  We calculate the branching ratio for B -> J/psi + anything, within the
color-singlet approximation for J/psi production, but including perturbative
QCD corrections beyond the leading logarithm approximation. Such higher order
corrections are necessary, in order to obtain a result that is not strongly
dependent on the renormalization scale. As in the earlier work of Bergstrom and
Ernstrom, we use a double expansion in alpha_s and in the small ratio of Wilson
coefficients L_0/L_2, to identify the dominant terms in the decay amplitude. We
complete their work by calculating all the leading order terms in this double
expansion. The predicted branching ratio is then BR(B -> J/psi + anything) =
0.09 (+1.1)(-0.3) %, which is well below the experimental value
BR(experimental) = 0.80 (+-0.08) %. This confirms the suspicion that
non-perturbative corrections to the color-singlet approximation for J/psi
production in B decays are important.
