$ψ'$ Polarization due to Color-Octet Quarkonia Production

Abstract

We calculated the polarization of ψ' due to gg \to Q\bar{Q}[^3P_J^(8)]g \to ψ^λcolor-octet quarkonia production. We find that at low transverse momenta the ψ' is unpolarized due to the contributions proportional to the L=S=0 and L=S=1 color-octet matrix elements. As p_\perp increases, the ψ' mesons become 100% polarized, as predicted by fragmentation calculations. Polarization due to lowest order color-singlet production is also considered, which qualitatively has a similar shape to the color-octet production.

Figures (1)

• Figure 1: Coefficient $\alpha$ which governs the lepton angular distribution in $\psi' \to \ell^+ \ell^-$ decay plotted as a function of $p_\perp$. The solid and dashed curves illustrate $\alpha$ for $\psi'$ production at the Tevatron when $\langle {\mathcal{O}}_8^{\psi'}({}^3P_0) \rangle$ and $\langle {\mathcal{O}}_8^{\psi'}({}^1S_0) \rangle$ respectively vanish. The shaded region shows the effect of the uncertainty in the extraction of the matrix elements. The dotted line corresponds to the lowest order, color-singlet production.