Locating the QCD critical end point through peaked baryon number susceptibilities along the freeze-out line

Abstract

We investigate the baryon number susceptibilities up to fourth order along different freeze-out lines in a holographic QCD model with a critical end point (CEP), and we propose that the peaked baryon number susceptibilities along the freeze-out line can be used as a clean signature to locate the CEP in the QCD phase diagram. On the temperature and baryon chemical potential plane, the cumulant ratio of the baryon number susceptibilities (up to fourth order) forms a ridge along the phase boundary, and develops a sword-shaped "mountain" standing upright around the CEP in a narrow and oblate region. The measurement of baryon number susceptibilities from heavy-ion collision experiments is along the freeze-out line. If the freeze-out line crosses the foot of the CEP mountain, then one can observe the peaked baryon number susceptibilities along the freeze-out line, and the kurtosis of the baryon number distributions has the highest magnitude. The data from the first phase of the beam energy scan program at the Relativistic Heavy Ion Collider indicates that there should be a peak of the kurtosis of the baryon number distribution at a collision energy of around 5 GeV, which suggests that the freeze-out line crosses the foot of the CEP mountain and the summit of the CEP should be located nearby, around a collision energy of 3-7 GeV.