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Hadron production in elementary nucleon-nucleon reactions from low to ultra-relativistic energies

We study the hadron production in $p+p$, $p+n$ and $n+n$ reactions within the microscopic Parton-Hadron-Dynamics (PHSD) transport approach in comparison to PYTHIA 8.2. We discuss the details of the "PHSD tune" of the Lund string model (realized by event generators FRITIOF and PYTHIA) in the vacuum (as in $N+N$ collisions) as well as its in-medium modifications relevant for heavy-ion collisions where a hot and dense matter is produced. We compare the results of PHSD and PYTHIA 8.2 (default version) for the excitation function of hadron multiplicities as well as differential rapidity $y$, transverse momentum $p_T$ and $x_F$ distributions in $p+p$, $p+n$ and $n+n$ reactions with the existing experimental data in the energy range $\sqrt{s_{NN}} = 2.7 - 7000$ GeV. We discuss the production mechanisms of hadrons and the role of final state interactions (FSI) due to the hadronic rescattering. We also show the influence of the possible quark-gluon plasma (QGP) formation on hadronic observables in $p+p$ collisions at LHC energies. We stress the importance of developing a reliable event generator for elementary reactions from low to ultra-relativistic energies in view of actual and upcoming heavy-ion experiments.