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

Abstract

We compute the fully–differential ¯B → Xul¯ν 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 O(CF βn−1 0 αns ) 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 O(CF β0α2s ) triple–differential NNLO correction. This result can be used to improve the determination of |Vub| from inclusive ¯B → Xul¯ν measurements at the B factories with a variety of kinematic cuts.