Combined B->X_sψand B-> X_sη_c decays as a test of factorization

We calculate the inclusive decays $B\to X_sψ$ and $B\to X_sη_c$ 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 $f^2_{η_c}/f^2_ψ$, it is shown that the ratio $R=Γ(B\to X_sη_c )/Γ(B\to X_sψ)$ can be used as a possible test of factorization assumption.

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