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Gluon transverse momenta and charm quark-antiquark pair production in $p-\bar p$ collisions at Tevatron

We discuss and compare different approaches to include gluon transverse momenta for heavy quark-antiquark pair production. The correlations in azimuthal angle and in heavy quark, heavy antiquark transverse momenta are studied in detail. The results are illustrated with the help of different unintegrated gluon distribution functons (UGDF) from the literature. We compare results obtained with on-shell and off-shell matrix elements and kinematics and quantify where these effects are negligible and where they are essential. We concentrate on the region of asymmetric transverse momenta of charm quark and charm antiquark. Most of UGDFs lead in this corner of the phase space to almost full decorellation in azimuthal angle. We propose correlation observables to be best suited in order to test the existing models of UGDFs.