Factorization for power corrections to B→Xsγ and B→Xuℓν¯

We derive factorization theorems for ΛQCD/mb power corrections to inclusive B-decays in the endpoint region, where mX2∼mbΛQCD. In B→Xuℓν¯ our results are for the full triply differential rate. A complete enumeration of ΛQCD/mb corrections is given. We point out the presence of new ΛQCD/mb-suppressed shape functions, which arise at tree level with a 4π-enhanced coefficient, and show that these previously neglected terms induce an additional significant uncertainty for current inclusive methods of measuring |Vub| that depend on the endpoint region of phase space.