A Study of the Properties of the QCD Phase Diagram in High-Energy Nuclear Collisions
AArticle
A Study of the Properties of the QCD Phase Diagram inHigh-Energy Nuclear Collisions
Xiaofeng Luo , Shusu Shi * ,† , Nu Xu and Yifei Zhang Key Laboratory of Quark & Lepton Physics (MOE) and Institute of Particle Physics, Central China NormalUniversity, Wuhan 430079, China; xfl[email protected] (X.L.); [email protected](N.X.) Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China State Key Laboratory of Particle Detection and Electronics, University of Science and Technology of China, Hefei230026, China; [email protected] * Correspondence: [email protected]† The authors contribute equally to this paper.Received: 28 February 2020; Accepted: 24 March 2020; Published: date (cid:1)(cid:2)(cid:3)(cid:1)(cid:4)(cid:5)(cid:6)(cid:7)(cid:8) (cid:1) (cid:1)(cid:2)(cid:3)(cid:4)(cid:5)(cid:6)(cid:7)
Abstract:
With the aim of understanding the phase structure of nuclear matter created in high-energynuclear collisions at finite baryon density, a beam energy scan program has been carried out at RelativisticHeavy Ion Collider (RHIC). In this mini-review, most recent experimental results on collectivity, criticalityand heavy flavor productions will be discussed. The goal here is to establish the connection betweencurrent available data and future heavy-ion collision experiments in a high baryon density region.
Keywords: baryon density; collectivity; criticality; hadron gas; heavy flavor; QCD phase diagram;Quark-gluon-plasma (QGP)
1. Introduction
Most of the visible matter in our universe can be described by the Quantum Chromdynamics (QCD),the standard theory of strong interactions. In the beginning of the century, the new form of matter,the quark-gluon plasma (QGP) in which quarks and gluons are ‘freed’ in a much larger volume comparedto that of nucleon’s, was discovered in the largest heavy-ion colliders RHIC and LHC [1–4] at vanishingbaryonic density. Soon after the discovery, a serious question was asked: what is the structure of thenuclear matter at high baryonic density?Tremendous efforts from both experimental and theoretical sides have launched in order to address thequestion. Figure 1 summarizes the current status of the studies. At the zero baryonic density, the transitionfrom QGP to hadronic matter is a smooth-crossover at T = 150 −
160 MeV [5–9], see dashed-line in thefigure. These results are extracted from the state of the art Lattice gauge theory calculations. At highbaryonic density, on the other hand, one would expect a first-order phase transition, shown as a blacksolid-line. Thermodynamically the first-order phase boundary line must end at finite baryonic density,this is the illusive QCD critical point (CP). Again, recent Lattice calculations have concluded that the QCDcritical is ‘unfavored’ [10,11] when µ B / T < Particles , xx a r X i v : . [ nu c l - e x ] A p r articles , xx , 5 2 of 33 µ B /T = 2 µ B /T = 3 Gas-Liquid C he m i c a l f r ee z e - ou t Baryonic Chemical Potential µ B (MeV) Quark-Gluon PlasmaHadron Gas T e m pe r a t u r e T ( M e V ) LHC SPS AGS SIS CSR
RHIC RHIC FXTFAIRNICA HIAF
Figure 1. (Color online) Schematic Quantum Chromdynamics (QCD) phase diagram in the thermodynamicparameter space spanned by the temperature T and baryonic-chemical potential µ B . Experimentallyextracted chemical freeze-out parameters are shown as the red-line [12]. The dashed-line near µ B = µ B / T < < µ B / T < Experimental status on the beam energy scan (BES) is highlighted in Figure 2. Plot (a) shows thechemical freeze-out temperature T ch as a function of the baryonic chemical potential µ B . Both ALICE atLHC and STAR at RHIC results clearly show that at the vanishing baryon density, i.e., at high collisionenergy, the data driven freeze-out temperature is consistent with the Lattice calculation, T ch ∼ µ B ≤
400 MeV, the µ B dependence of the freeze-out temperature is quite weak andthe value of the freeze-out temperature is around 150–160 MeV. More dramatic drop of the temperature isseen in the high baryon density region. Plot (b) is the kaon over pion yield ratios, extracted from centralheavy-ion collisions, as a function of the collision energies. While one observes the smooth increase ofthe negative kaon over pion ratio with the collision energy, the positive ratio shows a broad peak around √ s NN ∼ √ s NN ≥ N + N → N + Λ + K + ,positive kaons carry information on baryon density. The peak in plot (b) implies the maximum freeze-outdensity reached at 8 GeV. Later in the discussions, we attribute the region of 2 ≤ √ s NN ≤ articles , xx , 5 3 of 33 Au+Au at RHICPb+Pb at LHC
A. Andronic, et al., NPA834, 237(10)J. Cleymans, et al., PRC73, 34905(06)Lattice fits (a) Chemical Freeze-out
Chemical Potential µ B (MeV) T e m pe r a t u r e T c h ( M e V ) (b) N(K)/N( π ) Ratio Collision Energy √ s NN (GeV) M i d - y H ad r on R a t i o s K + / π + K − / π − STAR DataThermal fits
Figure 2. (Color online) ( a ) Experimental results of chemical freeze-out temperature as a function of thebaryonic chemical potential from the RHIC BES-I [12] and LHC [25,26]. Red-circles and black-squaresrepresent results from the top 5% and 60–80% Au+Au collisions at RHIC, respectively. Open-circle is fromthe 2.76 TeV 0–5% Pb+Pb collisions at LHC. The hatched green-band represents the Lattice results [7,27].The yellow-line shows the empirical thermal fits results [28,29]. ( b ) Mid-rapidity particles of positive andnegative kaons over pions shown as circles and triangles, respectively. The results [30] of thermal modelfits are shown as hatched-bands in the plot and the high-baryon-density region is highlighted in yellow. Collective flow (collectivity) and the critical behavior (criticality) are important aspects in high-energynuclear collisions. In this short review, we will discuss the experimental status including the results oncollectivity and criticality from high-energy nuclear collisions. RHIC has provided most recent data sowe will focus on the information. At the end we will address the importance of the future fixed-targetexperiments such as STAR fixed-target program in BES-II, CBM at FAIR [16] as well the CEE at HIAF [17].
2. Beam Energy Dependence of the Collectivity
The main goal of high energy heavy-ion collisions, such as collisions at LHC and top energy collisionsat RHIC, is to study the properties of new form of matter QGP. QGP is a thermalized (or nearly) systemwith partonic degree of freedom. The elliptic flow measurement of multi-strange hadrons and φ mesonsindicates the partonic collectivity has been built up at the top energy heavy-ion collisions at RHIC [31–37].The Heavy Flavor Tracker, a high resolution silicon detector system, which was installed in the year of2013, provides high vertex position resolution. The significance of charmed hadron reconstruction issignificantly improved. Thus the precise measurement of D becomes possible. Figure 3 shows the v results for D , Ξ − , Λ and K S [38]. A number of constituent quark ( n q ) is tested by scaling both v and m T − m with n q . A simple quark coalescence or recombination model suggests the baryon v would be1.5 times of the meson v assuming the collectivity has been attained in the partonic stage, as the numberof constituent quarks for baryons is 3 where it is 2 for mesons. When discussing the n q scaling, we usuallyfocus on the intermediate p T range in which the v value saturates. The D v follows the n q scalings withselected multi-strange and strange hadrons in Figure 3. It indicates the collectivity of parton level has beenbuilt up from light flavor u , d quarks to strange and charm quarks. Since the mass of the charm-quark ismuch larger than the temperature reached in the system, the observed strong charm-quark collectivity canbe interpreted as the thermalization of the medium created in the 200 GeV Au+Au collisions at RHIC [38].To some extent, this result justified the phase diagram sketched in Figure 1. articles , xx , 5 4 of 33 (GeV/c) T p A n i s o t r op y P a r a m e t e r , v D Ξ Λ S K = 200 GeV NN sSTAR Au+Au 10 40% a) ) (GeV/c q ) / n m T (m q / n A n i s o t r op y P a r a m e t e r , v D Ξ Λ S K = 200 GeV NN sSTAR Au+Au 10 40% Figure 3. (Color online) The number of constituent quark ( n q ) scaled v as a function of ( m T − m ) / n q in10%–40% Au+Au collisions for D , Ξ − , Λ and K S (from [38]). Where m T is square root of the rest masssquared plus transverse momentum squared. The main motivation of BES program is to explore the QCD phase boundary and critical point. Thelogic is straightforward: as the collision energy decreases, the conditions of QGP formation are no longersatisfied at some point. It offers us a unique experimental way to investigate the QCD phase structure.The transverse radial flow velocity β is obtained by fitting the transverse momentum p T spectra with ablast wave model [39]: dNp T dp T ∝ (cid:90) R r dr m T I ( p T sinh ρ ( r ) T kin ) × K ( m T cosh ρ ( r ) T kin ) (1)where I and K are the modified Bessel functions and ρ ( r ) = tanh − β . The model assumes a radiallyboosted thermalized source with two key parameters, kinetic freeze-out temperature T kin and a transversecollective flow velocity β .Plot (a) of Figure 4 shows the extracted parameter β as a function of collision energy. The data pointsare taken from E802 [40–43], E866 [44,45], E877 [46], E895 [47], NA49 [48–51], STAR [12,52,53] and ALICEexperiments [54] and references therein. The p T spectra of π ± , K ± , p and ¯ p are fitted simultaneously withthe blast wave model. The p T range for simultaneous fitting are similar across all RHIC BES and LHCenergies. A rapid increase of (cid:104) β (cid:105) is observed at low energies (<5 GeV), then a steady increase follows up toLHC energy. The six points from RHIC BES (7.7–39 GeV) are almost flat within uncertainties. articles , xx , 5 5 of 33 > b < ALICESTARNA49E895E877E866E802 (a)
FAIRNICA - - v ALICESTARPHENIXPHOBOSCERESE877E895FOPI (b)
FAIRNICA
Collision Energy √ s NN (GeV) Figure 4. (Color online) ( a ) The transverse radial flow velocity as a function of collision energy fromcentral heavy-ion collisions. The data points are taken from E802 [40–43], E866 [44,45], E877 [46], E895 [47],NA49 [48–51], STAR [12,52,53] and ALICE experiments [54] and references therein. The data points ofRHIC and LHC are from 0–5% central collisions. AGS and SPS energies are mostly from 0–5% and 0–7%central collisions respectively. ( b ) The p T -integrated v in 20%–30% most central collisions (or similarcentrality) from various collision energies. The data points are from E895 [55] for protons, NA49 [56] forpions and FOPI [57], E877 [58], CERES [59], STAR and ALICE [60] for charged hadrons. The RHIC resultsof inclusive charged particles for 130 and 200 GeV are from refs. [61–65]. The RHIC BES data are fromrefs. [66,67]. The energy regions of future collider and fix-target experiments, NICA and FAIR, are indicatedin both plots. The (cid:104) β (cid:105) parameter extracted from blast wave model reflects the transverse radial flow built-upin the collision system. The second order coefficient of final azimuth distribution in the momentumspace, v , is sensitive to the initial geometry and interactions of early stage of the collisions. It suggeststhat a non-monotonic variation could be observed around the so-called, “softest point of EOS” [68,69].The “softest point of EOS” is usually defined as a strong drop of speed of sound (a minimum value) ora reduction in the pressure of the system during the dynamic evolution. Plot (b) of Figure 4 shows the p T -integrated v from 20%–30% or similar centrality as a function of collision energy. The data pointsare from E895 [55] for protons, NA49 [56] for pions and FOPI [57], E877 [58], CERES [59], STAR andALICE [60] for charged hadrons. The RHIC results of inclusive charged particles for 130 and 200 GeV arefrom refs. [61–65]. The RHIC BES data are from refs. [66,67]. The negative v ( √ s NN < p T integrated v from AGS toLHC. It appears that the slope of v with collision energy is steeper for 3–7.7 GeV compared to 7.7–2760GeV, which is consistent with that we observe for (cid:104) β (cid:105) parameter. The v of charged hadrons as a functionof p T does not change significantly at RHIC BES and LHC energies. Due to the rise in mean p T which isexpected from larger radial flow, the p T -integrated v increases. It is consistent with the collision energydependence of (cid:104) β (cid:105) parameter, as discussed in panel (a) of Figure 4. Non-monotonic behavior which ispredicted by the softening of the equation of state for a system close to the critical temperature [68] isnot observed.The first order coefficient of final azimuth distribution in the momentum space, v (rapidity-odd),as a function of rapidity is sensitive to the system expansion during the early stage of collisions. Bothhydrodynamic and nuclear transport models indicate that v in the midrapidity region offers sensitivity to articles , xx , 5 6 of 33 details of the expansion of the participant matter during the early collision stages [70–72]. Hydrodynamicplus first-order phase transition calculations suggest a minimum of net-baryon v slope ( dv / dy ) nearmid-rapidity is a signal of phase transition between QGP and hadronic matter [73,74]. Net-particleis defined as the excess yield of a particle type over its anti-particle [75,76]. The v of net-particle isdefined as: v X = r ( y ) v X + [ − r ( y )] v − X , where X represents particle, ¯ X represents the correspondinganti-particle, r ( y ) is the ratio of particle to anti-particle yield. Plot (a) of Figure 5 shows the v slope relativeto rapidity for net-proton, net- Λ and net-kaon. Similar energy dependence is observed for net-proton andnet- Λ . The non-monotonic behavior is consistent with the hydrodynamical calculations with first-orderphase transition [73,74]. Large divergence between dv / dy of net-kaon and net-proton (net- Λ ) is observedbelow √ s NN <
20 GeV, whereas all three agrees well at and above 20 GeV. More theoretical inputs areneeded to understand the difference. At the same time the measurements of centrality dependence inthe future BES program will further verify the energy dependence and constrain model calculations. InRef. [76], the dv / dy of φ mesons shows larger magnitude than pions and kaons at and above 14.5 GeV, andmore interesting, the φ meson slope seems to increase sharply at 11.5 GeV. Because of the large statisticaluncertainties, it is still not conclusive. It opens a new direction for both experimental and theoreticalinvestigation on directed flow [77]. - - y = / d y | d v STAR BESNet - proton L Net - Net - Kaon
FAIR NICA (a) - ) X ( ( X )- v v - p - + p - -K + K pp- L - L + X - - X STAR BES (b)
FAIR NICA
Collision Energy √ s NN (GeV) Figure 5. (Color online) ( a ) The slope of v at mid-rapidity ( dv / dy ) as a function of collision energyin 10%–40% Au+Au collisions for net-proton, net- Λ and net-kaon [75,76]. ( b )The v difference betweenparticles and the corresponding anti-particles as a function of collision energy [78–80]. The energy regionsof future collider and fix-target experiments, NICA and FAIR, are indicated in both plots. As discussed above, the v of multi-strange hadrons and φ mesons are more sensitive to the partonlevel collectivity as their hadronic cross sections are smaller than light flavor hadrons [81–83]. The resultsfrom RHIC BES I suggest a possible drop of φ meson v compared to other hadrons in Au+Au collisions at √ s NN = 11.5 and 7.7 with ∼ σ effect [78–80]. Data of high precision will be available with RHIC BES II. Asignificant difference in the v values between particles and the corresponding anti-particles is observedat low energy heavy-ion collisions at RHIC. As shown in plot (b) of Figure 5, the difference is morepronounced for v of baryons and anti-baryons when the collision energy is less than 20 GeV [78–80].These differences naturally break the n q scaling discussed previously, as the number of constituentquarks are same for particle and the corresponding anti-particle. Several models try to explain the articles , xx , 5 7 of 33 data [84–88]: the hydro + transport (UrQMD) calculation can reproduce the proton data, but not themeson data [84]; A analytic hydro model can quantitatively reproduce the π , K and proton data, but theflavor dependence ( ∆ v p > ∆ v Λ > ∆ v Ξ > ∆ v Ω ) is not consistent with data [85]; A Nambu-Jona-Lasino(NJL) model incorporating partonic and hadronic potentials can describe the data qualitatively, but notquantitatively [86,87]. New data from RHIC BES II, especially data of multi-strange hadrons, could offermore constrains on the model calculation.
3. Beam Energy Dependence of the Higher-Order Cumulants of Net-Particle MultiplicityDistributions and Light Nuclei Productions
Fluctuations of conserved quantities, such as net-baryon ( B ), net-charge ( Q ) and net-strangeness( S ), are sensitive observables to search for the QCD critical point in heavy-ion collisions [89–93].The higher-order cumulants ( C n , the n th order cumulants), which can be used to quantify the fluctuationsand describe the shape of the event-by-event multiplicity distributions, are predicted to be sensitive tothe correlation length ( ξ ) of the system as C ∝ ξ and C ∝ ξ [90,94]. The various order cumulantsand cumulant ratios can be expressed in terms of moments as C = σ , C = S σ , C = κσ and C / C = σ / M , C / C = S σ , C / C = κσ , where σ , S and κ are variance, skewness and kurtosis,respectively [95]. The various order cumulants are extensive quantities and are proportional to the systemvolume, which is difficult to be measured in heavy-ion collisions. By taking the ratio between variousorder cumulants, the system volume can be cancelled to the first order and are directly related to the ratiosof the thermodynamic susceptibilities ( χ ) as C m / C n = χ ( m ) / χ ( n ) [89,93,96].Figure 6 (left) shows the density plot of fourth order cumulant of order parameter as a functionof temperature and baryon chemical potential ( T and µ B ) by mapping the Ising equation of state ontothe QCD equation of state near the critical point [97]. The red and blue regions in the density plotdenote the negative and positive contributions to the fourth order cumulant, respectively. Experimentally,by tuning the beam energy, the T and µ B at chemical freeze-out are varied accordingly. The greendashed line represents the chemical freeze-out points ( T , µ B ) passing through the critical region whenone varies the beam energies. Figure 6 (right) shows fourth order fluctuation κσ as a function of baryonchemical potential ( µ B ). Due to the negative and positive critical contributions near the critical point,the κσ will show a non-monotonic energy or µ B dependence with respect to the non-critical baseline.This is the characteristic experimental signature of the critical point we are looking for in the heavy-ioncollision experiment. Theoretically, the properties of QCD phase diagram at finite baryon density and thesignatures of conserved charge fluctuations near the QCD critical point have been extensively studiedby various model calculations, such as Lattice QCD [10,18–22,98], NJL, PNJL model [99–106], PQM, FRGmodel [107–109], Dyson-Schwinger Equation (DSE) method [110–113], chiral hydrodynamics [114] andother effective models [94,115–119]. However, one should keep in mind that the above results are under theassumption of thermal equilibrium with infinite and static medium. In the real heavy-ion collisions, thereexists the effects of finite size/time [120–122], non-equilibrium [123–127] and thermal blurring effects [128].Dynamical modeling of heavy-ion collisions by implementing both the critical and those backgroundeffects are ongoing [129–131]. articles , xx , 5 8 of 33 Figure 6. (Color online) (Left) Density plot of fourth order cumulant of order parameter as a function oftemperature and baryon chemical potential ( T and µ B ) by mapping the Ising equation of state onto theQCD equation of state near the critical point [97]. The red and blue regions in the density plot denote thenegative and positive contributions to the fourth order cumulant, respectively. The green dashed line isthe chemical freeze-out points ( T , µ B ) passing through the critical region when we scan the beam energies.(Right) Normalized fourth order proton cumulant κσ as a function of collision energy or µ B along thechemical freeze-out line. Before turning to the experimental status, we would like to stress that there is a long history of usingthe higher-order cumulants to extract the information on that state created in high-energy nuclear collisions.As extensively discussed in Ref. [26], hadron yields or their ratios, which are the first order moment of themultiplicity distributions, have been used for determine the nature of thermalization in such collisions.Once the thermalization is established [132], on the other hand, the higher-orders cumulants of the verysame distributions can be used to study the fine structures of the QCD matter. For example, the criticalpoint [94], the nature of the crossover transition [5,107] and the phase boundary [133] at vanishing andlarge net-baryon region, respectively.Experimentally, the fluctuation of the net-proton and net-kaon are used as a proxy of net-baryonand net-strangeness fluctuations, respectively. The STAR experiment has measured the higher-ordercumulants ( C – C ) and second-order off-diagonal cumulants of net-proton [134–139], net-charge [140] andnet-kaon [141] multiplicity distributions in Au+Au collisions at √ s NN = 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4 and200 GeV, which are collected during the first phase of RHIC beam energy scan program (2010–2014) [142].To make precise measurements, various corrections and techniques have been applied in the data analysis,those include : (1) Select proper collision centralities to avoid auto-correlations and suppress volumefluctuations [143,144], (2) Detector Efficiency Correction [145–149], (3) Centrality Bin Width Correction(CBWC) [143], (4) Statistical error estimation with Delta theorem and/or Bootstrap [143,150]. Figure 7shows the measured event-by-event net-charge, net-kaon and net-proton multiplicity distributions ofthree different centralities in Au+Au collisions at √ s NN = 14.5 GeV. Those are raw distributions andnot corrected for detector efficiency and acceptance. One should apply the efficiency correction andCBWC to obtain the final efficiency corrected cumulants. In Ref. [150], we have shown that the statisticaluncertainties of the cumulants ( C n ) strongly depend on the width of the distributions (error ∝ σ n / √ N).In general, the widths of the distributions in central collisions are wider and with larger mean values thanthose from peripheral collisions. Further, the widths of the net-charge distributions are much wider thanthose of net-proton and net-kaon in the same centrality. That’s the reason why we observe larger statisticaluncertainties in central collisions than those from peripheral. Assuming the measured particles are emittedfrom many independent sources in the fire ball, the multiplicity distributions in central collisions would bemore symmetric and close to Gaussian distribution than the peripheral based on the central limit theorem articles , xx , 5 9 of 33 (CLT). If those sources are identical and uncorrelated, the cumulant ratios are expected to be a constant asa function of collision centralities. -50 0 50-50 0 50
10 10 | < 0.5 η < 2 (GeV/c),| T p NN S Au+Au -50 0 50-50 0 50
10 10
10 < 1.6 (GeV/c),|y| < 0.5 T p -50 0 50-50 0 50
10 10
10 < 2 (GeV/c),|y| < 0.5 T p STAR Preliminary ) K N ∆ Net-Kaon ( ) Ch N ∆ Net-Charge ( ) P N ∆ Net-proton ( N u m be r o f E v en t s Figure 7. (Color online) The STAR measured raw event-by-event net-charge, net-kaon and net-protondistributions of three centralities (0–5%, 30%–40% and 70%–80%) in Au+Au collisions at √ s NN = 14.5 GeV [151]. Figure 8 shows the energy dependence of cumulant ratios ( σ / M , S σ /Skellam, κσ ) of net-charge,net-kaon and net-proton multiplicity distributions in Au+Au collisions measured by STAR. The bluebands are the results obtained from UrQMD model calculations without including the physics of criticalpoint [92,152,153]. The S σ values are normalized by the Skellam expectations, which are constructed withthe measured mean values of proton and anti-proton by assuming they are distributed as independentPoisson distributions. The deviation of S σ /skellam from unity would indicate the deviation of S σ fromPoisson statistical fluctuations (Poisson baseline). For S σ /Skellam and κσ , their Poisson baselines are unity,which are plotted as the dashed lines. We found that the σ / M of net-charge, net-kaon and net-protonmonotonically increase when increasing the collision energy. The S σ /Skellam and κσ show weak energydependence for net-charge and net-kaon measurements. We didn’t observe significant deviations ofnet-charge and net-kaon cumulant ratios S σ /Skellam and κσ from the Poisson expectations and UrQMDcalculations within uncertainties. However, a clear non-monotonic energy dependence of net-proton κσ was observed in top 0–5% central Au+Au collisions. The 0–5% net-proton κσ values are close to unityfor energies above 39 GeV and show large deviations below unity around 19.6 and 27 GeV, and thenincreasing above unity below 19.6 GeV. The UrQMD calculations of net-proton κσ displaying a strongsuppression below unity at lower energies is due to the effects of baryon number conservation [154–157].However, this suppression is not observed at low energies in the STAR data. Another transport model(JAM model) study further demonstrates that the resonance weak decay and hadronic re-scattering havevery small effects on the proton number fluctuations ( C – C ) at low energies [158]. articles , xx , 5 10 of 33 / M s Net-Charge
Au+Au collision at RHIC | < 0.5 h ) < 2.0, | c (GeV/ T p Net-Kaon
Au+Au collision at RHIC) < 1.6, |y| < 0.5 c (GeV/ T p Net-Proton
Au+Au collision at RHIC) < 2.0, |y| < 0.5 c (GeV/ T p - / S k e ll m an s S STAR Preliminary - - sk
10 20 40 60 100 200 2 - -
012 10 20 40 60 100 200 01234
10 20 40 60 100 200 (GeV) NN sCollision Energy Figure 8. (Color online) Energy dependence of cumulant ratios ( σ / M , S σ /Skellam, κσ ) of net-charge,net-kaon and net-proton multiplicity distributions for top 0–5% and 70%–80% peripheral collisions. The Poissonexpectations are denoted as dotted lines and UrQMD calculations are shown as bands. The statistical andsystematical errors are shown in bars and brackets, respectively. In Figure 9, we summarize the energy dependence of κσ of net-charge, net-kaon and net-protonmultiplicity distributions in Au+Au collisions measured by the STAR experiment. For comparison,the net-charge results in Au+Au collisions at √ s NN = 7.7, 19.6, 27, 39, 62.4 and 200 GeV measured bythe PHENIX experiment [159] are shown in the panel (b). We found that the κσ of the net-charge andnet-kaon multiplicity distributions measured by the STAR experiment show larger statistical uncertaintiesthan those of net-proton κσ . This can be understood as the statistical uncertainties of κσ depend onthe width ( σ ) of the multiplicity distributions and the particle detecting efficiencies ( (cid:101) ) in the detector as error ( C n / C ) ∝ σ n − / ( √ N (cid:101) n ) [146]. The width of the net-charge distributions are larger than those ofnet-proton and net-kaon. Meanwhile, due to decays, the efficiency of kaon ( ∼ ∼ κσ from STAR, we observe weak energy dependencewithin current statistical uncertainties. The PHENIX net-charge κσ are with much smaller statisticaluncertainties than the results from STAR. This is due to smaller acceptance of PHENIX detector thanthe STAR detector, thus the width of the net-charge multiplicity distributions measured by the PHENIXexperiment is much narrower than those measured by STAR. We observe a clear non-monotonic energydependence for net-proton κσ in the most central (0–5%) Au+Au collisions with a minimum around19.6 GeV. This non-monotonic behavior cannot be described by various model calculations without thephysics of phase transition and critical point. articles , xx , 5 11 of 33 -15-10-50510 [[ [[[[ [[ [[ [[ [[ [[ N e t - Q κ σ (a) STAR Net-charge δφ = 2 π | η | < < p T <
70 - 80% 0 - 5%
Au+Au Collisions at RHIC -1012 [[ [[ [[ [[ [[ [[ N e t - Q κ σ (b) PHENIX Net-charge δφ = π /2+ π /2| η | < < p T < -4-202 [[ [[[[ [[ [[ [[ [[ [[
10 20 505 100 200 N e t - K κ σ (c) STAR Net-Kaon δφ = 2 π |y K | < < p T <
70 - 80% 0 - 5% [[ [[[[ [[ [[ [[ [[ [[
10 20 505 100 200
Collision Energy √ s NN (GeV) N e t - p κ σ (d) STAR Net-proton δφ = 2 π |y p | < < p T <
70 - 80% 0 - 5% , Figure 9. (Color online) The STAR measured energy dependence of κσ of net-charge (top left), net-kaonand net-proton distributions in Au+Au collisions at √ s NN = 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4 and 200 GeV.The net-charge fluctuations measured by the PHENIX experiment in Au+Au collisions at √ s NN = 7.7, 19.6,27, 39, 62.4 and 200 GeV are shown in top right panel.The statistical and systematical errors are shown inbars and brackets, respectively. Figure 10 shows the energy dependence of the fourth-order fluctuations ( κσ ) of net-proton from thetop 5% central Au+Au collisions measured by STAR experiment [139]. Recent result from the HADESexperiment is also shown in the figure. Note that there are differences in the data shown in Figure 10 : whileSTAR data points are from the top 5% central collisions and | y | < < p T < | y | < < p T < κσ of net-proton multiplicitydistributions and one can observe a strong enhancement at the highest µ B ∼
420 MeV, correspondingto the Au+Au central collisions at √ s NN = 7.7 GeV. This might indicate attractive correlations betweennucleons in nature at the large baryon density region. However, interestingly, the strong enhancement inthe fourth-order fluctuation seems disappeared as shown by the HADES result at √ s NN = 2.4 GeV [160].Indeed, in the high baryon density region, between √ s NN = 2 GeV and 8 GeV, there might be a peak in thefourth order fluctuations as speculated in Ref. [92,97,133]. If the peak structure is confirmed, that wouldbe the experimental indication of the QCD critical point and/or the first order phase transition created insuch high-energy nuclear collisions. On the other hand, it is possible that from √ s NN = 2 GeV to 8 GeVdata points are smoothly connected without any peaks or dips. Results from the future experiments likeNICA, CBM, and CEE will certainly provide the answer. articles , xx , 5 12 of 33 [[ [[ [[ [[ [[ [[ [[ [[ STAR: net-proton
HADES BES-II uncertainties for net-pUrQMD for net-pHigh baryon density region
Au + Au Collisions at RHIC < < p T < NICACBMCEE
Collision Energy √ s NN (GeV) κ σ Figure 10. (Color online) Energy dependence of the mid-rapidity net-proton 4th order cumulants ratiosfrom central 0–5% Au+Au collisions, STAR experiment ( | y | < < p T < | y | < < p T < In Figure 10, the results from the transport model UrQMD (grey band) show a monotonic decreasefrom low to high baryon density region, which is due to the effect of baryon number conservation inhigh-energy nuclear collisions. Note that in the Poisson limit, the absence of criticality or other dynamicalcorrelations, the κσ is expected to be unity. The green band in the figure is the projected statistical errorof the fourth-order fluctuations κσ of net-protons in the second phase of the RHIC Beam Energy Scan(BES-II, 2019–2021) program [161]. The BES-II program, which is scheduled between 2019 and 2021 for theAu+Au collisions at 7.7–19.6 GeV, will take about 10 to 20 times higher statistics (depending on energy) toconfirm the non-monotonic behavior observed in the fourth order fluctuations ( κσ ) of net-proton andproton in Au+Au collisions in the BES-I at RHIC. Assuming the data in the figure is related to the criticalregion, one must study the net-proton fluctuations at even higher baryon density region, i.e., at lowercollision energies. The yellow band shown in the figure represents the high baryon density region ( √ s NN = 2–8 GeV) covered by future FAIR/CBM fixed target (FXT) experiment ( √ s NN = 2–5 GeV) [162] and theNICA/MPD collider experiment ( √ s NN = 4–11 GeV) [163]..Besides the conserved charge fluctuations, the light nuclei production is predicted to be sensitive tothe baryon density fluctuations assuming that the light nuclei is formed from the nucleon coalescence.Model calculations show that the yield ratio between deuteron, triton and proton, N t × N p / N d is relatedto the neutron density fluctuations, thus can be used to search for the QCD critical point in heavy-ioncollisions [164,165]. Experimentally, the STAR experiment has measured the production of deuteron articles , xx , 5 13 of 33 ( d ) and triton ( t ) in the Au+Au collisions at √ s NN = 7.7, 11.5, 14.5, 19.6, 27, 39, 54.4, 62.4 and 200 GeV.As shown in Figure 11, non-monotonic energy dependence is observed for the yield ratio, N t × N p / N d ,in 0–10% central Au+Au collisions with a peak around 20–30 GeV [166–168]. The yield ratios measured bySTAR experiment below 20 GeV are consistent with the results calculated from NA49 experiment [164].Since there is no critical physics implemented in the JAM model, the results of central ( b < (GeV) NN sCollision Energy d2 / N p N · t N Au + Au CollisionsSTAR Preliminary = 0.3 GeV/c d/t P D JAM (b < 3 fm), = 3.4 fm t R D = 4.0 fm, d R D STAR (0-10%)NA49 from PLB 781,499 (2018)
Figure 11. (Color online) Energy dependence of the light nuclei yield ratio N t × N p / N d in central (0–10%)heavy-ion collisions. The red solid circles are the results measured in central (0–10%) Au+Au collisions atBES energies by the STAR experiment and the open squares are the results calculated from the Pb+Pb dataof NA49 experiment. The blue band represents the results of central Au+Au collisions ( b <
4. Beam Energy Dependence of the Heavy-Flavor Production
Since the masses of heavy flavor quarks are much larger than the temperature of the system created inthe high-energy nuclear collisions, they can be used as clean probes of the medium properties at early stageof the collisions. As shown in Figure 12, heavy flavor quark masses are all generated in the electro-weaksector while light quarks ( u , d , and s ) are dominated by the spontaneous breaking of chiral symmetryin QCD. Thus heavy quarks keep massive when participating in strong interactions. Due to their largemasses, these heavy flavor quarks are primarily pair-created in initial hard pQCD processes. These factsmaking heavy quark hadrons are ideal for studying the medium effects including the thermalization ofthe system. One example has already discussed in previous section, see Figure 3. articles , xx , 5 14 of 33 Total quark mass (MeV) H i gg s qua r k m a ss ( M e V ) tbcsdu QCD Vacuum c c symmetry breakingHiggs VacuumElectroweak symmetry breaking Figure 12. (Color online) Quark masses in the QCD vacuum and the Higgs vacuum. A large fraction of thelight quark mass is due the the chiral symmetry breaking in the QCD vacuum. The numerical values weretaken from reference [169]. The plot is taken from Ref. [170].
The QCD calculations can evaluate the charm production cross sections at high energies via aperturbation scheme in p + p collisions [171,172]. Figure 13 shows the charm production cross sectionsat midrapidity as a function of p T in p + p collisions at √ s = articles , xx , 5 15 of 33 (GeV/c) T Transverse Momentum p ( m b / ( G e V / c )) cc y = d y | T / dp s d -8 -6 -4 -2
10 1 pp 200 GeVpp 500 GeV [x10]] pp 7 TeV [x10 ( S T AR ) * + D D ( S T AR ) * + D D ( C D F ) D ( A L I CE ) D + X * /D D fi ) pp + p( FONLL
Figure 13. (Color online) Charm production cross sections at midrapidity as a function of p T . Symbolsfrom top to bottom are experiment results at √ s = In heavy-ion collisions, charm quark interacts with the QGP matter when traversing in the medium.The transverse momentum of charm quark is modified by the medium via energy loss or collective flow.However, the total number of charm quarks may keep conserved since they are produced in initial hardprocesses before the QGP formation and there is no more charm quark created later via thermal productionat RHIC energies. Figure 14 shows the p T -integrated cross section for D production per nucleon-nucleoncollision d σ NN / dy | y = from different centrality bins in √ s NN = 200 GeV Au+Au collisions for the full p T range (a) and for p T > c (b), respectively [177]. The result from the p + p measurement at the samecollision energy is also shown in both panels [175]. > 0 GeV/c T p STAR Au+Au = 200 GeV NN s p+p (a) p+p > 4 GeV/c T p(b) b ) m ( y = / d y | NN s d æ part N Æ Number of Participants ) part Number of participant (N
Figure 14. (Color online) Integrated D cross section per nucleon-nucleon collision at mid-rapidity in √ s NN =
200 GeV Au+Au collisions for p T > 0 ( a ) and p T > 4 GeV/ c ( b ) as a function of centrality N part .The statistical and systematic uncertainties are shown as bars and brackets on the data points. The greenboxes on the data points depict the overall normalization uncertainties in p + p and Au+Au data respectively. The high p T ( > c ) d σ NN / dy | y = shows a clear decreasing trend from peripheral to mid-centraland central collisions and the result in peripheral collisions is consistent with p + p collisions within articles , xx , 5 16 of 33 uncertainties. This is consistent with charm quarks lose more energy in more central collisions at high p T .However, for the d σ NN / dy | y = integrated over full p T range shows approximately a flat distribution as afunction of N part . The values for the full p T range in mid-central to central Au+Au collisions are smallerthan that in p + p collisions with ∼ σ effect considering the large uncertainties from the p + p measurements.The total charm quark yield in heavy-ion collisions is expected to follow the number-of-binary-collisionscaling since charm quarks are conserved at RHIC energies. However, the cold nuclear matter (CNM) effectincluding shadowing could also play an important role. In addition, hadronization through coalescencecould alter the hadrochemistry distributions of charm quark in various charmed-hadron states which maylead to the reduction in the observed D yields in Au+Au collisions [178]. For instance, hadronizationthrough coalescence can lead to an enhancement of the charmed baryon Λ + c over D yield [179–181],and together with the strangeness enhancement in the hot QCD medium and sequential hadronization,can also lead to an enhancement in the charmed strange meson D + s yield relative to D [180–182].The STAR Heavy Flavor Tracker (HFT) with a silicon pixel detector achieved ∼ µ m spacialresolution of the track impact parameter to the primary vertex allows a topological reconstruction of thedecay vertices of open charm hadrons. Figure 15 left panels show the charmed baryon over meson ratiocompared with light and strange baryon over meson ratios [183,184] (a) and various models (b). The Λ c / D ratio is comparable in magnitude to the Λ / K s and p / π ratios and shows a similar p T dependence inthe measured region. A significant enhancement is seen compared to the calculations from the latestPYTHIA 8.24 release (Monash tune [185]) without (green solid curve) and without (magenta dot-dashedcurve) color reconnections (CR) [186]. The implementation with CR is found to enhance the baryonproduction with respect to mesons. However, both calculations fail to fully describe the data and its p T dependence. Figure 15b also shows the comparison to various models with coalescence hadronization ofcharm quarks [179–182]. The comparisons suggest coalescence hadronization plays an important role incharm-quark hadronization in the presence of QGP. Also, the data can be used to constrain the coalescencemodel calculations and their model parameters. articles , xx , 5 17 of 33 (GeV/c) T Transverse Momentum p ) D + ) / ( D - c L + + c L ( D+ D -c L + +c L - p + + p pp + s0 L + L STAR
Au+Au 10-80% = 200 GeV NN s (a) ) D + ) / ( D - c L + + c L ( Transverse
Ko et.al: three quark (0-5%)Ko et.al: di-quark, (0-5%)Ko et.al: with flow (0-10%)Catania, coal.+frag. (10-80%)Catania, coal. (10-80%)Tshingua (10-80%)Rapp et.al (0-20%)PYTHIAPYTHIA,CRTHERMUS (b) ) D + ) / ( D - s + D + s ( D STARAu+Au 0-10% = 200 GeV NN s (c) Catania, coal.Catania, coal.+frag.Cao,KoHe,Rapp, 0-20%PYTHIA p+p ) D + ) / ( D - s + D + s ( D STARAu+Au 10-40% = 200 GeV NN s (d) (GeV/c) T Momentum p
Tsinghua, seq. coal.Tsinghua, sim. coal.Cao, Ko
Figure 15. (Color online) Left panels: The measured Λ c / D ratio at midrapidity ( | y | <
1) as a functionof p T for Au+Au collisions at √ s NN = 200 GeV in 10%–80% centrality, compared to the baryon-to-mesonratios for light and strange hadrons ( a ) and various model calculations ( b ). The p T -integrated Λ c / D ratiofrom the THERMUS [187] model calculation with a freeze-out temperature of T ch =
160 MeV is shownas a horizontal bar on the left axis of the plot. Right panels: ( c ) The integrated D s / D ratio (black solidcircles) of 1.5 < p T < c as a function of p T compared to model calculation (curves) in 0–10%Au+Aucollisions at √ s NN = 200 GeV. ( d ) Same D s / D ratio as (c) but with 10–40% centrality. The vertical linesand brackets on the data points indicate statistical and systematic uncertainties respectively. Figure 15 right panel shows the D s / D ratio as a function of p T compared to coalescence modelcalculations for 0–10% (c) and 10%–40% (d) collision centralities. Several models incorporating coalescencehadronization of charm quarks and strangeness enhancement are used to describe the p T dependence of D s / D ratio. Those models assume that D ± s mesons are formed by recombination of charm quarks withequilibrated strange quarks in the QGP [179–182]. In particular, the sequential coalescence model togetherwith charm quark conservation [180] considers that more charm quarks are hadronized to D ± s mesonsthan D since the former is created earlier in the QGP, which results in further enhancement of D s / D ratio in Au+Au collisions relative to p + p collisions. D meson R AA and v have been observed similar as light flavor hadrons in 200 GeV Au+Aucollisions [177], which indicates charm is thermalized in the system with T ∼
170 MeV. In low energyregion, such as the energies in RHIC beam energy scan program, it is of particular interest to measureopen charm hadron production in a relative smaller and colder system compared to top energy at 200GeV. This may provide a chance to tell us in what temperature charm behaves different from light flavors.However, in low energy region, the perturbation algorithm in theoretical calculations of charm productioncross section becomes invalid, which may result in large theoretical uncertainties. Meanwhile the charmproduction cross section drops rapidly when collision energy decreases, it is very challenging to measureopen charm production at low energies. The previous measurements at SPS energies are with largeuncertainties [188,189]. Since the HFT detector was taken out from STAR for the BES-II runs togetherwith low cross section, it is impossible to reconstruct open charm hadrons via hadronic decay channels, articles , xx , 5 18 of 33 the electron production from heavy flavor semi-leptonic decays becomes the unique way to measure heavyflavor productions at low energy.Figure 16 shows the v of electrons from heavy flavor decays as a function of p T in √ s NN =
54 and200 GeV Au+Au collisions [190] as solid circles and open stars, respectively. A semi-empirical exponentialfunction [191] is used to fit all the data points and the ratios of data over the fit function are shown in thebottom panel. The result in 54 GeV agrees with that in 200 GeV within uncertainties, which may suggestcharm quarks are still thermalized in 54 GeV Au+Au collisions. On the other hand, it is of interest torepeat the same measurement in lower energies, such as 27 GeV from STAR BESII experiment. H F e l e c t r on v STAR Au+Au 0-60%
200 GeV54.4 GeV PreliminaryEmpirical-Exp fit (GeV/c) T Transverse Momentum p D a t a / F i t Figure 16. (Color online) Upper panel: v of electrons from heavy flavor decays as a function of p T in √ s NN =
54 (blue solid circles) and 200 (open stars) GeV Au+Au collisions [190]. Red curve denotes anempirical reversed exponential fit [191] to all the data points. Bottom panel: The ratios of data over the fitfunction. Vertical bars and brackets denote statistical and systematic uncertainties, respectively.
STAR experiment extracted the total charm production cross section per binary nucleon collision atmidrapidity in √ s NN =
200 GeV Au+Au collisions by summing all yields of the open charm hadron statesand reported as d σ NN / dy | y = = 152 ±
13 (stat) ±
29 (sys) µ b [192], which is consistent with that in p + p collisions d σ / dy | y = = 130 ±
30 (stat) ±
26 (sys) µ b [175] within uncertainties. This result is consistentwith charm quark conservation in heavy-ion collisions at RHIC top energy.The total charm production cross section in full rapidity region can be calculated from above charmcross section at midrapidity multiplying an equivalent correction factor (4.7 ± p + p [175] and Au+Au [192] results are shown as blue solidsquare and red star, respectively. As for comparison, the total cross section of charmonium measuredfrom CERN-PS [195], WA39 [196], IHEP [197], E288 [198], E331 [199], E444 [200], E595 [201], E672 [202],E705 [203], E706 [202], E771 [204], E789 [205], NA3 [206], NA38 [207], NA50 [208], NA51 [209], UA6 [210],HERA-B [211], ISR [212], PHENIX [213] experiments (open diamonds) and NRQCD (long-dashed curve)are shown as well over a broad collision energy region [214]. articles , xx , 5 19 of 33 (GeV)sCollision Energy b ) m ( NN cc s -4 -2
10 1 STAR Au+Au Preliminary STAR p+p PHENIX Pamir/Muon SPS/FNAL ALICE UA2 y J/ FONLLc c NLO pQCDc c PYTHIAc c NRQCD y J/ FAIRNICA
Figure 17. (Color online) Charm and J/ ψ total production cross sections per nucleon-nucleon as afunction of collision energy. The open diamonds denote the charmonium cross section from worldwideexperiments [195–213]. The other open symbols are the experiment results of charm total cross sectiontaken from Ref. [188,189,194]. STAR p + p [175] and Au+Au [192] results are shown as blue solid squareand red star, respectively. Model calculations from FONLL [172], NLO pQCD [215], PYTHIA [193] andNRQCD [214] are represented as dot-dashed, dotted, dashed and long-dashed curves, respectively.
5. Future Upgrades and Physics Program at High Baryon Density Region
The RHIC BES program II and future FAIR and NICA experiments will focus on collision energybelow 20 GeV offering us a unique opportunity to explore the QCD phase structure at high baryondensity region. In Figure 18, interaction rates from both collider experiments and fixed-target experimentsare shown. The region for the high baryon density, largely covered by the fixed-target experiments, ishighlighted with yellow. In the following, we discuss few key measurements with the future experimentalfacilities. Again the discussions are arranged around the headlines of Collectivity, Criticality and HeavyFlavor Productions.
Collectivity : The flow results from top energy heavy-ion collisions at RHIC indicate that the partoniccollectivity has been built up from light u , d and s quarks to heavy c quark as well. This is one of themost important experimental evidences for the creation of the QGP in high-energy nuclear collisions [1–4].As a function of the collision energy, both radial and elliptic flow show an increasing trend, say above √ s NN ≈
15 GeV (Figure 4). Above that energy, the v slope of net-particles for both baryons and mesons,is observed to be almost the same, the v difference between particle and anti-particle also becomessimilar (Figure 5). While the dv / dy shows large divergence between net-kaon and net-proton (andnet- Λ ), the particle and anti-particle v difference splits between baryons and mesons dramatically below √ s NN =
15 GeV, see Figure 5. All of these observations imply that the medium properties created inheavy-ion collisions would be different above/below √ s NN =
15 GeV.In collectivity, two noticeable observations are the splitting between baryon’s and meson’s v and v in the low energy. Mesons such as kaons and φ − mesons are important, especially the φ − meson as it hasthe similar mass of proton. The precise results of φ − meson’s v and v will reveal the origin of collectivityat the high baryon density region. In addition, the ratio of N ( K − ) / N ( φ ) will shed light on the production articles , xx , 5 20 of 33 mechanism. It could be treated as a micro-laboratory for understanding the quarkonia productions innucleus-nucleus collisions. Criticality : One of the main goal of RHIC Beam Energy Scan program is to search for the QCD criticalpoint, which is the end point of the first order phase boundary in the QCD phase diagram. The experimentalconfirmation of the existence of the CP will be a landmark of exploring the QCD phase structure. Near theQCD critical point, the density fluctuations and correlation length will diverge. The conserved chargefluctuations and light nuclei productions have been proposed as sensitive observables to search for thesignature of QCD phase transition and the QCD critical point. Experimentally, the STAR experiment hasmeasured the higher order cumulants of net-particle distributions and light nuclei productions (deuteronand triton) in Au+Au collisions at √ s NN = 7.7 to 200 GeV. In Figures 10 and 11, it has been observedthat both fourth order fluctuations of net-proton ( κσ ) and light nuclei yield ratio N t × N p / N d shownon-monotonic energy dependence in central Au+Au collisions, with a minimum and peak around 20 GeV,respectively. Although the two measurements are of different order of fluctuations, the two observationsare consistent with the expectation of model calculations with CP physics and might suggest that thecreated system skims close by the CP receiving the contributions from critical fluctuations. To confirm theabove two observed non-monotonic energy dependence trends in BES-I, the second phase of Beam EnergyScan (BES-II) has been planned at RHIC (2019–2021). It will allow us to have 10–20 times more statistics atenergies √ s NN = 7.7–19.6 GeV. In addition, one observes large changes between 19.6 and 14.5 GeV in theenergy dependence of net-proton kurtosis (Figure 10) and light nuclei yield ratio N t × N p / N d (Figure 11)measured in the RHIC BES-I data. This could indicate that the QCD critical point is put by nature betweenthe thermodynamic condition ( T , µ B ) of 19.6 and 14.5 GeV. Thus, it is important to conduct a finer beamenergy scan between these two energies, i.e., 19.6 GeV ( µ B =
205 MeV) and 14.5 GeV ( µ B =
266 MeV).Therefore, we propose to take the data of a new energy point of Au+Au collisions at √ s NN = 16.7 GeV( µ B =
235 MeV), which is just between 19.6 and 14.5 GeV with equal µ B gap, on each side. Based onthe net-proton fluctuations measured from HADES and STAR experiments, and the model calculations,there might be a peak in the fourth order net-proton fluctuations in Au+Au collisions between √ s NN = 2 GeV and 8 GeV. In order to experimentally map out the QCD phase diagram at the higher baryondensity region, the future heavy-ion collision experiments like MPD/NICA, CBM/FAIR and CEE/CSRare certainly necessary and important. articles , xx , 5 21 of 33 Collision Energy √ s NN (GeV) Heavy Ion CollisionInteraction Rates (Hz)
STAR BES-II
NICA
HIAF
FAIR SIS100
HADES
STAR FXT ALICEsPHENIX F i x ed - T a r ge t C o lli de r B
750 500 375 200 100 25
Figure 18. (Color online) Interaction rates for high-energy nuclear collision facilities: the second phase RHICbeam energy scan (filled blue circles: BES-II, 7.7 < √ s NN < < √ s NN < On the other hand, it is predicted that the higher order conserved charge fluctuations, such as sixthorder ( C ) or eighth order ( C ) cumulants, should be more sensitive to the phase transition. If the chemicalfreeze-out temperature in heavy-ion collisions are close enough to the phase boundary, the sixth and eighthorder fluctuations could show negative values [98,107]. STAR experiment has measured the centralitydependence of sixth order ( C / C ) of net-proton distributions in Au+Au collisions at √ s NN = 54.4 and200 GeV. Negative values are observed for net-proton C / C from mid-central to central collisions at 200GeV, while positive values are observed at 54.4 GeV [216,217]. The negative sign of net-proton C / C observed at 200 GeV could be an experimental evidence of smooth crossover at small baryon chemicalpotential [98,107]. In future fixed target experiments, with much more statistics of low energy data, we canperform precise measurements of those higher order cumulants of conserved charges at the high baryondensity region. Heavy Flavor Production : FAIR-CBM and NICA-MPD experiments with advanced fast detectortechnology under high luminosity beam condition will provide unique chance to measure open andhidden charm hadrons with large statistics close to the production energy threshold [162,218]. It isexpected that this measurements will improve the precision of the total charm cross section at low energiesand will provide constraints on pQCD calculations, as well as the unknown interactions between charmedparticles and cold hadronic medium. Taking the prediction of the HSD model [219], the yield obtained inone week of running of CBM detectors with 10 MHz event rate would be about 300 J/ ψ for central Au+Aucollisions at 10A GeV, and about 600 J/ ψ for central Ni+Ni collisions at 15A GeV. In the latter case, alsoopen charm production can be studied at a rate of 300 kHz with a silicon vertex detector MVD in operationfor charmed hadron decay vertex reconstruction. As a result, the expected yield in central Ni+Ni collisionsat 15A GeV will be about 30 D mesons per week. This would be sufficient for cross section measurement articles , xx , 5 22 of 33 and an analysis of charmonium propagation and absorption in dense baryonic matter based on the ratio ofhidden to open charm at low energy.In order to extend the coverage to even larger baryon density region, STAR has developed afixed-target (FXT) program. As shown in Figure 18, a gold-target (1% interaction length) is placedat the right entrance of TPC. The end cap time-of-flight wall will be constructed at approximately the otherside of the TPC entrance. The time-of-flight detectors are on loan from the CBM experiment at FAIR [220,221].In addition, the inner-TPC upgrade [222] will extend the rapidity coverage, essential for the search for theQCD critical point measurement. STAR will be setup in such a way that data taking from both collidingand FXT modes will take place concurrently. With this configuration, STAR detector system will measureparticle productions and correlations in Au+Au collisions from √ s NN = 3–19.6 GeV, extending its coverageof baryon chemical potential from about µ B = 400 MeV to µ B ∼
750 MeV. The center of mass energy fromthe highest energy of the FXT mode is overlay with the lowest colliding mode at √ s NN = 7.7 GeV and thelower part of the FXT energies overlap with the future collision energies provided by CBM at FAIR [16].These allow systematic crosschecks on many of the observables in STAR experiment, for both collidingand FXT modes, and CBM experiment for the FXT mode. The BES program II and future FAIR and NICAexperiments will focus on the high baryon density region (<20 GeV), offer us a unique opportunity toexplore the QCD phase structure.In summary, the precise flow measurements of φ mesons and multi-strange hadrons with STARBES-II and future fixed-target experiments will reveal the degree of freedom originates from partonic orhadronic level at the high baryon density region. The confirmation of non-monotonic energy dependencein central Au+Au collisions for net-proton κσ and/or light nuclei yield ratio N t × N p / N d with STARBES-II and future fixed-target experiments will provide crucial experimental evidences for establishing thecase for the discovery of the QCD critical point. The energy dependence of heavy flavor measurements willprovide crucial information on thermalization of the system and provide unique opportunity to study theunknown interactions between heavy quark and the cold nuclear matter. A great deal of new informationon the QCD phase diagram will be extracted with current and planned heavy-ion collision programs. Author Contributions:
X.L., S.S., N.X. and Y.Z. contribute equally to this paper. All authors have read and agreed tothe published version of the manuscript.
Funding:
This work is supported by the National Key Research and Development Program of China (2018YFE0205200),the National Natural Science Foundation of China (No.11890711, 11890712, 11828501 and 11861131009).
Acknowledgments:
We thank Xin Dong, ShinIchi Esumi, Lokesh Kumar, Volker Koch, Bedangadas Mohantyfor discussions.
Conflicts of Interest:
The authors declare no conflicts of interest.
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