  We evaluate the transverse momentum spectrum of J/Psi (up to semi-hard
momenta) in pA and AA collisions taking into account only the initial state
effects, but resumming them to all orders in \alpha_s^2 A^{1/3}. In our
previous papers we noticed that cold nuclear matter effects alone could not
explain the experimental data on rapidity and centrality dependencies of the
J/Psi yield in AA collisions indicating the existence of an additional
suppression mechanism. Our present calculations indicate that the discrepancy
persists and even increases at semi-hard transverse momenta, implying a
significant final state effect on J/Psi production in this kinematical domain.
The QCD dipole model we employ is only marginally applicable for J/Psi
production at mid-rapidity at RHIC energies but its use is justified in the
forward rapidity region. At LHC energies we can quantitatively evaluate the
magnitude of cold nuclear matter effects in the entire kinematical region of
interest. We present our calculations of J/Psi transverse momentum spectra in
pA and AA collisions at LHC and RHIC energies.
