Dominant spin-flip effects for the hadronic-producedJ/ψpolarization at the Tevatron

Abstract

Dominant spin-flip effects for the direct and prompt $J/\ensuremath{\psi}$ polarizations at Tevatron run II with collision energy 1.96 TeV and rapidity cut $|{y}^{J/\ensuremath{\psi}}|<0.6$ are systematically studied. The spin-flip effect for the transition of $(c\overline{c}{)}_{8}[^{3}S_{1}]$ into $J/\ensuremath{\psi}$ is especially discussed with care. It is found that the spin-flip effect shall always dilute the $J/\ensuremath{\psi}$ polarization, and with a suitable choice of the parameters ${a}_{0,1}$ and ${c}_{0,1,2}$, the $J/\ensuremath{\psi}$ polarization puzzle can be solved to a certain degree. At large transverse momentum ${p}_{t}$, $\ensuremath{\alpha}$ for the prompt $J/\ensuremath{\psi}$ is reduced by $\ensuremath{\sim}50%$ for ${f}_{0}={v}^{2}$ and by $\ensuremath{\sim}80%$ for ${f}_{0}=1$. We also study the indirect $J/\ensuremath{\psi}$ 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.