Running-coupling effects in the triple-differential charmless semileptonic decay width

We compute the fully-differential B̄ → Xulν̄ decay width to all orders in perturbation theory in the large-β0 limit. Each of the five structure functions that build the hadronic tensor is expressed as a Borel integral, summing up script O sign(CFβ 0n-1αsn) corrections for any n. We derive analytic expressions for the Borel transforms of both real and virtual diagrams with a single dressed gluon, and perform an all-order infrared subtraction, where the Borel parameter serves also as an infrared regulator. Expanding the result we recover the known triple-differential NLO coefficient, and obtain an explicit expression for the script O sign(CFβ 0αs2) triple-differential NNLO correction. This result can be used to improve the determination of |V ub| from inclusive B̄ → Xulν̄ measurements at the B factories with a variety of kinematic cuts. © SISSA 2006.