$ψ'$ Polarization as a test of colour octet quarkonium production

Abstract

We calculate the $α_s$ corrections to the transverse polarization fraction of $ψ^\prime$'s produced at the Tevatron. If the `$ψ^\prime$-anomaly' is explained by gluon fragmentation into a colour octet Fock component of the $ψ^\prime$, the $ψ^\prime$'s should be $100\%$ transversely polarized at leading order in $α_s$, up to spin symmetry breaking long-distance corrections. We find that the short-distance correction to the transverse polarization fraction is a few percent, so that a polarization measurement would provide a reliable test of the colour octet mechanism.

Figures (2)

• Figure 1: (a) Leading order gluon fragmentation into $c\bar{c}[^3\!S^{(8)}_1]$. (b) Charm fragmentation. (c), (d) Real and virtual fragmentation diagrams at order $\alpha_s^2$. The black boxes denote nonperturbative evolution of the $c\bar{c}$-pair into a $\psi^\prime$ through soft gluon emission.
• Figure 2: The short-distance correction $\delta\xi_{SD}$ as function of $p_T$. The solid line shows the prediction for $\mu=p_T$ and $\langle {\cal O}^{\psi^\prime}_8(^3\!P_0)\rangle/ \langle {\cal O}^{\psi^\prime}_8(^3\!S_1)\rangle =1$. The two dash-dotted lines are for $\mu=p_T/2$ (upper curve) and $\mu=2 p_T$ (lower curve) at fixed $\langle {\cal O}^{\psi^\prime}_8(^3\!P_0)\rangle/ \langle {\cal O}^{\psi^\prime}_8(^3\!S_1)\rangle =1$. The two dashed lines correspond to variation of $\langle {\cal O}^{\psi^\prime}_8(^3\!P_0)\rangle/ \langle {\cal O}^{\psi^\prime}_8(^3\!S_1)\rangle$ between 0.5 and 2 at fixed $\mu=p_T$.