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Analytical expressions for the Transverse Momentum Dependent (TMD, orunintegrated) gluon and sea quark densities in nuclei are derived at leadingorder of QCD running coupling. The calculations are performed in the frameworkof the rescaling model and Kimber-Martin-Ryskin (KMR) prescription, where theBessel-inspired behavior of parton densities at small Bjorken $x$ values,obtained in the case of flat initial conditions in the double scaling QCDapproximation, is applied. The derived expressions are used to evaluate theinclusive heavy flavor production in proton-lead collisions at the LHC. We finda good agreement of our results with latest experimental data collected by theCMS and ALICE Collaborations at $\sqrt s = 5.02$ GeV.

TMD gluon density in nuclei versus experimental data on heavy flavor production at LHC