Search for QCD critical point by transverse velocity dependence of anti-deuteron to deuteron ratio

We propose the transverse velocity(β_T) dependence of the anti-deuteron to deuteron ratio as a new observable to search for the QCD critical point in heavy-ion collisions.The QCD critical point can attract the system evolution trajectory in the QCD phase diagram,which is known as the focusing effect.To quantify this effect,we employ the thermal and hadronic transport model to simulate the dynamical particle emission along a hypothetical focusing trajectory near the critical point.We found that the focusing effect can lead to anomalous β_T dependence on ■/p,■/d and ■/~3 He ratios.We examined the β_T dependence of ■/p and ■/d ratios of central Au+Au collisions at ■=7.7 to 200 GeV measured by the STAR experiment at RHIC.Surprisingly,we only observe a negative slope in β_T dependence of ■/d ratio at ■=19.6 GeV,which indicates the trajectory evolution has passed through the critical region.In the future,we could constrain the location of the critical point and/or width of the critical region by conducting precise measurements on the β_T dependence of the ■/d ratio at different energies and rapidity.

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.

Machine learning phase transitions of the three-dimensional Ising universality class

Exploration of the QCD phase diagram and critical point is one of the main goals in current relativistic heavy-ion collisions.The QCD critical point is expected to belong to a three-dimensional(3D)Ising universality class.Machine learning techniques are found to be powerful in distinguishing different phases of matter and provide a new way to study the phase diagram.We investigate phase transitions in the 3D cubic Ising model using supervised learning methods.It is found that a 3D convolutional neural network can be trained to effectively predict physical quantities in different spin configurations.With a uniform neural network architecture,it can encode phases of matter and identify both second-and first-order phase transitions.The important features that discriminate different phases in the classification processes are investigated.These findings can help study and understand QCD phase transitions in relativistic heavy-ion collisions.

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.

Cumulants in the 3-dimensional Ising, O(2) and O(4) spin models

Based on the universal properties of a critical point in different systems and that the QCD phase transitions fall into the same universality classes as the 3-dimensional Ising, O（2） or O（4） spin models, the critical behavior of cumulants and higher cumulant ratios of the order parameter from the three kinds of spin models is studied. We found that all higher cumulant ratios change dramatically the sign near the critical temperature. The qualitative critical behavior of the same order cumulant ratio is consistent in these three models.

Study on higher moments of net-charge multiplicity distributions using a multiphase transport model

The moments and moment products of conserved charges are believed to be sensitive to critical fluctuations,which have been adopted in determining the QCD critical point.Using a dynamical multiphase transport model,we reproduce the centrality and energy dependences of moments and moment products of net-charge multiplicity distributions in Au+Au collisions,measured by the Beam Energy Scan program at the RHIC.No non-monotonic energy dependence is observed.We infer that the moment products develop during the dynamical evolution of heavy-ion collisions.The observed difference based on the expectation of the Poisson baseline indicates a positive two-particle correlation between positively and negatively charged particles,which can arise from different dynamical processes at different stages.Therefore,to adopt moments and moment products of net-charge multiplicity distributions in determining the QCD critical point of relativistic heavy-ion collisions,it is essential to consider the dynamical evolution.

Event-by-event efficiency fluctuations and efficiency correction for cumulants of superposed multiplicity distributions in relativistic heavy-ion collision experiments

We performed systematic studies on the effects of event-by-event efficiency fluctuations on efficiency correction for cumulant analysis in relativistic heavy-ion collision experiments. Experimentally, particle eficiencies of events measured under different experimental conditions should be different. For fluctuation measurements, the final event-by-event multiplicity distributions should be the superposed distributions of various type of events measured under different conditions. We demonstrate efficiency fluctuation effects using numerical simulation, in which we construct an event ensemble consisting of events with two different efficiencies. By using the mean particle efficiencies, we find that the efficiency corrected cumulants show large deviations from the original inputs when the discrepancy between the two efficiencies is large. We further studied the effects of efficiency fluctuations for the cumulants of net-proton distributions by implementing the UrQMD events of Au＋Au collisions at √SNN=7.7 GeV in a realistic STAR detector acceptance. We consider the unequal efficiency in two sides of the Time Projection Chamber （TPC）, multiplicity dependent efficiency, and the event-by-event variations of the collision vertex position along the longitudinal direction （Vz）. When the efficiencies fluctuate dramatically within the studied event sample, the effects of efficiency fluctuations have significant impacts on the efficiency corrections of cumulants with the mean efficiencies. We find that this effect can be effectively suppressed by binning the entire event ensemble into various sub-event samples, in which the efficiency variations are relatively small. The final efficiency corrected cumulants can be calculated from the weighted average of the corrected factorial moments of the sub-event samples with the mean efficiencies.

Effects of centrality fluctuation and deuteron formation on the proton number cumulant in Au+Au collisions at√SNN=3 GeV from the JAM model

We studied the effects of centrality fluctuation and deuteron formation on the cumulant(C_(n))and correlation functions(K_(n))of protons up to the sixth order in the most central(b<3 fm)Au+Au collisions at√SNN=3 GeV in a microscopic transport model(JAM).The results are presented as a function of rapidity acceptance within the transverse momentum 0.4<p T<2 GeV/c.We compared the results obtained by the centrality bin width correction(CBWC)using charged reference particle multiplicities with the CBWC using impact parameter bins.It was found that,at low energies,the centrality resolution for determining the collision centrality using charged particle multiplicities is not sufficient to reduce the initial volume fluctuation effect for higher-order cumulant analysis.New methods need to be developed to classify events with high centrality resolution for heavy-ion collisions at low energies.Finally,we observed that the formation of deuterons suppresses the higher-order cumulants and correlation functions of protons and found it to be similar to the efficiency effect.This work can serve as a noncritical baseline for the QCD critical point search in the high baryon density region.

Efficiency corrections for mutually inclusive variables and particle identification effect for mixed-cumulants in heavy-ion collisions

Mix-cumulants of conserved charge distributions are sensitive observables for probing properties of the QCD medium and phase transition in heavy-ion collisions.To perform precise measurements,efficiency correction is one of the most important step.In this study,using the binomial efficiency model,we derive efficiency correction formulas for mutually exclusive and inclusive variables.The UrQMD model is applied to verify the validity of these formulas for different types of correlations.Furthermore,we investigate the effect of the multiplicity loss and contamination emerging from the particle identifications.This study provides important steps toward future measurements of mixed-cumulants in relativistic heavy-ion collisions.