We compute the fully–differential ¯B → Xul¯ν decay width to all orders inperturbation theory in the large–β0 limit. Each of the five structure functions that buildthe hadronic tensor is expressed as a Borel integral, summing up O(CF βn−10 αns) correctionsfor any n. We derive analytic expressions for the Borel transforms of both real and virtualdiagrams with a single dressed gluon, and perform an all–order infrared subtraction, wherethe Borel parameter serves also as an infrared regulator. Expanding the result we recoverthe known triple–differential NLO coefficient, and obtain an explicit expression for theO(CF β0α2s) triple–differential NNLO correction. This result can be used to improve thedetermination of |Vub| from inclusive ¯B → Xul¯ν measurements at the B factories with avariety of kinematic cuts.
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