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 2 b-quark decay to an energetic massless quark, which constitutes the last missing piece required for an O(alpha(2)(s)) determination Of vertical bar V-ub vertical bar from inclusive semi-leptonic (b) over bar -> Xul (v) over bar decays in the shape-function region. (c) 2008 Elsevier B.V. All rights reserved.