Quark Number Susceptibility around the Chiral Critical End Point

We calculate the quark number susceptibility （QNS） around the chiral critical end point （CEP）. The CEP is found to be located at （μc,Tc）= （80 MeV, 148 MeV） where μc and Tc are the critical chemical potential and temperature, respectively. The QNS is found to have the highest and sharpest peak at the CEP. It is also found that, when the chemical potential μ is in the range of 60MeV≤ μ ≤ 110MeV, the QNS near the transition temperature is larger than the free field result, which indicates that the space-like damping mode dominates the degree of freedom of motion near the CEP.

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

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 Ge V, 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.

The entanglement properties of holographic QCD model with a critical end point

We investigated different entanglement properties of a holographic QCD(hQCD)model with a critical end point at the finite baryon density.Firstly,we considered the holographic entanglement entropy(HEE)of this hQCD model in a spherical shaped region and a strip shaped region.It was determined that the HEE of this hQCD model in both regions can reflect QCD phase transition.Moreover,although the area formulas and minimal area equations of the two regions were quite different,the HEE exhibited a similar behavior on the QCD phase diagram.Therefore,we assert that the behavior of the HEE on the QCD phase diagram is independent of the shape of the subregions.However,the HEE is not an ideal parameter for the characterization of the entanglement between different subregions of a thermal system.As such,we investigated the mutual information(MI),conditional mutual information(CMI),and the entanglement of purification(Ep)in different strip shaped regions.We determined that the three entanglement quantities exhibited some universal behavior;their values did not change significantly in the hadronic matter phase but increased rapidly with the increase in T andμin the QGP phase.Near the phase boundary,these three entanglement quantities changed smoothly in the crossover region and continuously but not smoothly at CEP;they exhibited discontinuous behavior in the first phase transition region.These properties can be used to distinguish between the different phases of strongly coupled matter.

Characterizing variable for the critical point in momentum space

The possible experimentally observable signal in momentum space for the critical point, which is free from the contamination of statistical fluctuations, is discussed. It is shown that the higher order scaled moment of transverse momentum can serve as an appropriate signal for the critical point, provided the transverse momentum distribution has a sudden change when energy increases passing through this point. A 2-D percolation model with a linear temperature gradient is constructed to check this suggestion. A sudden change of third order scaled moment of transverse momentum is observed.

Reconstruction of baryon number distributions

The maximum entropy method(MEM)and Gaussian process(GP)regression,which are both well-suited for the treatment of inverse problems,are used to reconstruct net-baryon number distributions based on a finite number of cumulants of the distribution.Baryon number distributions across the chiral phase transition are reconstructed.It is deduced that with the increase of the order of cumulants,distribution in the long tails,i.e.,far away from the central number,would become increasingly important.We also reconstruct the distribution function based on the experimentally measured cumulants at the collision energy sNN−−−√=7.77 GeV.Given the sizable error of the fourth-order cumulant measured in the experiments,the calculation of MEM shows that with the increasing fourth-order cumulant,there is another peak in the distribution function developed in the region of the large baryon number.This unnaturalness observed in the reconstructed distribution function could in turn be used to constrain the cumulants measured in the experiments.

Chiral phase transition and equation of state in chiral imbalance

The chiral phase transition and equation of state are studied within a novel self-consistent mean-field approximation of the two-flavor Nambu-Jona-Lasinio model.In this newly developed model,modifications to the chemical μand chiral chemical μ5 potentials are naturally included by introducing vector and axial-vector channels from Fierz-transformed Lagrangian to the standard Lagrangian.In the proper-time scheme,the chiral phase transition is a crossover in the T-μ plane.However,when μ5 is incorporated,our study demonstrates that a first order phase transition may emerge.Furthermore,the chiral imbalance will soften the equation of state of quark matter.The mass-radius relationship and tidal deformability of quark stars are calculated.The maximum mass and radius decrease as μ5 increases.Our study also indicates that the vector and axial-vector channels exhibit an opposite influence on the equation of state.