Proof of Color Octet NRQCD Factorization of P-Wave Heavy Quarkonium Production at All Orders in Coupling Constant

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).