Nonfactorizable Effects in Exclusive Charmless B Decays

Nonfactorizable effects in charmless $B\to PP, VP$ decays can be lumped into the effective parameters a_i that are linear combinations of Wilson coefficients, or equivalently absorbed into the effective number of colors N_c. Naive factorization with N_c=3 fails to explain the CLEO data of $B^\pm \to \omega K^\pm$, showing the first evidence for the importance of nonfactorizable contributions to the penguin amplitude. The decays $B^\pm \to \omega\pi^\pm$ dominated by tree amplitudes are sensitive to the interference between external and internal W-emission diagrams. Destructive interference implied by $N_c=\infty$ leads to a prediction of ${\cal B}(B^\pm \to \omega \pi^\pm)$ which is about $2\sigma$ too small compared to experiment. Therefore, the CLEO data of $B^\pm \to \omega K^\pm, \omega\pi^\pm$ suffice to rule out N_c=3 and strongly disfavor $N_c=\infty$ for rare charmless B decays. Factorization based on $N_c\approx 2$ can accommodate the data of $B^\pm \to \omega K^\pm$, but it predicts a slightly smaller branching ratio of $B^\pm \to \omega\pi^\pm$ with ${\cal B}(B^\pm \to \omega\pi^\pm)/{\cal B} (B^\pm \to \omega K^\pm)=0.6$. We briefly explain why the 1/N_c expansion is still applicable to the B meson decay once the correct large-N_c counting rule for the Wilson coefficient c_2(m_b) is applied.