  In this paper, we present the study of the hadroproduction rate of $h_c$ at
next-to-leading order in $\alpha_s$ under the nonrelativisitic QCD (NRQCD)
factorization framework, using long-distance matrix elements obtained from the
fit of $\chi_c$ production measurements by LHCb. We consider the problem of
NRQCD scale dependence for the first time, and find that, for some experimental
conditions, the choice of this scale can substantially affect the final
results. Up to this order, color-octet channel still contribute the most part
of the production rate.
