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

TL;DR

This paper investigates how dominant spin-flip effects influence the polarization of $J/eta$ mesons produced at TEVATRON, showing that these effects can dilute polarization and help resolve existing polarization puzzles.

Contribution

It systematically studies spin-flip effects on $J/eta$ polarization, especially for the transition of $(car{c})_8[^3S_1]$ into $J/eta$, and suggests parameter choices to address polarization discrepancies.

Findings

Spin-flip effects dilute $J/eta$ polarization.

Proper parameter choices can partially solve the polarization puzzle.

Indirect $J/eta$ polarization from $b$-decays is less affected by spin-flip effects.

Abstract

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