Nonfactorizable Contributions to Nonleptonic Weak Decays of Heavy Mesons

Abstract

Nonfactorizable contributions to exclusive two-body nonleptonic weak decays of heavy mesons arising from color octet currents, characterized by the parameter $r_2$, are extracted from the data. It is found that $r_2$ is equal to $\sim -0.67\,$, $-(0.9\sim 1.1),~-(1.2\sim 1.3)$, $\sim 0.36$ respectively for $D\to \bar{K}\pi,~\bar{K}^*\pi,~\bar{K}^*\rho,~\bar{B}\to D\pi$ decays. As expected, soft-gluon effects become stronger when the decay particles are less energetic, allowing more time for significant final-state strong interactions. As a consequence, the parameter $a_2$ is not universal and is channel or class dependent, contrary to the anticipation of the factorization approach. The leading $1/N_c$ expansion works most successfully for $D\to\bar{K}\pi$ decays as the subleading $1/N_c$ factorizable contribution is almost compensated by the soft-gluon effect. We argue that, in contrast to what happens in $B^-\to D^{(*)} \pi(\rho)$ decays, the nonfactorizable term and the subleading $1/N_c$ factorizable term in $\bar{B}\to \psi\bar{K}^{(*)}$ decays are opposite in signs, in accordance with a recent QCD sum rule calculation. Implications are discussed.