In this paper, the inclusive Pomeron-Pomeron, Reggeon-Reggeon, Pomeron-Reggeon as well as gluon-Pomeron(-Reggeon) and photon-Pomeron(-Reggeon) interactions for the $rm eta_{c}$ at the LHC energies have been examined in proton-proton, proton-nucleus and nucleus-nucleus collision modes. The cross section has been computed based on the NRQCD factorization and Regge theory formalism. The cross exchange of Pomeron-Reggeon contribution is important in $rm pp$ and $rm pA$ modes. The Pomeron-Pomeron contribution is significant in $rm AA$ mode. The Pomeron contribution is considerable for $rm AA$ and $rm pA$ modes in single diffractive process where $rm A$ undergoes the diffractive process. Reggeon contribution is sizable in $rm pp$ and $rm pA$ modes where $rm p$ only undergoes the diffractive process. The Pomeron and Reggeon contributions in photon-Pomeron and-Reggeon process remain smaller than that of gluon-Pomeron and-Reggeon processes. Our results show that the experimental study of Reggeon, Pomeron and their cross exchange can be carried out in certain kinematic windows with the specific choice of the mode at the LHC. The investigation can be useful to better constrain the Reggeon and Pomeron parton content. The inclusive process serves as the background to related exclusive processes which should be predicted.
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