Probing Factorization in Color-Suppressed $B \rightarrow \psi(2S) + K(K^*)$ Decay

Abstract

In order to probe the factorization hypothesis in color-suppressed $B \rightarrow \psi (2S) + K (K^*)$ decays we have studied three ratios: $ R \equiv B (B \rightarrow \psi K) / B (B \rightarrow \psi(2S) K)$, $ R' \equiv B (B \rightarrow \psi K^*) / B (B \rightarrow \psi(2S) K^*)$ and $ P_L^\prime \equiv \Gamma_L (B \rightarrow \psi(2S) K^*)/\Gamma (B \rightarrow \psi(2S) K^*)$ in several scenarios for the $ q^2$-dependence of the form factors involved. We find that measurements of R and $R' $, which exist, do not yield scenario-independent tests of factorization. However, the predicted range of $ P_L^\prime$ in all scenarios lies in a narrow range, $ 0.50 {\ \lower-1.2pt\vbox{\hbox{\rlap{$<$}\lower5pt\vbox{\hbox{$\sim$}}}}\ } P_L^\prime \leq 0.67$, and could test factorization.