Colour-octet Contributions to $x_F$ Distributions in $J/ψ$ Hadro-production at Fixed Target Energies

We study $J/\psi$ production at fixed-target energies, including the colour-octet production mechanisms predicted by NRQCD. In an earlier paper, we found that the octet components were crucial in understanding $p_T$-integrated forward ($x_F > 0$) cross-sections. Here we make a detailed comparison of the theoretical predictions with measured $x_F$ distributions from fixed-target experiments. We find that the model predictions agree well with data. Taking into account higher orders in NRQCD, we argue that $\sigma(\chi_1)/ \sigma(\chi_2)=0.6$, in excellent agreement with data. Similiar arguments also predict that $\sigma(\chi)/\sigma(J/\psi)$ is roughly equal in photo- and hadro-production.