We investigate hadron production as well as transverse hadron spectra from proton-proton, proton-nucleus and nucleus-nucleus collisions from 2 $Acdot$GeV to 21.3 $Acdot$TeV within two independent transport approaches (HSD and UrQMD) that are based on quark, diquark, string and hadronic degrees of freedom. The comparison to experimental data on transverse mass spectra from $pp$, $pA$ and C+C (or Si+Si) reactions shows the reliability of the transport models for light systems. For central Au+Au (Pb+Pb) collisions at bombarding energies above $sim$ 5 A$cdot$GeV, furthermore, the measured $K^{pm}$ transverse mass spectra have a larger inverse slope parameter than expected from the default calculations. We investigate various scenarios to explore their potential effects on the $K^pm$ spectra. In particular the initial state Cronin effect is found to play a substantial role at top SPS and RHIC energies. However, the maximum in the $K^+/pi^+$ ratio at 20 to 30 A$cdot$GeV is missed by ~40% and the approximately constant slope of the $K^pm$ spectra at SPS energies is not reproduced either. Our systematic analysis suggests that the additional pressure - as expected from lattice QCD calculations at finite quark chemical potential $mu_q$ and temperature $T$- should be generated by strong interactions in the early pre-hadronic/partonic phase of central Au+Au (Pb+Pb) collisions.
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