The Rule of Discarding $1/N_c$ in Inclusive Weak Decays

Abstract

We continue to investigate the effects of the (dominant) subleading operator of the $\vec\sigma\vec H$ type in the $1/N_c$ parts of the weak nonleptonic amplitudes. If the previous work concentrated on exclusive decays now we analyse inclusive widths in a certain kinematic limit. Deviations from the parton model predictions are found due to soft-gluon color exchange. In the interference (i.e. $1/N_c$) terms they are stronger than in the non-interference terms. The sign is negative so that the $1/N_c$ parts tend to cancel. The absolute value of the effect is of order 1 in D-mesons and of order 0.50 in B mesons.