Dominant Spin-Flip Effects for the Hadronic Produced $J/ψ$ Polarization at TEVATRON

Abstract

Dominant spin-flip effects for the direct and prompt $J/ψ$ polarizations at TEVATRON run II with collision energy 1.96 TeV and rapidity cut $|y^{J/ψ}|<0.6$, have been systematically studied, especially, the spin-flip effect for the transition of $(c\bar{c})_8[^3S_1]$ into $J/ψ$ has been carefully discussed. It is found that the spin-flip effect shall always dilute the $J/ψ$ polarization, and with a suitable choice of the parameters $a_{0,1}$ and $c_{0,1,2}$, the $J/ψ$ polarization puzzle can be solved to a certain degree. At large transverse momentum $p_t$, $α$ for the prompt $J/ψ$ is reduced by $\sim50%$ for $f_0 = v^2$ and by $\sim80%$ for $f_0=1$. We also study the indirect $J/ψ$ 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.