Quantum Chromodynamics Phase Diagram Research Articles

Critical end point in the presence of a chiral chemical potential

A class of Polyakov-loop-modified Nambu--Jona-Lasinio (PNJL) models have been used to support a conjecture that numerical simulations of lattice-regularized quantum chromodynamics (QCD) defined with a chiral chemical potential can provide information about the existence and location of a critical endpoint in the QCD phase diagram drawn in the plane spanned by baryon chemical potential and temperature. That conjecture is challenged by conflicts between the model results and analyses of the same problem using simulations of lattice-regularized QCD (lQCD) and well-constrained Dyson-Schwinger equation (DSE) studies. We find the conflict is resolved in favor of the lQCD and DSE predictions when both a physically-motivated regularization is employed to suppress the contribution of high-momentum quark modes in the definition of the effective potential connected with the PNJL models and the four-fermion coupling in those models does not react strongly to changes in the mean-field that is assumed to mock-up Polyakov loop dynamics. With the lQCD and DSE predictions thus confirmed, it seems unlikely that simulations of lQCD with $\mu_5>0$ can shed any light on a critical endpoint in the regular QCD phase diagram.

Overview of recent results from the STAR experiment

The Solenoidal Tracker at RHIC (STAR) experiment utilizes its excellent mid-rapidity tracking and particle identification capabilities to study the emergent properties of Quantum Chromodynamics (QCD). The STAR heavy-ion program at vanishingly small baryon density is aimed to address questions about the quantitative properties of the strongly-interacting Quark Gluon Plasma (QGP) matter created in high energy collisions (η/s, qˆ, chirality, transport parameters, heavy quark diffusion coefficients…). At finite baryon density, the questions concern the phases of nuclear matter (the QCD phase diagram) and the nature of the phase transition, namely: what is the onset collision energy for the formation of QGP? What is the nature of phase transition in heavy-ion collisions? Are there two phase transition regions? If yes, where is the critical point situated? At Quark Matter 2015, the STAR collaboration has presented a wealth of new experimental results which address these questions. In these proceedings I highlight a few of those results.

Nf=2QCD chiral phase transition with Wilson fermions at zero and imaginary chemical potential

The order of the thermal phase transition in the chiral limit of Quantum Chromodynamics (QCD) with two dynamical flavors of quarks is a long-standing issue and still not known in the continuum limit. Whether the transition is first or second order has important implications for the QCD phase diagram and the existence of a critical endpoint at finite densities. We follow a recently proposed approach to explicitly determine the region of first order chiral transitions at imaginary chemical potential, where it is large enough to be simulated, and extrapolate it to zero chemical potential with known critical exponents. Using unimproved Wilson fermions on coarse $N_t=4$ lattices, the first order region turns out to be so large that no extrapolation is necessary. The critical pion mass $m_\pi^c\approx 560$ MeV is by nearly a factor 10 larger than the corresponding one using staggered fermions. Our results are in line with investigations of three-flavour QCD using improved Wilson fermions and indicate that the systematic error on the two-flavour chiral transition is still of order 100\%.

The QCD critical point: an exciting Odyssey in the Femto-world

Strongly interacting matter, which makes up the nuclei of atoms, is described by a theory called quantum chromodynamics (QCD). A critical point in the phase diagram of QCD, if established either theoretically or experimentally, would be as profound a discovery as the familiar gas–liquid critical point discovered in the nineteenth century. Due to the extremely short-lived nature of the concerned phases, novel experimental techniques are needed to search for it. The Relativistic Heavy Ion Collider (RHIC) in USA has an experimental programme which can fit the bill to do so. Theoretical techniques of Lattice QCD, which is QCD defined on a discrete space-time lattice, have provided glimpses into where the QCD critical point may be, and how to search for it in the experimental data. A brief overview of the theoretical and experimental attempts is provided.

Measurement of higher cumulants of net-charge multiplicity distributions inAu+Aucollisions atsNN=7.7–200GeV

We report the measurement of cumulants ($C_n, n=1\ldots4$) of the net-charge distributions measured within pseudorapidity ($|\eta|<0.35$) in Au$+$Au collisions at $\sqrt{s_{_{NN}}}=7.7-200$ GeV with the PHENIX experiment at the Relativistic Heavy Ion Collider. The ratios of cumulants (e.g. $C_1/C_2$, $C_3/C_1$) of the net-charge distributions, which can be related to volume independent susceptibility ratios, are studied as a function of centrality and energy. These quantities are important to understand the quantum-chromodynamics phase diagram and possible existence of a critical end point. The measured values are very well described by expectation from negative binomial distributions. We do not observe any nonmonotonic behavior in the ratios of the cumulants as a function of collision energy. The measured values of $C_1/C_2 = \mu/\sigma^2$ and $C_3/C_1 = S\sigma^3/\mu$ can be directly compared to lattice quantum-chromodynamics calculations and thus allow extraction of both the chemical freeze-out temperature and the baryon chemical potential at each center-of-mass energy.

The First Moment of Azimuthal Anisotropy in Nuclear Collisions from AGS to LHC Energies

We review topics related to the first moment of azimuthal anisotropy (v1), commonly known as directed flow, focusing on both charged particles and identified particles from heavy-ion collisions. Beam energies from the highest available, at the CERN LHC, down to projectile kinetic energies per nucleon of a few GeV per nucleon, as studied in experiments at the Brookhaven AGS, fall within our scope. We focus on experimental measurements and on theoretical work where direct comparisons with experiment have been emphasized. The physics addressed or potentially addressed by this review topic includes the study of Quark Gluon Plasma and, more generally, investigation of the Quantum Chromodynamics phase diagram and the equation of state describing the accessible phases.

Energy dependence ofKπ,pπ, andKpfluctuations in Au + Au collisions fromsNN=7.7to 200 GeV

A search for the quantum chromodynamics (QCD) critical point was performed by the STAR experiment at the Relativistic Heavy Ion Collider, using dynamical fluctuations of unlike particle pairs. Heavy-ion collisions were studied over a large range of collision energies with homogeneous acceptance and excellent particle identification, covering a significant range in the QCD phase diagram where a critical point may be located. Dynamical $K\pi$, $p\pi$, and $Kp$ fluctuations as measured by the STAR experiment in central 0-5\% Au+Au collisions from center-of-mass collision energies $\rm \sqrt{s_{NN}}$ = 7.7 to 200 GeV are presented. The observable $\rm \nu_{dyn}$ was used to quantify the magnitude of the dynamical fluctuations in event-by-event measurements of the $K\pi$, $p\pi$, and $Kp$ pairs. The energy dependences of these fluctuations from central 0-5\% Au+Au collisions all demonstrate a smooth evolution with collision energy.

Experimental studies of the quantum chromodynamics phase diagram at the STAR experiment

We review the STAR experiment’s results to date from the Beam Energy Scan (BES) at Brookhaven’s Relativistic Heavy Ion Collider, and outline future plans and prospects in this area. BES Phase-I is based on Au + Au data taken in 2010 and 2011 at \(\sqrt {s_{NN}}= 7.7\), 11.5, 19.6, 27 and 39 GeV, and when interpreted in conjunction with the large datasets available at 62.4 and 200 GeV, permits an initial exploration of the phase diagram of quantum chromodynamics (QCD) matter. The three goals of BES Phase-I are as follows: (1) a search for turn-off of the promising signatures of quark gluon plasma (QGP) already reported at the top RHIC energies; (2) a search for evidence of a possible first-order phase transition such as a signature of softening of the QCD equation of state (EoS); (3) a search for a critical end point as expected in a scenario where there is a cross-over transition from hadronic matter to QGP at the highest RHIC energies, but a first-order phase transition at lower energies with finite net-baryon density. We summarize several analyses of BES data from 2010 and 2011 that are either published or submitted, as well as several more that have been reported at meetings in preliminary forms. The physics interpretation of BES Phase-I measurements is frequently limited by the increasing statistical error bars as the beam energy decreases, and the planned BES Phase-II will have much improved capabilities in this regard.

QCD critical point: The race is on

A critical point in the phase diagram of quantum chromodynamics (QCD), if established either theoretically or experimentally, would be as profound a discovery as the good-old gas–liquid critical point. Unlike the latter, however, first-principles-based approaches are being employed to locate it theoretically. Due to the short-lived nature of the concerned phases, novel experimental techniques are needed to search for it. The Relativistic Heavy Ion Collider (RHIC) in USA has an experimental programme to do so. This short review is an attempt to provide a glimpse of the race between the theorists and the experimentalists as well as the synergy between them.

Spinodal density enhancements in nuclear collisions at the CBM experiment

We discuss a novel approach to describe the evolution of a fireball, created in a high-energy nuclear collision, experiencing spinodal instabilities due to the first-order deconfinement phase transition of quantum chromo dynamics (QCD). We show that initial density fluctuations in these collisions are enhanced in the mechanically unstable region of the QCD phase diagram. In our study we find that the most favorable energy range for observing these density enhancements is at the lower end of the SIS100 accelerator at FAIR, currently under construction. Furthermore we discuss how one can distinguish and constrain different types of QCD phase transitions, one of hadron-quark type and one of liquid-gas type, leading to strong differences in the dynamical evolution of the QCD medium.

Fluctuations of Conserved Quantities in High Energy Nuclear Collisions at RHIC

Fluctuations of conserved quantities in heavy-ion collisions are used to probe the phase transition and the QCD critical point for the strongly interacting hot and dense nuclear matter. The STAR experiment has carried out moment analysis of net-proton (proxy for net- baryon (B)), net-kaon (proxy for net-strangeness (S)), and net-charge (Q). These measurements are important for understanding the quantum chromodynamics phase diagram. We present the analysis techniques used in the moment analysis by the STAR experiment and discuss the moments of net-proton and net-charge distributions from the first phase of the Beam Energy Scan program at the Relativistic Heavy Ion Collider.

Net-proton measurements at RHIC and the quantum chromodynamics phase diagram

Two measurements related to the proton and antiproton production near midrapidity in \(\sqrt {s_{{NN}}} = 7.7\), 11.5, 19.6, 27, 39, 62.4 and 200 GeV Au+Au collisions using the STAR detector at the Relativistic Heavy Ion Collider (RHIC) are discussed. At intermediate impact parameters, the net-proton midrapidity dv1/dy, where v1 and y are directed flow and rapidity, respectively, shows non-monotonic variation as a function of beam energy. This non-monotonic variation is characterized by the presence of a minimum in dv1/dy between \(\sqrt {s_{NN}} = 11.5\) and 19.6 GeV and a change in the sign of dv1/dy twice between \(\sqrt {s_{{NN}}}\) = 7.7 and 39 GeV. At small impact parameters the product of the moments of net-proton distribution, kurtosis × variance (κσ2) and skewness × standard deviation (Sσ) are observed to be significantly below the corresponding measurements at large impact parameter collisions for \(\sqrt {s_{{NN}}}\) = 19.6 and 27 GeV. The κσ2 and Sσ values at these beam energies deviate from the expectations from Poisson statistics and that from a hadron resonance gas model. Both these measurements have implications towards understanding the quantum chromodynamics (QCD) phase structures, the first-order phase transition and the critical point in the high baryonic chemical potential region of the phase diagram.

The QCD phase diagram from Schwinger–Dyson equations

We study the phase diagram of quantum chromodynamics (QCD). For this purpose we employ the Schwinger–Dyson equations (SDEs) technique and construct a truncation of the infinite tower of equations by demanding a matching with the lattice results for the quark–anti-quark condensate at finite temperature (T), for zero quark chemical potential (μ), that is, the region where lattice calculations are expected to provide reliable results. We compute the evolution of the phase diagram away from T = 0. To chart the chiral symmetry restoration transition, we follow the evolution of the derivative of the condensate with respect to the temperature as a function of T and μ. The behavior of this thermodynamic variable clearly demonstrates the existence of a cross-over for μ less than a critical value. However, the derivative of the condensate with respect to the temperature develops a singularity near μ ≈ 0.22 GeV marking the onslaught of a first order phase transition characterized by the existence of a critical point. The critical line continues until μ ≈ 0.44 GeV where Tc = 0 and thus chiral symmetry is finally restored. For the deconfinement transition we look for the violation of the axiom of reflection positivity in the quark propagator. The critical end point appears to be the same as observed for the transition to chirally symmetric phase. However, near T = 0 axis, due to lack of data points, we are unable to claim against coincidental chiral symmetry restoration and deconfinement transitions along that axis.

REVIEW OF RECENT RESULTS FROM THE RHIC BEAM ENERGY SCAN

We review recent results from the RHIC beam energy scan (BES) program, aimed to study the Quantum Chromodynamics (QCD) phase diagram. The main goals are to search for the possible phase boundary, softening of equation of state or first order phase transition, and possible critical point. Phase-I of the BES program has recently concluded with data collection for Au+Au collisions at center-of-mass energies [Formula: see text] of 7.7, 11.5, 19.6, 27 and 39 GeV. Several interesting results are observed for these lower energies where the net-baryon density is high at the mid-rapidity. These results indicate that the matter formed at lower energies (7.7 and 11.5 GeV) is hadron dominated and might not have undergone a phase transition. In addition, a centrality dependence of freeze-out parameters is observed for the first time at lower energies, slope of directed flow for (net)-protons measured versus rapidity shows an interesting behavior at lower energies, and higher moments of net-proton show deviation from Skellam expectations at lower energies. An outlook for the future BES Phase-II program is presented and efforts for the detailed study of QCD phase diagram are discussed.

THE STUDY OF QCD PHASE TRANSITION AT FINITE TEMPERATURE AND CHIRAL CHEMICAL POTENTIAL IN A DYSON–SCHWINGER EQUATION MODEL

In this paper, we use a separable gluon propagator model to study the Quantum Chromodynamics (QCD) phase transition at finite temperature and chiral chemical potential. Using this model, we calculate the quark condensate and the chiral susceptibility at finite temperature and chiral chemical potential both in the chiral limit and at finite current quark mass. Based on these, we obtain the QCD phase diagram in the μ5-T plane.

Sign-posting the phase diagram of quantum chromodynamics

The good agreement between lattice predictions and data for the shape of the distribution of event-by-event fluctuations of the baryon number is discussed. Such comparisons can give fine probes of thermalization, and can be used to provide a direct determination of the cross-over temperature Tc of QCD. The logic of these comparisons and the systematics involved are discussed. The same methods can be used to further explore the phase diagram.

Lattice QCD at nonzero isospin chemical potential

Quantum chromodynamics (QCD) at non-zero isospin chemical potential is studied in a canonical approach by analyzing systems of fixed isospin number density. To construct these systems, we develop a range of new algorithms for performing the factorially large numbers of Wick contractions required in multi-hadron systems. We then use these methods to study systems with the quantum numbers of up to 72 $\pi^+$'s on three ensembles of gauge configurations with spatial extents $L\sim$ 2.0, 2.5 and 3.0 fm, and light quark masses corresponding to a pion mass of {390 MeV}. The ground state energies of these systems are extracted and the volume dependence of these energies is utilized to determine the two- and three- body interactions amongst $\pi^+$'s. The systems studied correspond to isospin densities of up to $\rho_I\sim 9\ {\rm fm}^{-3}$ and probe isospin chemical potentials, $\mu_I$, in the range $m_\pi\ \lsim \mu_I\ \lsim 4.5\ m_\pi$, allowing us to investigate aspects of the QCD phase diagram at low temperature and for varying isospin chemical potential. By studying the energy density of the system, we provide numerical evidence for the conjectured transition of the system to a Bose-Einstein condensed phase at $\mu_I\ \gsim m_\pi$.

Investigation of superdense baryonic matter during a collision of heavy ions (CBM Experiment)

The compressed baryonic matter (CBM) is intended for studying high-energy nuclear-nuclear collisions in the FAIR international heavy-ion facility. The objective of the experiment is to study the phase diagram of quantum chromodynamics at high baryonic density and at moderate temperature. The experimental problem is to identify hadrons and leptons and to record rare processes occurring in ion collisions under conditions with very high multiplicity of charged and neutral particles. More than 50 scientific centers are participating in the experiment. About 150 Russian physicists are participating in the work on almost all subsystems of the experiment.

Beam Energy Scan program at RHIC-experimental approach to the QCD Phase Diagram

The Beam Energy Scan (BES) program at RHIC was launched with the specific aim to explore the QCD (Quantum Chromodynamics) Phase Diagram. Particular emphasis was given to the search for phase boundaries and the location of the Critical Point (CP). The first run with AuAu collisions at 7.7, 11.5, and 39 GeV took place in 2010, and the next one, with energies of 18 and 27 GeV, will start in a few months. The results of the first stage of the BES program obtained by the STAR (Solenoidal Tracker at RHIC) experiment are presented and discussed, as well as plans for the future of the program.

Critical end point of quantum chromodynamics detected by chirally imbalanced quark matter

We suggest the idea, supported by concrete calculations within chiral models, that the critical endpoint of the phase diagram of Quantum Chromodynamics with three colors can be detected, by means of Lattice simulations of grand-canonical ensembles with a chiral chemical potential, $\mu_5$, conjugated to chiral charge density. In fact, we show that a continuation of the critical endpoint of the phase diagram of Quantum Chromodynamics at finite chemical potential, $\mu$, to a critical end point in the temperature-chiral chemical potential plane, is possible. This study paves the way of the mapping of the phases of Quantum Chromodynamics at finite $\mu$, by means of the phases of a fictitious theory in which $\mu$ is replaced by $\mu_5$.