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We compute NRQCD long-distance matrix elements that appear in the inclusiveproduction cross sections of $P$-wave heavy quarkonia in the framework ofpotential NRQCD. The formalism developed in this work applies to stronglycoupled charmonia and bottomonia. This makes possible the determination ofcolor-octet NRQCD long-distance matrix elements without relying on measuredcross section data, which has not been possible so far. We obtain results forinclusive production cross sections of $\chi_{cJ}$ and $\chi_{bJ}$ at the LHC,which are in good agreement with measurements.

Inclusive Hadroproduction of $P$-wave Heavy Quarkonia in pNRQCD