Combined B->X_s\psi and B-> X_s\eta_c decays as a test of factorization

Abstract

We calculate the inclusive decays $B\to X_s\psi$ and $B\to X_s\eta_c$ using factorization assumption. To investigate the bound state effect of the decaying B meson in these inclusive decays we take into account the motion of the $b$ quark using a Gaussian momentum distribution model. The resulting correction to free quark decay approximation is around 6% at most. Utilizing a potential model evaluation of the ratio of the decay constants $f^2_{\eta_c}/f^2_\psi$, it is shown that the ratio $R=\Gamma (B\to X_s\eta_c )/\Gamma (B\to X_s\psi )$ can be used as a possible test of factorization assumption.