  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.
