  Recently we have proved color octet NRQCD factorization of S-wave heavy
quarkonium production at all orders in coupling constant at high energy
colliders in Eur. Phys. J. C76 (2016) 448. In this paper we extend this to
prove color octet NRQCD factorization of P-wave heavy quarkonium production at
all orders in coupling constant at high energy colliders. We find that while
the color octet NRQCD S-wave non-perturbative matrix element contains two
gauge-links in the adjoint representation of SU(3), the color octet NRQCD
P-wave non-perturbative matrix element contains four gauge-links in the
fundamental representation of SU(3).
