  In the framework of NRQCD and parton model, we estimate in detail,the
production cross section for polarized J/psi from B meson decays. In order to
contrast with data, we also take into account additional J/psi production due
to decay of excited charmonium states. We calculate the helicity parameter,
alpha, and as an application, we study our results for the Tevatron. This is in
contrast to the earlier studies which were performed for prompt J/psi
production from p pbar collisions. Our estimates are, for J/psi from B decays,
alpha_{J/psi} = -0.04 +- 0.06 and for B decays to psi', alpha_{psi'}= -0.03 +-
0.07. These results have been evaluated in the J/psi transverse momentum
interval, 10 GeV < k_T < 30 GeV. In the limit of the color singlet model, alpha
shows a direct dependence on the Peterson parameter, thereby reflecting the
dynamics of the b quark hadronization. With Run II of the Tevatron, it is
expected that the fits for alpha will improve by about a factor of 50, leading
to better limits on the matrix elements.
