Hadro-production of Quarkonia in Fixed Target Experiments

TL;DR

This paper tests the NRQCD color-octet framework against fixed-target hadroproduction data for charmonium and bottomonium, showing that octet channels are needed to match total cross sections and the direct J/ψ fraction, while arguing that universality of matrix elements across processes is delicate due to velocity-expansion differences and higher-twist effects. It provides explicit LO formulas and parameter choices, fits octet matrix elements from fixed-target data, and compares with Tevatron and photo-production results, uncovering tensions in χ_c1/χ_c2 ratios and polarization that point to substantial higher-twist contributions. The work highlights both the successes and the limits of the color-octet mechanism in fixed-target environments and emphasizes the need for more polarization measurements and bottomonium studies to constrain NRQCD parameters. Overall, the study supports color-octet production as essential but calls into question simple universality assumptions, inviting further exploration of higher-twist dynamics in quarkonium production.

Abstract

We analyze charmonium and bottomonium production at fixed target experiments. We find that inclusion of color octet production channels removes large discrepancies between experiment and the predictions of the color singlet model for the total production cross section. Furthermore, including octet contributions accounts for the observed direct to total $J/ψ$ production ratio. As found earlier for photo-production of quarkonia, a fit to fixed target data requires smaller color octet matrix elements than those extracted from high-$p_t$ production at the Tevatron. We argue that this difference can be explained by systematic differences in the velocity expansion for collider and fixed-target predictions. While the color octet mechanism thus appears to be an essential part of a satisfactory description of fixed target data, important discrepancies remain for the $χ_{c1}/χ_{c2}$ production ratio and $J/ψ$ ($ψ'$) polarization. These discrepancies, as well as, the differences between pion and proton induced collisions emphasize the need for including higher twist effects in addition to the color octet mechanism.

Figures (6)

• Figure 1: Total (solid) and singlet only (dotted) $\psi^\prime$ production cross section in proton-nucleon collisions ($x_F>0$ only). The solid line is obtained with $\Delta_8(\psi')=5.2\cdot 10^{-3}\,$GeV${}^3$.
• Figure 2: $J/\psi$ production cross sections in proton-nucleon collisions for $x_F>0$. The dotted line is the direct $J/\psi$ production rate in the CSM and the dashed line includes the contribution from the color-octet processes. The total cross section (solid line) includes radiative feed-down from the $\chi_{cJ}$ and $\psi'$ states. The solid line is obtained with $\Delta_8(J/\psi)=3.0\cdot 10^{-2}\,$GeV${}^3$.
• Figure 3: Ratio of direct to total $J/\psi$ production in proton-nucleon collisions as a function of the charm quark mass in the CSM and after inclusion of color octet processes at $E=300\,$GeV. The experimental value is $0.62\pm 0.04$.
• Figure 4: Total (solid) and singlet only (dotted) $\psi^\prime$ production cross section in pion-nucleon collisions ($x_F>0$ only). The solid line is obtained with $\Delta_8(\psi')=5.2\cdot 10^{-3}\,$GeV${}^3$.
• Figure 5: $J/\psi$ production cross sections in pion-nucleon collisions for $x_F>0$. Direct $J/\psi$ production in the CSM (dashed line) and after inclusion of color-octet processes (dotted line). The total cross section (solid line) includes radiative feed-down from the $\chi_{cJ}$ and $\psi'$ states. The solid line is obtained with $\Delta_8(J/\psi)=3.0\cdot 10^{-2}\,$GeV${}^3$.