Higher Orders in the Colour-Octet Model of J/psi Production

We study the hadro- and photo-production of $\bar cc$ and $\bar bb$ mesons at low transverse momentum to high orders in the relative velocity of the pair, v, in non-relativistic QCD. We evaluate cross sections to order v^7 for $\eta_c$, sufficient for studies of photo-production in the almost-elastic region. For all other charmonium states we find the cross section to order v^9, sufficient for studies of the ratio of $\chi_{c1}$ and $\chi_{c2}$ production rates. We find recurrence formulae for generating terms at even higher orders, should they be needed.