We present the leading order differential and total rates for J/psi product
ion at CERN LEP. By leading order we mean all terms of the form alpha(s)[al
pha(s) log(M-Z(2)/M-psi(2))](n) and alpha(s)(n+1) log(1)(z(2))log(m)(M-Z(2)
/M-psi(2)), (l+m=2n-1), in the regions z = 2E(psi)/M-Z similar to O(1) and
z much less than 1, respectively. In the intermediate region we interpolate
using the available data. This resummation eliminates the O[alpha(s)(M-psi
)/alpha(s)(M-Z)]similar to 2 theoretical uncertainties in previous calculat
ions. The log(z) resummation results in a suppression of the small z region
due to coherent gluon emission. Comparing the zeroth moment with the LEP d
ata we find the value for the effective octet matrix element to be [(O) ove
r cap(8)(psi)(S-3(1))] = 0.019 GeV3. The theoretical uncertainties are subs
tantially smaller than those from Fermilab Tevatron extractions. Using this
value of the octet matrix element we make a prediction for the first momen
t of the differential rate and find that the resummed differential decay ra
te is in much better agreement with preliminary data than the color singlet
result or the unresummed color octet prediction. [S0556-2821(99)04605-6].