Decayb→(cc¯)sin the leading logarithm approximation

Abstract

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 heavy quark effective theory (HQET), soft-collinear effective theory (SCET), and a covariant modification of nonrelativistic QCD (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 electroweak (EWET) Lagrangian in the next-to-leading logarithm approximation are calculated at the matching scale of the decay. The differential decay rate for the inclusive decay $B\ensuremath{\rightarrow}J/\ensuremath{\psi}+h$ in the effective theory framework is evaluated.