Quartic cumulant of baryon number in the presence of QCD critical point

Abstract

In the context of the ongoing search for the QCD critical point at the Relativistic Heavy-Ion Collider, we study the equation of state near the critical point in the temperature and baryon chemical potential plane. We use the parametric representation introduced in earlier literature, which maps the universal 3D Ising equation of state onto the QCD phase diagram using several non-universal parameters. We focus on the quartic cumulant of the baryon number, or baryon number susceptibility χ B 4 , which can be accessed experimentally via net-proton fluctuation kurtosis measurements. It was originally predicted, through universality arguments based on the leading singular contribution, that χ B 4 and net-proton kurtosis should show a specific non-monotonic behavior due to the critical point. In particular, when following the freeze-out curve on the phase diagram by decreasing beam energy, the kurtosis is expected to dip, and then peak, when the beam energy scan passes close to the critical point. We study the effects of the non-universal and thus far unknown parameters of the Ising-to-QCD mapping on the behavior of χ B 4 . We find that, while the peak remains a solid feature, the presence of the critical point does not necessarily cause a dip in χ B 4 on the freezeout line below the transition temperature. The critical point contribution to the dip appears only for a narrow set of mapping parameters, when subleading singular terms are sufficiently suppressed.

Hot and dense quark-gluon plasma thermodynamics from holographic black holes

“…Additionally, next generation experiments such as FAIR at the GSI ( √ s NN = 2.9 − 4.9 GeV) [5][6][7][8] and NICA in Dubna ( √ s NN = 3 − 5 GeV) [9,10] are being built to precisely determine the QCD equation of state (EOS) and the properties of the strongly interacting quark-gluon plasma (QGP) at large baryon densities. Relevant observables in this quest include fluctuations of conserved charges [11][12][13][14][15][16][17][18], flow [19], and particle yields [20]. For recent reviews see Refs.…”

“…In the case of the most recent lattice QCD transition line obtained from the inflection point of the chiral condensate and its susceptibility in the crossover region, the values of κ 2 and κ 4 are 0.0153 (18) and 0.00032 (67), respectively [74]. It should be noted, however, that these expansion coefficients for the minimum of c 2 s and for the inflection of the chiral condensate do not need to agree, since the corresponding transition curves are actually different in the crossover region.…”

The BEST framework for the search for the QCD critical point and the chiral magnetic effect

“…[207]. Recently, the BEST EoS has been used to study the behavior of the critical fourthorder cumulant of baryon number on conjectured freezeout trajectories in the QCD phase diagram [208]. It was found that subleading and non-singular terms have a significant effect on the behavior of the fourth order cumulant (kurtosis).…”

Diagnosing the Quark-Gluon Plasma

“…[22]); this will likely change in the near future when better data from RHIC for the formation of QGP near a possible critical point will become available. The primary tool for this investigation will be critical fluctuations [23,24]. As scientists begin to look at the data from the high-statistics RHIC beam energy scan that has just concluded, they will analyze the data for the possible presence of such fluctuations because they can tell us something about the existence of a critical point in the QCD phase diagram.…”