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Recently we have proved NRQCD color octet factorization of S-wave and P-waveheavy quarkonia production at all orders in coupling constant in QCD in vacuumat high energy colliders in Eur. Phys. J. C76 (2016) 448 and inarXiv:1807.04722 [hep-ph] respectively. In this paper we extend this to proveNRQCD color octet factorization of P-wave heavy quarkonium production innon-equilibrium QCD at RHIC and LHC at all orders in coupling constant. Thisproof is necessary to study the quark-gluon plasma at RHIC and LHC.

Proof of NRQCD Color Octet Factorization of P-Wave Heavy Quarkonium Production In Non-Equilibrium QCD at RHIC and LHC