Quantum Chromodynamics Critical Point Research Articles

Dynamical development of proton cumulants and correlation functions in Au+Au collisions at sNN=7.7 GeV from a multiphase transport model

Higher-order cumulants of the distributions of conserved charges, such as net-baryon number, are sensitive to the quantum chromodynamics(QCD) phase transition and the QCD critical point. We calculate the cumulants and correlation functions of proton, antiproton, and net-proton multiplicity distributions in Au+Au collisions at $\sqrt{s_{NN}} = 7.7$ GeV using a multiphase transport model(AMPT). The AMPT model can basically describe the trends of cumulants, cumulant ratios, (normalized) correlation functions of the proton and net-proton measured by the STAR experiment. The multiproton (baryon) correlations in the AMPT model are consistent with the expectation from baryon number conservation. We demonstrate that multiproton (baryon) correlations suffer the dynamical evolution of heavy-ion collisions. Our results provide a baseline for searching for the possible critical behaviors at the critical end point in relativistic heavy-ion collisions.

Net-proton number fluctuations and the Quantum Chromodynamics critical point: Supplemental material

Net-proton number fluctuations and the Quantum Chromodynamics critical point: Supplemental material

Hadron resonance gas with van der Waals interactions

An overview of a hadron resonance gas (HRG) model that includes van der Waals (vdW) interactions between hadrons is presented. Applications of the excluded volume HRG model to heavy-ion collision data and lattice quantum chromodynamics (QCD) equation of state are discussed. A recently developed quantum vdW HRG model is covered as well. Applications of this model in the context of the QCD critical point are elaborated.

Elliptic flow splittings between particles and their antiparticles in relativistic heavy-ion collisions

Relativistic heavy-ion collisions are an important experimental way of studying the new state of matter as well as the phase diagram of the quantum chromodynamics (QCD) under extremely high temperatures and high densities. The elliptic flow is an important experimental observable in relativistic heavy-ion collisions. In recent years, the beam-energy scan program has been carried out on the relativistic heavy-ion collider at Brookhaven National Laboratory in USA, where phenomena different from those in heavy-ion collisions at extremely high energies, such as the elliptic flow splittings between particles and their antiparticles, are observed. Based on an extended multiphase transport model, this phenomenon can be explained through different mean-field potentials for particles and their antiparticles. In the almond-shaped medium produced in these collisions, particles affected by the repulsive potential are more likely to leave the system, while those affected by the attractive potential are more likely to be trapped in the system, enhancing and reducing their respective elliptic flow. The partonic mean-field potentials are extracted from an extended 3-flavor Nambu-Jona-Lasinio (NJL) model. Quarks are affected by more repulsive potentials compared with their antiquarks as a result of the vector-isoscalar coupling, while d quarks are affected by a more repulsive potential compared with u quarks as a result of the vector-isovector coupling, in the baryon-rich and d -quark-rich medium. The hadronic mean-field potentials are also incorporated through the relativistc mean-field model for baryons and antibaryons, and through the chiral effective field theory for kaons and antikaons as well as for π + and π − . In the baryon-rich and neutron-rich medium, antinucleons, antikaons, and π + are affected by more attractive potentials than nucleons, kaons, and π − , respectively. It is found that a strong vector-isoscalar and vector-isovector coupling are needed to reproduce the elliptic flow splittings between nucleons and antinucleons, kaons and antikaons, as well as π + and π − , as observed experimentally by the STAR Collaboration. On the other hand, the NJL model can be used to study the spontaneous chiral symmetry breaking and the phase diagram of the chiral phase transition. In order to describe both the chiral and deconfinement phase transition, one needs to extend the NJL model by incorporating the Polyakov-loop contribution (pNJL). Although the temperature of the crtical point for the chiral phase transition is higher in the pNJL model, it is found that the position or the behavior of the critical point is sensitive to the strength of the vector-isoscalar and the vector-isovector couplings in both the NJL and the pNJL model. In addition, the equation of state of baryon-rich and d -quark-rich quark matter is sensitive to these couplings as well. With these couplings constrainted by the elliptic flow splittings between particles and their antiparticles, information of the quark matter equation of state as well as the QCD phase diagram at finite baryon and isospin chemical potentials can be thus extracted. The study shows that the QCD critical point may be at very low temperatures or does not even exist, while the strong vector-isoscalar and vector-isovector couplings favor a stiff equation of state of quark matter at high net-baryon and isovector densities. In future studies, the transport framework can be further extended to incorporate the Polyakov-loop contribution.

Probing the QCD phase structure with higher order baryon number susceptibilities within the NJL model * * Supported in part by the National Natural Science Foundation of China (11475085, 11535005, 11690030, 11575069, 11221504), and the MoST of China 973-Project ( 2015CB856901)

Conserved charge fluctuations can be used to probe the phase structure of strongly interacting nuclear matter in relativistic heavy-ion collisions. To obtain the characteristic signatures of the conserved charge fluctuations for the quantum chromodynamics (QCD) phase transition, we study the susceptibilities of dense quark matter up to eighth order in detail, using an effective QCD-based model. We studied two cases, one with the QCD critical end point (CEP) and one without owing to an additional vector interaction term. The higher order susceptibilities display rich structures near the CEP and show sign changes as well as large fluctuations. These can provide us information about the presence and location of the CEP. Furthermore, we find that the case without the CEP also shows a similar sign change pattern, but with a relatively smaller magnitude compared with the case with the CEP. Finally, we conclude that higher order susceptibilities of conserved charge can be used to probe the QCD phase structures in heavy-ion collisions.

Phenomenological Review on Quark–Gluon Plasma: Concepts vs. Observations

In this review, we present an up-to-date phenomenological summary of research developments in the physics of the Quark–Gluon Plasma (QGP). A short historical perspective and theoretical motivation for this rapidly developing field of contemporary particle physics is provided. In addition, we introduce and discuss the role of the quantum chromodynamics (QCD) ground state, non-perturbative and lattice QCD results on the QGP properties, as well as the transport models used to make a connection between theory and experiment. The experimental part presents the selected results on bulk observables, hard and penetrating probes obtained in the ultra-relativistic heavy-ion experiments carried out at the Brookhaven National Laboratory Relativistic Heavy Ion Collider (BNL RHIC) and CERN Super Proton Synchrotron (SPS) and Large Hadron Collider (LHC) accelerators. We also give a brief overview of new developments related to the ongoing searches of the QCD critical point and to the collectivity in small (p + p and p + A) systems.

Functional renormalization group analysis of the soft mode at the QCD critical point

We make an intensive investigation of the soft mode at the quantum chromodynamics (QCD) critical point on the basis of the functional renormalization group (FRG) method in the local potential approximation. We calculate the spectral functions $\rho_{\sigma, \pi}(\omega,\, p)$ in the scalar ($\sigma$) and pseudoscalar ($\pi$) channels beyond the random phase approximation in the quark--meson model. At finite baryon chemical potential $\mu$ with a finite quark mass, the baryon-number fluctuation is coupled to the scalar channel and the spectral function in the $\sigma$ channel has a support not only in the time-like ($\omega\,>\,p$) but also in the space-like ($\omega\,<\, p$) regions, which correspond to the mesonic and the particle--hole phonon excitations, respectively. We find that the energy of the peak position of the latter becomes vanishingly small with the height being enhanced as the system approaches the QCD critical point, which is a manifestation of the fact that the phonon mode is the {\em soft mode} associated with the second-order transition at the QCD critical point, as has been suggested by some authors. Moreover, our extensive calculation of the spectral function in the $(\omega, p)$ plane enables us to see that the mesonic and phonon modes have the respective definite dispersion relations $\omega_{\sigma.{\rm ph}}(p)$, and it turns out that $\omega_{\sigma}(p)$ crosses the light-cone line into the space-like region, and then eventually merges into the phonon mode as the system approaches the critical point more closely. This implies that the sigma-mesonic mode also becomes soft at the critical point. We also provide numerical stability conditions that are necessary for obtaining the accurate effective potential from the flow equation.

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.

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.

Results from the STAR Beam Energy Scan Program

The main aim of the beam energy scan (BES) program at the Relativistic Heavy-Ion Collider (RHIC) is to explore the quantum chromodynamics (QCD) phase diagram. The specific physics goal is to search for the phase boundary and the QCD critical point. We present results from Au+Au collisions at various energies collected in the BES program by the Solenoidal Tracker At RHIC (STAR) experiment. First results on transverse momentum ( p T ) spectra, d N / d y , and average transverse mass ( 〈 m T 〉 ) for identified hadrons produced at mid-rapidity for s N N = 7.7 GeV are presented. Centrality dependence of d N / d y and 〈 p T 〉 are also discussed and compared to corresponding data from other energies. In addition, first results on charged hadron directed ( v 1 ) and elliptic flow ( v 2 ) for s N N = 7.7 , 11.5 and 39 GeV are presented. New results on event-by-event fluctuations (particle ratio, net-proton and net-charge higher moments) are presented for s N N = 39 GeV .

Exploring the quantum chromodynamics landscape with high-energy nuclear collisions

A quantum chromodynamics (QCD) phase diagram is usually plotted as the temperature (T) versus the chemical potential associated with the conserved baryon number (μB). Two fundamental properties of QCD, related to confinement and chiral symmetry, allow for two corresponding phase transitions when T and μB are varied. Theoretically, the phase diagram is explored through non-perturbative QCD calculations on a lattice. The energy scale for the phase diagram (ΛQCD∼200 MeV) is such that it can be explored experimentally by colliding nuclei at varying beam energies in the laboratory. In this paper, we review some aspects of the QCD phase structure as explored through experimental studies using high-energy nuclear collisions. Specifically, we discuss three observations related to the formation of a strongly coupled plasma of quarks and gluons in the collisions, the experimental search for the QCD critical point on the phase diagram and the freeze-out properties of the hadronic phase.

Two-color quark matter:U(1)Arestoration, superfluidity, and quarkyonic phase

We discuss the phase structure of quantum chromodynamics (QCD) with two colors and two flavors of light quarks. This is motivated by the increasing interest in the QCD phase diagram as follows: (1) The QCD critical point search has been under intensive dispute and its location and existence suffer from uncertainty of effective $\mathrm{U}(1{)}_{\mathrm{A}}$ symmetry restoration. (2) A new phase called quarkyonic matter is drawing theoretical and experimental attention but it is not clear whether it can coexist with diquark condensation. We point out that two-color QCD is nontrivial enough to contain essential ingredients for (1) and (2) both, and most importantly, is a system without the sign problem in numerical simulations on the lattice. We adopt the two-flavor Nambu--Jona-Lasinio model extended with the two-color Polyakov loop and make quantitative predictions that can be tested by lattice simulations.

Dynamical Density Fluctuations around QCD Critical Point Based on Dissipative Relativistic Fluid Dynamics: Possible Fate of Mach Cone at the Critical Point

The purpose of this paper is twofold. Firstly, we study the dynamical density fluctuations around the critical point(CP) of Quantum Chromodynamics(QCD) using dissipative relativistic fluid dynamics in which the coupling of the density fluctuations to those of other conserved quantities is taken into account. We show that the sound mode which is directly coupled to the mechanical density fluctuation is attenuated and in turn the thermal mode becomes the genuine soft mode at the QCD CP. We give a speculation on the possible fate of a Mach cone in the vicinity of the QCD CP as a signal of the existence of the CP on the basis of the above findings. Secondly, we clarify that the so called first-order relativistic fluid dynamic equations have generically no problem to describe fluid dynamic phenomena with long wave lengths contrary to a naive suspect whereas even Israel-Stewart equation, a popular second-order equation, may not describe the hydrodynamic mode in general depending on the value of the relaxation time.

Multiplicity fluctuations in nucleus-nucleus collisions: Dependence on energy and atomic mass number

Event-by-event multiplicity fluctuations in central C$+$C, S$+$S, In$+$In, and Pb$+$Pb as well as $p+p$ collisions at bombarding energies from 10 to 160 AGeV are studied within the hadron string dynamics and ultrarelativistic quantum molecular dynamics microscopic transport approaches. Our investigation is directly related to the future experimental program of the NA61 Collaboration at the SPS for a search of the quantum chromodynamics (QCD) critical point. The dependence on energy and atomic mass number of the scaled variances for negative, positive, and all charged hadrons is presented and compared to the results of the model of independent sources. Furthermore, the nucleus-nucleus results from the transport calculations are compared to inelastic proton-proton collisions for reference. We find a dominant role of the participant number fluctuations in nucleus-nucleus reactions at finite impact parameter $b$. To reduce the influence of the participant numbers fluctuations on the charged particle multiplicity fluctuations only the most central events have to be selected. Accordingly, the samples of the 1% most central nucleus-nucleus collisions with the largest numbers of the projectile participants are studied. The results are compared with those for collisions at zero impact parameter. A strong influence of the centrality selection criteria on the multiplicity fluctuations is pointed out. Our findings are essential for an optimal choice of colliding nuclei and bombarding energies for the experimental search of the QCD critical point.