Higher moments of net proton multiplicity distributions at RHIC

Beam Energy Dependence of Fifth- and Sixth-Order Net-Proton Number Fluctuations in Au+Au Collisions at RHIC

We report the beam energy and collision centrality dependence of fifth and sixth order cumulants (C_{5}, C_{6}) and factorial cumulants (κ_{5}, κ_{6}) of net-proton and proton number distributions, from center-of-mass energy (sqrt[s_{NN}]) 3 GeV to 200 GeV Au+Au collisions at RHIC. Cumulant ratios of net-proton (taken as proxy for net-baryon) distributions generally follow the hierarchy expected from QCD thermodynamics, except for the case of collisions at 3 GeV. The measured values of C_{6}/C_{2} for 0%-40% centrality collisions show progressively negative trend with decreasing energy, while it is positive for the lowest energy studied. These observed negative signs are consistent with QCD calculations (for baryon chemical potential, μ_{B}≤110  MeV) which contains the crossover transition range. In addition, for energies above 7.7 GeV, the measured proton κ_{n}, within uncertainties, does not support the two-component (Poisson+binomial) shape of proton number distributions that would be expected from a first-order phase transition. Taken in combination, the hyperorder proton number fluctuations suggest that the structure of QCD matter at high baryon density, μ_{B}∼750  MeV at sqrt[s_{NN}]=3  GeV is starkly different from those at vanishing μ_{B}∼24  MeV at sqrt[s_{NN}]=200  GeV and higher collision energies.

Measurements of Proton High-Order Cumulants in sqrt[s_{NN}]=3 GeV Au+Au Collisions and Implications for the QCD Critical Point

We report cumulants of the proton multiplicity distribution from dedicated fixed-target Au+Au collisions at sqrt[s_{NN}]=3.0  GeV, measured by the STAR experiment in the kinematic acceptance of rapidity (y) and transverse momentum (p_{T}) within -0.5<y<0 and 0.4<p_{T}<2.0  GeV/c. In the most central 0%-5% collisions, a proton cumulant ratio is measured to be C_{4}/C_{2}=-0.85±0.09 (stat)±0.82 (syst), which is 2σ below the Poisson baseline with respect to both the statistical and systematic uncertainties. The hadronic transport UrQMD model reproduces our C_{4}/C_{2} in the measured acceptance. Compared to higher energy results and the transport model calculations, the suppression in C_{4}/C_{2} is consistent with fluctuations driven by baryon number conservation and indicates an energy regime dominated by hadronic interactions. These data imply that the QCD critical region, if created in heavy-ion collisions, could only exist at energies higher than 3 GeV.

Measurement of the Sixth-Order Cumulant of Net-Proton Multiplicity Distributions in Au+Au Collisions at sqrt[s_{NN}]=27, 54.4, and 200 GeV at RHIC

According to first-principle lattice QCD calculations, the transition from quark-gluon plasma to hadronic matter is a smooth crossover in the region μ_{B}≤T_{c}. In this range the ratio, C_{6}/C_{2}, of net-baryon distributions are predicted to be negative. In this Letter, we report the first measurement of the midrapidity net-proton C_{6}/C_{2} from 27, 54.4, and 200 GeV Au+Au collisions at the Relativistic Heavy Ion Collider (RHIC). The dependence on collision centrality and kinematic acceptance in (p_{T}, y) are analyzed. While for 27 and 54.4 GeV collisions the C_{6}/C_{2} values are close to zero within uncertainties, it is observed that for 200 GeV collisions, the C_{6}/C_{2} ratio becomes progressively negative from peripheral to central collisions. Transport model calculations without critical dynamics predict mostly positive values except for the most central collisions within uncertainties. These observations seem to favor a smooth crossover in the high-energy nuclear collisions at top RHIC energy.

Isospin Effect on Baryon and Charge Fluctuations from the pNJL Model

We have studied the possible isospin corrections on the skewness and kurtosis of net-baryon and net-charge fluctuations in the isospin asymmetric matter formed in relativistic heavy-ion collisions at RHIC-BES energies, based on a 3-flavor Polyakov-looped Nambu–Jona–Lasinio model. With typical scalar–isovector and vector–isovector couplings leading to the splitting of u and d quark chiral phase transition boundaries and critical points, we have observed considerable isospin effects on the susceptibilities, especially those of net-charge fluctuations. Reliable experimental measurements at even lower collision energies are encouraged to confirm the observed isospin effects.

A Brief Review of Chiral Chemical Potential and Its Physical Effects

Nontrivial topological gluon configuration is one of the remarkable features of the Quantum Chromodynamics (QCD). Due to chiral anomaly, the chiral imbalance between right- and left-hand quarks can be induced by the transition of the nontrivial gluon configurations between different vacuums. In this review, we will introduce the origin of the chiral chemical potential and its physical effects. These include: (1) the chiral imbalance in the presence of strong magnetic and related physical phenomena; (2) the influence of chiral chemical potential on the QCD phase structure; and (3) the effects of chiral chemical potential on quark stars. Moreover, we propose for the first time that quark stars are likely to be a natural laboratory for testing the destruction of strong interaction CP.

Theoretical Studies of Heavy Ion Collisions via Holography

Applications of holographic bottom-up QCD models to the studies of Heavy Ion Collisions (HIC) are discussed.

QCD critical end point from a realistic PNJL model

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 (μEB = 720MeV; TE = 93MeV). The extracted freeze-out line from heavy ion collisions is close to the chiral phase transition boundary in the rPNJL model, and the kurtosis kσ2 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 kσ2 is determined by the relationship between the freeze-out line and chiral phase transition line at low baryon density region, and the peak structure can be regarded as a clean signature for the existence of CEP.

Enhancements of high order cumulants across the 1st order phase transition boundary

In this proceeding, we investigate the dynamical evolution of the σ field with a trajectory across the 1st order phase transition boundary, using the Langevin equation from the linear sigma model. We find the high order cumulants of the σ field are largely enhanced during the dynamical evolution, compared with the equilibrium values, due to the supercooling effect of the first order phase transition.

Equation of State and Freezeout in QCD with Staggered Quarks

We report the equation of state at finite chemical potential, namely the baryon number density and the baryonic contribution to the pressure, using a resummation of the Taylor expansion. We also report the freezeout conditions for a measure of fluctuations. We examine the major sources of systematic and statistical errors in all of these measurements.

van der Waals Interactions in Hadron Resonance Gas: From Nuclear Matter to Lattice QCD

An extension of the ideal hadron resonance gas (HRG) model is constructed which includes the attractive and repulsive van der Waals (VDW) interactions between baryons. This VDW-HRG model yields the nuclear liquid-gas transition at low temperatures and high baryon densities. The VDW parameters a and b are fixed by the ground state properties of nuclear matter, and the temperature dependence of various thermodynamic observables at zero chemical potential are calculated within the VDW-HRG model. Compared to the ideal HRG model, the inclusion of VDW interactions between baryons leads to a qualitatively different behavior of second and higher moments of fluctuations of conserved charges, in particular in the so-called crossover region T∼140-190  MeV. For many observables this behavior resembles closely the results obtained from lattice QCD simulations. This hadronic model also predicts nontrivial behavior of net-baryon fluctuations in the region of phase diagram probed by heavy-ion collision experiments. These results imply that VDW interactions play a crucial role in the thermodynamics of hadron gas. Thus, the commonly performed comparisons of the ideal HRG model with the lattice and heavy-ion data may lead to misconceptions and misleading conclusions.

Beam energy dependence of moments of the net-charge multiplicity distributions in Au+Au collisions at RHIC

We report the first measurements of the moments--mean (M), variance (σ(2)), skewness (S), and kurtosis (κ)--of the net-charge multiplicity distributions at midrapidity in Au+Au collisions at seven energies, ranging from sqrt[sNN]=7.7 to 200 GeV, as a part of the Beam Energy Scan program at RHIC. The moments are related to the thermodynamic susceptibilities of net charge, and are sensitive to the location of the QCD critical point. We compare the products of the moments, σ(2)/M, Sσ, and κσ(2), with the expectations from Poisson and negative binomial distributions (NBDs). The Sσ values deviate from the Poisson baseline and are close to the NBD baseline, while the κσ(2) values tend to lie between the two. Within the present uncertainties, our data do not show nonmonotonic behavior as a function of collision energy. These measurements provide a valuable tool to extract the freeze-out parameters in heavy-ion collisions by comparing with theoretical models.

Energy dependence of moments of net-proton multiplicity distributions at RHIC

We report the beam energy (sqrt[sNN]=7.7-200  GeV) and collision centrality dependence of the mean (M), standard deviation (σ), skewness (S), and kurtosis (κ) of the net-proton multiplicity distributions in Au+Au collisions. The measurements are carried out by the STAR experiment at midrapidity (|y|<0.5) and within the transverse momentum range 0.4<pT<0.8  GeV/c in the first phase of the Beam Energy Scan program at the Relativistic Heavy Ion Collider. These measurements are important for understanding the quantum chromodynamic phase diagram. The products of the moments, Sσ and κσ2, are sensitive to the correlation length of the hot and dense medium created in the collisions and are related to the ratios of baryon number susceptibilities of corresponding orders. The products of moments are found to have values significantly below the Skellam expectation and close to expectations based on independent proton and antiproton production. The measurements are compared to a transport model calculation to understand the effect of acceptance and baryon number conservation and also to a hadron resonance gas model.

Freeze-out parameters: lattice meets experiment

We present our results for ratios of higher order fluctuations of electric charge as functions of the temperature. These results are obtained in a system of 2+1 quark flavors at physical quark masses and continuum extrapolated. We compare them to preliminary data on higher order moments of the net electric charge distribution from the STAR collaboration. This allows us to determine the freeze-out temperature and chemical potential from first principles. We also show continuum-extrapolated results for ratios of higher order fluctuations of baryon number. These will allow us to test the consistency of the approach, by comparing them to the corresponding experimental data (once they become available) and thus, extracting the freeze-out parameters in an independent way.

Freeze-out conditions in heavy ion collisions from QCD thermodynamics

We present a determination of freeze-out conditions in heavy ion collisions based on ratios of cumulants of net electric charge fluctuations. These ratios can reliably be calculated in lattice QCD for a wide range of chemical potential values by using a next-to-leading order Taylor series expansion around the limit of vanishing baryon, electric charge and strangeness chemical potentials. From a computation of up to fourth order cumulants and charge correlations we first determine the strangeness and electric charge chemical potentials that characterize freeze-out conditions in a heavy ion collision and confirm that in the temperature range 150 MeV ≤ T ≤ 170 MeV the hadron resonance gas model provides good approximations for these parameters that agree with QCD calculations on the 5%-15% level. We then show that a comparison of lattice QCD results for ratios of up to third order cumulants of electric charge fluctuations with experimental results allows us to extract the freeze-out baryon chemical potential and the freeze-out temperature.

Scale for the phase diagram of quantum chromodynamics

Matter described by quantum chromodynamics (QCD), the theory of strong interactions, may undergo phase transitions when its temperature and the chemical potentials are varied. QCD at finite temperature is studied in the laboratory by colliding heavy ions at varying beam energies. We present a test of QCD in the nonperturbative domain through a comparison of thermodynamic fluctuations predicted in lattice computations with the experimental data of baryon number distributions in high-energy heavy ion collisions. This study provides evidence for thermalization in these collisions and allows us to find the crossover temperature between normal nuclear matter and a deconfined phase called the quark gluon plasma. This value allows us to set a scale for the phase diagram of QCD.

The Limits of Ordinary Matter

The temperature at which quarks escape the confines of protons and neutrons has been determined from high-energy particle collision data.