Proof of Factorization of ${\chi }_{cJ}$ Production in Non-Equilibrium QCD at RHIC and LHC in Color Singlet Mechanism

Recently we have proved the factorization of NRQCD S-wave heavy quarkonium production at all orders in coupling constant. In this paper we extend this to prove the factorization of infrared divergences in ${\chi }_{cJ}$ production from color singlet $c\bar{c}$ pair in non-equilibrium QCD at RHIC and LHC at all orders in coupling constant. This can be relevant to study the quark-gluon plasma at RHIC and LHC.