the P+ spectrum to order αs2β0, and study its relation to the B → Xsγ photon spectrum to eliminate the leading dependence on nonperturbative effects. We compare the result of fixed order perturbation theory to the next-to-leading log renormalization group improved calculation, and argue that fixed order perturbation theory is likely to be a more appropriate expansion. Implications for the perturbative uncertainties in the determination of |Vub| from the P+ spectrum are discussed