Proof of factorization of \(\chi _{\text{cJ}}\) 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 \(\chi _{\text{cJ}}\) 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.