Threshold resummation in B → Xc l νl decays

We compute the QCD form factor resumming threshold logarithms in B → Xc + l + νl decays to next-to-leading logarithmic approximation. We present an interpolation formula including soft as well as collinear effects softened by the non-vanishing charm mass which, in the N-space, reads: {Mathematical expression}, where y = (mXc2 - mc2) / (Q2 - mc2), ρ = mc2 / (Q2 - mc2) and Q = EXc + | over(p, →)Xc |. The function A (ρ ; αS) describes soft radiation collinearly enhanced off the charm quark and reduces to the standard double-logarithmic function A (αS) in the massless limit ρ → 0. The function B (αS) describes hard collinear emission off the charm quark, being the standard jet function. D (αS) and Δ (αS) describe soft radiation not collinearly enhanced off the beauty and the charm quark respectively. © 2007 Elsevier B.V. All rights reserved