Second order QCD corrections to the nonleptonic decay of the $b$ quark in the slow charm limit

Abstract

The perturbative QCD corrections to the nonleptonic decay rate of the $b$ quark are discussed. By considering the limit where the final charmed quarks are slow, it is argued that the coefficients of the $\alpha_s^2$ terms, corresponding to next-to-next-to-leading order in the standard renormalization group expansion in $\ln (m_W/m_b)$, are naturally large. The large coefficients arise from the final-state gluon exchange between quarks and are associated with the region of rather low momenta, which may further enhance the phenomenological significance of these terms.