Dominant Spin-Flip Effects for the Hadronic Produced $J\mathrm{/}\psi$ Polarization at TEVATRON

Dominant spin-flip effects for the direct and prompt $J\mathrm{/}\psi$ polarizations at TEVATRON run II with collision energy 1.96 TeV and rapidity cut $\mathrm{\mid }{y}^{J\mathrm{/}\psi }\mathrm{\mid }<0.6$, have been systematically studied, especially, the spin-flip effect for the transition of $(c\bar{c}{)}_8{[}^3{S}_1]$ into $J\mathrm{/}\psi$ has been carefully discussed. It is found that the spin-flip effect shall always dilute the $J\mathrm{/}\psi$ polarization, and with a suitable choice of the parameters $a_{0,1}$ and $c_{0,1,2}$, the $J\mathrm{/}\psi$ polarization puzzle can be solved to a certain degree. At large transverse momentum $p_t$, $\alpha$ for the prompt $J\mathrm{/}\psi$ is reduced by $\sim 50$ for $f_0=v^2$ and by $\sim 80$ for $f_0=1$. We also study the indirect $J\mathrm{/}\psi$ polarization from the $b$-decays, which however is slightly affected by the same spin-flip effect and then shall provide a better platform to determine the color-octet matrix elements.