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

TL;DR

This paper develops an effective field theory combining HQET, SCET, and NRQCD to analyze the decay b -> (car{c}) s, calculating Wilson coefficients and the differential decay rate within the leading logarithm approximation.

Contribution

It introduces a novel effective theory framework for nonleptonic heavy quark decays and evaluates decay rates and Wilson coefficients beyond leading order.

Findings

Decay amplitude factorizes at leading logarithm approximation

Factorization beyond leading logarithm is doubtful

Differential decay rate for B -> J/psi + h is computed

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 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.