Relativistic corrections for polarizedJ/ψproduction inbdecay

We analyze the structure of relativistic corrections in the inclusive production of polarized $J/\psi$ from b-quark decay. The analysis is performed not only for the production channel in which the $c\overline{c}$ pair is a color singlet, but also for the channels in which the $c\overline{c}$ is a color octet. We find that the correction in the color-singlet channel at tree level is completely determined by the decay constant of $J/\psi ,$ while in the color-octet channels the corrections are characterized by three matrix elements defined in NRQCD, whose numerical values are unknown. We discuss the impact of these corrections on polarized $J/\psi$ production, and the impact is so significant that the predictions based on the analysis for the considered process may be unreliable. Finally, we propose an integrated spin observable to measure the polarization of $J/\psi .$