Searching for minimum in dependence of squared speed-of-sound on collision energy

Abstract

Experimental results of the rapidity distributions of negatively charged pions produced in proton-proton ($p$-$p$) and beryllium-beryllium (Be-Be) collisions at different beam momentums, measured by the NA61/SHINE Collaboration at the super proton synchrotron (SPS), are described by a revised (three-source) Landau hydrodynamic model. The squared speed-of-sound parameter $c^2_s$ is then extracted from the width of rapidity distribution. There is a local minimum (knee point) which indicates a softest point in the equation of state (EoS) appearing at about 40$A$ GeV/$c$ (or 8.8 GeV) in $c^2_s$ excitation function [the dependence of $c^2_s$ on incident beam momentum (or center-of-mass energy)]. This knee point should be related to the searching for the onset of quark deconfinement and the critical point of quark-gluon plasma (QGP) phase transition.