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

We compute the color singlet and color octet NRQCD long-distance matrix elements for inclusive production of $P$-wave quarkonia in the framework of pNRQCD. In this way, the color octet NRQCD long-distance matrix element can be determined without relying on measured cross section data, which has not been possible so far. We obtain inclusive cross sections of $\chi_{cJ}$ and $\chi_{bJ}$ at the LHC, which are in good agreement with data. In principle, the formalism developed in this work can be applied to all inclusive production processes of heavy quarkonia.