Extraction of the sound velocity from rapidity spectra: Evidence for QGP formation at FAIR/RHIC-BES energies

We analyze longitudinal pion spectra from $\ensuremath \sqrt{s_{NN}}=2$ GeV to $\ensuremath \sqrt{s_{NN}}=20$ GeV within Landau’s hydrodynamical model and the UrQMD hybrid approach. From the measured data on the widths of the pion rapidity spectra, we extract the sound velocity c s 2 in the dense stage of the reactions. It is found that the sound velocity has a local minimum (indicating the softest point in the equation of state, EoS) at $\ensuremath \sqrt{s_{NN}}=4\mbox{--}9$ GeV, an energy range accessible at the Facility for Antiproton and Ion Research (FAIR) as well as the RHIC-Beam Energy Scan (RHIC-BES). This softening of the EoS is compatible with the formation of a QGP at the onset of deconfinement. The extracted sound velocities are then used to calculate an excitation function for the mean transverse mass of pions from the hybrid model. We find that, above $\ensuremath \sqrt{s_{NN}} \approx 10$ GeV, even the lowest c s 2 gives a considerably larger $\ensuremath \langle m_T\rangle$ of pions compared to data