Inclusive $S-$wave charmonium productions in $B$ decays

Abstract

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 $\ddot{I}{ˆ}^{{}^{\prime }}$ puzzle at the Tevatron. We first consider relativistic and radiative corrections to $J/\ddot{I}ˆ\to e^{+}{e}^{-}$ and $J/\ddot{I}ˆ\to$ Light Hadrons (LH), in order to determine two nonperturbative parameters, $⟨J/\ddot{I}ˆ|O_1{(}^3{S}_1)|J/\ddot{I}ˆ⟩$, $⟨J/\ddot{I}ˆ|P_1{(}^3{S}_1)|J/\ddot{I}ˆ⟩$, 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 $J/\ddot{I}ˆ(\mathrm{or}\ddot{I}{ˆ}^{{}^{\prime }})+X$. Our results, $B(B\to J/\ddot{I}ˆ(\mathrm{or}\ddot{I}{ˆ}^{{}^{\prime }})+X)=0.58(0.23)\%$ for $M_b=5.3$ GeV, get closer to the recent CLEO data. As a byproduct, we prefer a larger decay rate for $\hat{I}{\cdot }_c\to$ LH compared to the present data.

12 pages