Inclusive S-wave charmonium productions in B decays

The inclusive S-wave charmonium production rates in B decays are considered using the Bodwin-Braaten-Lepage (BBL) approach, including the relativistic corrections and the color-octet mechanism suggested as a possible solution to the \psi^{'} puzzle at the Tevatron. We first consider relativistic and radiative corrections to J/\psi \rightarrow e^{+} e^{-} and J/\psi \rightarrow Light Hadrons (LH), in order to determine two nonperturbative parameters, \langle J/\psi | O_{1} (^{3}S_{1}) | J/\psi \rangle, \langle J/\psi | P_{1} (^{3}S_{1}) | J/\psi \rangle, in the factorization formulae for these decays. Using these two matrix elements and including the color-octet c\bar{c}(^{3}S_{1}) state contribution, we get a moderate increase in the decay rates for B decays into J/\psi ~({\rm or}~\psi^{'}) ~+ X. Our results, B(B \rightarrow J/\psi~({\rm or}~\psi^{'}) + X) = 0.58~(0.23) \% for M_{b} = 5.3 GeV, get closer to the recent CLEO data. As a byproduct, we prefer a larger decay rate for \eta_{c} \rightarrow LH compared to the present data