Color-singlet J/psi production at alpha_s⁶ in Upsilon decay

To clarify the conflict between the theoretical predictions and experimental measurements of the inclusive J/psi production in Upsilon decay, We consider the alpha_s^6 order color-singlet contributions of processes Upsilon --> J/psi+gg and Upsilon --> J/psi+gggg. Both the branching ratio and J/psi momentum spectrum are calculated, and the branching ratio 4.7 x 10^{-4} is larger than the leading-order contribution (alpha_s^5, Upsilon --> J/psi+c\bar{c}g). Together with the QCD and QED leading-order contributions considered in our previous work, the color-singlet prediction of the branching ratio for the direct J/psi production is Br(Upsilon--> J/psi_{direct}+X)=0.90^{+0.49}_{-0.31} x 10^{-4}, which is still about 3.8 times less than the CLEO measurement. We also obtain a preliminary color-singlet prediction of R_{cc}=sigma(Upsilon --> J/psi+c\bar{c}+X)/ sigma(Upsilon --> J/psi+X) and find the value 0.39^{+0.21}_{-0.20} is much larger than the color-octet predictions, and suggest to measure this quality in future experimental analysis.