We argue that the chemical freeze-out in heavy ion collisions at high baryon density is not associated to a phase transition or rapid crossover. We employ the linear nucleon-meson model with parameters fixed by the zero-temperature properties of nuclear matter close to the liquid-gas quantum phase transition. For the parameter region of interest this yields a reliable picture of the thermodynamic and chiral properties at non-zero temperature. The chemical freeze-out observed in low-energy experiments occurs when baryon densities fall below a critical value of about 15 percent of nuclear density. This region in the phase diagram is far away from any phase transition or rapid crossover.
The hadronic freeze-out line is calculated in terms of the net baryon density and the energy density instead of the usual T and mu_B. This analysis makes it apparent that the freeze-out density exhibits a maximum as the collision energy is decreased. This maximum freeze-out density is well within the parameters of the proposed NICA accelerator.
Systematics of the chemical freeze-out line in the high baryon density regime explored at SIS100
GSI Helmholtzzentrum für Schwerionenforschung GmbH（GSI亥姆霍兹重离子研究中心）；Liebfrauenschule Bensheim（本斯海姆圣母学校）；Department of Physics, Duke University（杜克大学物理系）；Department of Physics, University of Houston（休斯顿大学物理系）；Frankfurt Institute for Advanced Studies（法兰克福高等研究所）；Institut für Theoretische Physik, Goethe-Universität Frankfurt（歌德大学法兰克福理论物理研究所）；Helmholtz Research Academy Hesse for FAIR (HFHF)（黑森亥姆霍兹FAIR研究学院）
We determine chemical freeze-out conditions from strangeness observables measured at RHIC beam energies. Based on a combined analysis of lowest-order net-Kaon fluctuations and strange anti-baryon over baryon yield ratios we obtain visibly enhanced freeze-out conditions at high beam energies compared to previous studies which analyzed net-proton and net-charge fluctuations. Our findings are in qualitative agreement with the recent study [1] which utilizes the net-Kaon fluctuation data in combination with information from lattice QCD. Our complimentary approach shows that also strange hadron yie…
We investigate the baryon number susceptibilities up to fourth order along different freeze-out lines in a holographic QCD model with the 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 ratio of the baryon number susceptibilities (up to fourth order) forms a ridge along the phase boundary, and develops a sword shape mountain standing upright around the CEP in a narrow and oblate region. This fe…
Fluctuation measurements of hadron yields at heavy-ion collisions can reproduce the phase transition parameters of QCD matter. The fluctuation results produce accurate parameters near zero baryonic chemical potential($μ_B$) being very sensitive in that region. In this work, using the Hadron Resonance Gas Model(HRG), we determine the freeze-out temperatures of the hadrons using individual fluctuation results and find that sequential freeze-out of hadrons during the QCD phase transition near zero $μ_B$ is dependent on the mass of produced hadronic species. Using recently published results of net…
We discuss systematic uncertainties in the chemical freeze-out parameters from the $χ^2$ analysis of hadron multiplicity ratios in the heavy-ion collision experiments. The systematics due to the choice of specific hadron ratios are found to lie within the experimental uncertainties. The variations obtained by removing the usual constraints on the conserved charges show similar behavior. The net charge to net baryon ratios in such unconstrained systems are commensurate with the expected value obtained from the protons and neutrons of the colliding nuclei up to the center of mass energies $\sim …
Following the idea of nucleon clustering and light-nuclei production in relativistic heavy-ion collisions close to the QCD critical-end point, we address the quantum effects affecting the interaction of several nucleons at finite temperature. For this aim we use the $K$-harmonics method to four-nucleon states ($α$ particle), and also develop a novel semiclassical "flucton" method at finite temperature, based on certain classical paths in Euclidean time, and apply it to two- and four-particle configurations. To study possible effects on the light-nuclei production close to the QCD critical poin…
By analyzing the calculated baryon number susceptibility ratios ${χ_{1}^{B}}/{χ_{2}^{B}}$ and ${χ_{3}^{B}}/{χ_{1}^{B}}$ in two-flavor system via the Dyson-Schwinger equation approach of QCD, we determine the chemical freeze-out temperature and baryon chemical potential in cases of both thermodynamic limit and finite size. We calculate the center-of-mass energy dependence of the ${χ_{4}^{B}}/{χ_{2}^{B}}\, (κσ^{2})$ at the freeze-out line and find an excellent agreement with experimental data in $\sqrt{S_{NN}^{}} \geq 19.6\,$GeV region when taking into account the finite size effect. Our calcula…
Extracting freeze-out conditions in beam energy scan via functional QCD
Peking University（北京大学）；Justus-Liebig-Universität Gießen（吉森大学）；GSI Helmholtzzentrum für Schwerionenforschung（德国重离子研究中心）；Beijing Institute of Technology（北京理工大学）；Center for High Energy Physics, Peking University（北京大学高能物理中心）；Collaborative Innovation Center of Quantum Matter（量子物质协同创新中心）；Universität Heidelberg（海德堡大学）；ExtreMe Matter Institute EMMI, GSI（GSI极端物质研究所）
We calculate the mean and variance of net-baryon number and net-electric charge distributions from Quantum Chromodynamics (QCD) using a next-to-leading order Taylor expansion in terms of temperature and chemical potentials. We compare these expansions with experimental data from STAR and PHENIX, determine the freeze-out temperature in the limit of vanishing baryon chemical potential, and, for the first time, constrain the curvature of the freeze-out line through a direct comparison between experimental data on net-charge fluctuations and a QCD calculation. We obtain a bound on the curvature co…
We discuss medium effects on light cluster production in the QCD phase diagram within a generalized Beth-Uhlenbeck (GBU) approach by relating Mott transition lines to those for chemical freeze-out. We find that in heavy-ion collisions at highest energies provided by the LHC light cluster abundances should follow the statistical model because of low baryon densities. At low energies in the nuclear fragmentation region, where the freeze-out interferes with the liquid-gas phase transition, selfenergy and Pauli blocking effects are important. At intermediate energies the HADES, FAIR and NICA exper…
The baryon and energy densities attained in fragmentation regions in central Au+Au collisions in the energy range of the Beam Energy Scan (BES) program at the Relativistic Heavy-Ion Collider (RHIC) are estimated within the model of the three-fluid dynamics. It is shown that a considerable part of the baryon charge is stopped in the central fireball. Even at 39 GeV, approximately 70% of the total baryon charge turns out to be stopped. The fraction of this stopped baryon charge decreases with collision energy rise, from 100% at 7.7 GeV to $\sim$40% at 62 GeV. The highest initial baryon densities…
The chemical freeze-out parameters in central nucleus-nucleus collisions are extracted consistently from hadron yield data within the quantum van der Waals (QvdW) hadron resonance gas model. The beam energy dependences for skewness and kurtosis of net baryon, net electric, and net strangeness charges are predicted. The QvdW interactions in asymmetric matter, $Q/B \neq 0.5$, between (anti)baryons yield a non-congruent liquid-gas phase transition, together with a nuclear critical point (CP) with critical temperature of $T_c=19.5$ MeV. The nuclear CP yields the collision energy dependence of the …
Transverse densities describe the distribution of charge and current at fixed light-front time and provide a frame-independent spatial representation of hadrons as relativistic systems. We calculate the transverse densities of the octet baryons at peripheral distances b = O(M_pi^{-1}) in an approach combining chiral effective field theory (ChEFT) and dispersion analysis. The densities are represented as dispersive integrals of the imaginary parts of the baryon electromagnetic form factors in the timelike region (spectral functions). The spectral functions on the two-pion cut at t > 4 M_pi^2 ar…
We use the excluded volume Hadron Resonance Gas (HRG) model with the most up-to-date hadron list to calculate $ηT/w$ at low temperatures and at finite baryon densities $ρ_B$. This $ηT/w$ is then matched to a QCD-based shear viscosity calculation of the QGP for different profiles of $ηT/w$ across {T,$μ_{B}$} including cross-over and critical point transitions. When compared to ideal hydrodynamic trajectories across {T,$μ_{B}$}, we find that the $ηT/w(T,μ_B)$ profiles would require initial conditions at much larger baryon density to reach the same freeze-out point.
The centrality dependence of the $p/π$ ratio measured by the ALICE Collaboration in 5.02 TeV Pb-Pb collisions indicates a statistically significant suppression with the increase of the charged particle multiplicity once the centrality-correlated part of the systematic uncertainty is eliminated from the data. We argue that this behavior can be attributed to baryon annihilation in the hadronic phase. By implementing the $B\bar{B} \leftrightarrow 5π$ reaction within a generalized partial chemical equilibrium framework, we estimate the annihilation freeze-out temperature at different centralities,…
With parameters fixed by critical temperature and equation of state at zero baryon chemical potential, a realistic Polyakov--Nambu--Jona-Lasinio (rPNJL) model predicts a critical end point of chiral phase transition at $(μ_B^E= 720 {\rm MeV}, T^E=93 {\rm MeV})$. The extracted freeze-out line from heavy ion collisions is close to the chiral phase transition boundary in the rPNJL model, and the kurtosis $κσ^2$ of baryon number fluctuations from the rPNJL model along the experimental freeze-out line agrees well with the BES-I measurement. Our analysis shows that the dip structure of measured $κσ^…
Comparison of Chemical Freeze-Out Criteria in Heavy-Ion Collisions
在过去的二十年里，从重离子碰撞中出现的最显著的结果之一是在所有能量下粒子产额所显示的惊人的规律性。这导致了几个非常成功的建议，描述粒子产额在一个非常广泛的光束能量范围内，达到从1 A GeV到200 A GeV，只使用一个或两个参数。本文对这些建议进行了系统的比较。研究了粒子能量、重子+反重子密度、归一化熵密度以及逾渗模型的条件。最新的化学冻结出的参数中得到的粒子产量的热统计分析的结果进行了比较。分析和讨论了结果对参数的敏感性和依赖性。它示出，在能量范围内的顶部AGS能量以上，在目前的精度，所有的化学冻结出的标准给出了一个相当好的描述的粒子产率。然而，低能量重离子数据倾向于将恒定能量作为化学粒子冻结的统一条件。这种情况也显示出对模型假设和参数的敏感性最弱。
We compare lattice QCD results for appropriate combinations of net strangeness fluctuations and their correlations with net baryon number fluctuations with predictions from two hadron resonance gas (HRG) models having different strange hadron content. The conventionally used HRG model based on experimentally established strange hadrons fails to describe the lattice QCD results in the hadronic phase close to the QCD crossover. Supplementing the conventional HRG with additional, experimentally uncharted strange hadrons predicted by quark model calculations and observed in lattice QCD spectrum ca…
We study the transverse momentum spectra of identified pions, Kaons, protons and Lambdas produced at midrapidity (0 < y < 0.5)in most central p-Pb collisions at root(sNN) = 5.02 TeV in comparison with a Unified Statistical Thermal Freeze-out Model (USTFM). The measurements of pions are reported upto pT = 3 GeV, the kaons (K- + K+) are reported upto pT = 2.5 GeV, K0s is reported upto pT = 7 GeV and the baryons (protons and Lambdas) are reported upto pT = 3.5 GeV. A good agreement is seen between the calculated results and the experimental data points taken from the ALICE experiment. The transve…
The transverse momentum spectra of identified particles at midrapidity in Pb + Pb collisions at Root(sNN) = 2.76 TeV have been studied as a function of collision centrality by using a unified statistical thermal freeze-out model. The calculated results are found to be in good agreement with the experimental data measured by the ALICE experiment at LHC. The model calculations provide the thermal freeze-out conditions in terms of the temperature and collective flow parameters for different particle species. We observe a rise in the thermal freeze-out temperature but a mild decrease in the collec…
We describe two independent frameworks which provide unambiguous determinations of the deconfinement and the decoupling conditions of a relativistic gas at finite temperature. First, we use the Polyakov-Nambu-Jona-Lasinio model to compute meson and baryon masses at finite temperature and determine their melting temperature as a function of their strangeness content. Second, we analyze a simple expanding gas within a Friedmann-Robertson-Walker metric, which admits a well-defined decoupling mechanism. We examine the decoupling time as a function of the particle mass and cross section. We find ev…
We evaluate the third- and fourth-order baryon, charge and strangeness susceptibilities near a chiral critical point using the Nambu-Jona-Lasinio model. We identify robust qualitative behaviours of the susceptibilities along hypothetical freeze-out lines that agree with previous model studies. Quantitatively, baryon number fluctuations are the largest in magnitude and thus offer the strongest signal when freeze-out occurs farther away from a critical point. Charge and strangeness susceptibilities also diverge at a critical point, but the area where the divergence dominates is smaller, meaning …
We report on the application of a cascade + viscous hydro + cascade model for heavy ion collisions in the RHIC Beam Energy Scan range, $\sqrt{s_{\rm NN}}=6.3\dots200$ GeV. By constraining model parameters to reproduce the data we find that the effective(average) value of the shear viscosity over entropy density ratio $η/s$ decreases from 0.2 to 0.08 when collision energy grows from $\sqrt{s_{\rm NN}}\approx7$ to 39 GeV.
Kinetic equilibration of the matter and baryon densities attained in central region of colliding Au+Au nuclei in the energy range of $\sqrt{s_{NN}}=$ 3.3--39 GeV are examined within the model of the three-fluid dynamics. It is found that the kinetic equilibration is faster at higher collision energies: the equilibration time (in the c.m. frame of colliding nuclei) rises from $\sim$5 fm/c at $\sqrt{s_{NN}}=$ 3.3 GeV to $\sim$1 fm/c at 39 GeV. The chemical equilibration, and thus thermalization, takes longer. We argue that the presented time evolution of the net-baryon and energy densities in th…
$S$-matrix calculation of $BQ$ correlation at finite baryon density
Fakulta jaderná a fyzikálně inženýrská, České vysoké učení technické v Praze（捷克布拉格捷克理工大学核与物理工程学院）；Institute of Theoretical Physics, University of Wrocław（弗罗茨瓦夫大学理论物理研究所）；Fakulta prírodných vied, Univerzita Mateja Bela（马特乌·贝拉大学自然科学学院）
Collective Flow, Kinetic Freeze-Out, and a Data-Driven Baryon Chemical Potential in Au+Au Collisions at $\sqrt{s_{NN}} = 7.7$--$39$ GeV
Department of Physics, Aligarh Muslim University（阿利加尔穆斯林大学物理系）；School of Physical Sciences, National Institute of Science Education and Research（国家科学教育与研究学院物理科学学院）；Homi Bhabha National Institute（霍米·巴巴国立研究所）
