We compute the inclusive differential cross section production of the pseudo-scalar meson eta in high-energy proton-proton (pp) and proton-nucleus (pA) collisions. We use an effective coupling between gluons and eta meson to derive a reduction formula that relates the eta production to a field-strength tensor correlator. For pA collisions we take into account saturation effects on the nucleus side by using the Color Glass Condensate formalism to evaluate this correlator. We derive new results for Wilson line - color charges correlators in the McLerran-Venugopalan model needed in the computation of eta production. The unintegrated parton distribution functions are used to characterize the gluon distribution inside protons. We show that in pp collisions, the cross section depends on the parametrization of unintegrated parton distribution functions and thus, it can be used to put constraints on these distributions. We also demonstrate that in pA collisions, the cross section is sensitive to saturation effects so it can be utilized to estimate the value of the saturation scale.
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