  We carry out a global analysis of the experimental data on the $\chi_c$
production cross section and the ratio $\sigma(\chi_{c2})/\sigma(\chi_{c1})$ at
the LHC and the Tevatron. The related long-distance matrix elements (LDMEs) at
both leading order (LO) and next-to-leading order (NLO) in the QCD coupling
constant are renewed. We also present the transverse momentum distribution of
the $\chi_c$ production cross section and the ratio
$\sigma(\chi_{c2})/\sigma(\chi_{c1})$ for several experimental conditions and
find that NLO predictions agree with all sets of experimental data. By
contrast, at LO, one cannot explain all the data with a unique value of the
color-octet LDME. A brief analysis of the nonrelativistic QCD scale dependence
of the cross sections shows that, for the conditions we are concerned with in
this paper, the dependence can be almost totally absorbed into the LDME.
