NRQCD matrix elements in polarization ofJ/ψproduced frombdecay

We present the nonrelativistic QCD (NRQCD) prediction for the polarization of the $J/\psi$ promptly produced in $b\to J/\psi +X$, as well as the helicity-summed production rate. We propose that these observables can be of avail in measuring the three most important color-octet NRQCD matrix elements involved in $J/\psi$ production. Anticipating the measurement of the polarization parameter $\alpha$, we determine its expected range given current experimental bounds on the color-octet matrix elements. We find that the leading-order NRQCD prediction for the polarization parameter $\alpha$ is expected to lie in the range $-0.33$ to 0.05 whereas the color-singlet model prediction is $-0.40\pm 0.04$.