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

We study the hadro- and photo-production of $\bar{c}c$ and $\bar{b}b$ 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.