Decay b -> (c\bar{c}) s in the leading logarithm approximation

We consider an effective field theory for the nonleptonic decay in which a heavy quark decays into a pair of a heavy quark and antiquark having a small relative velocity and one relativistic (massless) quark. This effective theory is a combination of HQET, SCET, and a covariant modification of NRQCD. In the leading logarithm approximation the effective theory decay amplitude factorizes into the product of matrix elements of heavy-to-heavy and heavy-to-light currents. We discuss a possibility of factorization beyond the leading logarithm approximation and find it doubtful. The Wilson coefficients of the effective theory electro-weak (EWET) Lagrangian in the next-to-the leading logarithm approximation are calculated at the matching scale of the decay. The differential decay rate for the inclusive decay B -> J/\psi+h in the effective theory framework is evaluated.
Comment: 29 pages, 13 figures; v2: added preprint numbers, acknowledgements; v3: minor corrections and references added to match the journal version