Two-loop QCD correction to differential semi-leptonic b→u decays in the shape-function region

We calculate the two-loop QCD correction to the form factors of on-shell b-quark decay to an energetic massless quark, which constitutes the last missing piece required for an O(αs2) determination of |Vub| from inclusive semi-leptonic B¯→Xuℓν¯ decays in the shape-function region.