Quantum Chromodynamics Phase Diagram Research Articles

Simulations of Stochastic Fluid Dynamics near a Critical Point in the Phase Diagram.

We present simulations of stochastic fluid dynamics in the vicinity of a critical endpoint belonging to the universality class of the Ising model. This study is motivated by the challenge of modeling the dynamics of critical fluctuations near a conjectured critical endpoint in the phase diagram of quantum chromodynamics (QCD). We focus on the interaction of shear modes with a conserved scalar density, which is known as model H. We show that the observed dynamical scaling behavior depends on the correlation length and the shear viscosity of the fluid. As the correlation length is increased or the viscosity is decreased we observe a crossover from the dynamical exponent of critical diffusion, z≃4, to the expected scaling exponent of model H, z≃3. We use our method to investigate the time-dependent correlation function of non-Gaussian moments M^{n}(t) of the order parameter. We find that the relaxation time depends in a nontrivial manner on the power n.

Introducing the concept of the Widom line in the QCD phase diagram

Critical phenomena emerging from the critical end point of a first-order transition are ubiquitous in nature. Here we bring the concept of a supercritical crossover, the Widom line, initially developed in the context of fluids, into the interacting matter described by quantum chromodynamics (QCD). We show that the existence of the putative critical end point between hadron gas and quark-gluon plasma in the temperature versus chemical potential of the QCD phase diagram implies the existence of a Widom line emerging from it in the supercritical region. We survey the thermodynamic anomalies already identified in simplified theoretical models of QCD exhibiting a critical end point, to show that they can be interpreted in terms of a Widom line. Then we suggest possible directions where the Widom line concept could provide new light on the QCD phase diagram. Published by the American Physical Society 2024

Can rooted staggered fermions describe nonzero baryon density at low temperatures?

Research on the quantum chromodynamics (QCD) phase diagram with lattice field theory methods is dominated by the use of rooted staggered fermions, as they are the computationally cheapest discretization available. We show that rooted staggered fermions at a nonzero baryochemical potential μB predict a sharp rise in the baryon density at low temperatures and μB≳3mπ/2, where mπ is the Goldstone pion mass. We elucidate the nature of the nonanalyticity behind this sharp rise in the density by a comparison of reweighting results with a Taylor expansion of high order. While at first sight this nonanalytic behavior becomes apparent at the same position where the pion condensation transition takes place in the phase-quenched theory, the nature of the nonanalyticity in the two theories appears to be quite different: While at nonzero isospin density the data are consistent with a genuine thermodynamic (branch-point) singularity, the results at nonzero baryon density point to an essential singularity at μB=0. The effect is absent for four flavors of degenerate quarks, where rooting is not used. For the two-flavor case, we show numerical evidence that the magnitude of the effect diminishes on finer lattices. We discuss the implications of this technical complication on future studies of the QCD phase diagram. Published by the American Physical Society 2024

Role of Time-Varying Magnetic Field on QGP Equation of State

The phase diagram of quantum chromodynamics (QCD) and its associated thermodynamic properties of quark-gluon plasma (QGP) are studied in the presence of time-dependent magnetic field. The study plays a pivotal role in the field of cosmology, astrophysics, and heavy-ion collisions. In order to explore the structure of quark-gluon plasma to deal with the dynamics of quarks and gluons, we investigate the equation of state (EoS) not only in the environment of static magnetic field but also in the presence of time-varying magnetic fields. So, for determining the equation of state of QGP at nonzero magnetic fields, we revisited our earlier model where the effect of time-varying magnetic field was not taken into consideration. Using the phenomenological model, some appealing features are noticed depending upon the three different scales: effective mass of quark, temperature, and time-independent and time-dependent magnetic fields. Earlier the effective mass of quark was incorporated in our calculations, and in the current work, it is modified for static and time-varying magnetic fields. Thermodynamic observables including pressure, energy density, and entropy are calculated for a wide range of temperature- and time-dependent as well as time-independent magnetic fields. Finally, we claim that the EoS are highly affected in the presence of a magnetic field. Our results are notable compared to other approaches and found to be advantageous for the measurement of QGP equation of state. These crucial findings with and without time-varying magnetic field could have phenomenological implications in various sectors of high-energy physics.

QCD phase diagram and equation of state in background electric fields

The phase diagram and the equation of state of quantum chromodynamics (QCD) is investigated in the presence of weak background electric fields by means of continuum extrapolated lattice simulations. The complex action problem at nonzero electric field is circumvented by a novel Taylor expansion, enabling the determination of the linear response of the thermal QCD medium to constant electric fields—in contrast to simulations at imaginary electric fields, which, as we demonstrate, involve an infrared singularity. Besides the electric susceptibility of QCD matter, we determine the dependence of the Polyakov loop on the field strength to leading order. Our results indicate a plasma-type behavior with a negative susceptibility at all temperatures, as well as an increase in the transition temperature as the electric field grows. Published by the American Physical Society 2024

Fluctuations and correlations of baryonic chiral partners

The exploration of critical phenomena in phase transitions of strongly interacting matter governed by quantum chromodynamics (QCD) is one of the goals of present ultrarelativistic heavy-ion collision experiments at BNL and CERN. The key research direction is to locate the putative critical point on the phase diagram of QCD linked to the chiral symmetry restoration at finite temperature and/or density. One of the main theoretical tools used for this purpose is the fluctuations of conserved charges, such as the net-baryon number. However, due to experimental limitations, analyses of heavy-ion collision data suffer from a very doubtful basing of the net-proton number being a proxy for the total net-baryon number fluctuations. In this work, we use the parity doublet model to investigate the fluctuations of the net-baryon number density in hot and dense hadronic matter. The model accounts for chiral criticality within the mean-field approximation. We focus on the qualitative properties and systematics of the first- and second-order susceptibility of the net-baryon number density, and their ratios for nucleons of positive and negative parity, as well as their correlator. We show that the fluctuations of the positive-parity nucleon do not necessarily reflect the fluctuations of the total net-baryon number density at the phase boundary of the chiral phase transition. We also investigate the nontrivial structure of the correlator. Furthermore, we discuss and quantify the differences between the fluctuations of the net-baryon number density in the vicinity of the chiral and liquid-gas phase transition in nuclear matter. We indicate a possible relevance of our results with the interpretation of the experimental data on net-proton number fluctuations in heavy-ion collisions. Published by the American Physical Society 2024

The influence of quark anomalous magnetic moment in the Nambu–Jona‐Lasinio model with different regularizations

AbstractThe Nambu–Jona‐Lasinio model is known for its simplicity and capacity to reproduce some of the basic characteristics of the quantum chromodynamics phase diagram. However, since it is a nonrenormalizable model, there are regularization issues that should be treated conveniently. This is the case when considering the quark anomalous magnetic moment (AMM) when external constant magnetic fields are present. Regularization procedures based on entangled functions between the magnetic field and the cutoff of the model can predict first‐order phase transitions for chiral symmetry restoration at finite values of magnetic fields and inverse magnetic catalysis. The strengths of magnetic fields explored in NJL model and lattice QCD do not show first‐order phase transition. In the present work, we show that some of the previous results are regularization‐dependent effects and how to handle the divergences using the vacuum magnetic regularization scheme.

Mapping out the thermodynamic stability of a QCD equation of state with a critical point using active learning

The Beam Energy Scan Theory (BEST) collaboration's equation of state (EoS) incorporates a three-dimensional Ising model critical point into the quantum chromodynamics (QCD) equation of state from lattice simulations. However, it contains four free parameters related to the size and location of the critical region in the QCD phase diagram. Certain combinations of the free parameters lead to acausal or unstable realizations of the EoS that should not be considered. In this work, we use an active learning framework to rule out pathological EoS efficiently. We find that checking stability and causality for a small portion of the parameters' range is sufficient to construct algorithms that perform with $>96$% accuracy across the entire parameter space. Though in this work we focus on a specific case, our approach can be generalized to any EoS containing a parameter space-class correspondence.

Probing neutron-star matter in the lab: Similarities and differences between binary mergers and heavy-ion collisions

Binary neutron-star mergers and heavy-ion collisions are related through the properties of the hot and dense nuclear matter formed during these extreme events. In particular, low-energy heavy-ion collisions offer exciting prospects to recreate such {extreme} conditions in the laboratory. However, it remains unexplored to what degree those collisions can actually reproduce hot and dense matter formed in binary neutron star mergers. As a way to understand similarities and differences between these systems, we {discuss their geometry and }perform a direct numerical comparison of the thermodynamic conditions probed in both collisions. To enable a direct comparison, we employ a finite-temperature equation of state able to describe the entire high-energy phase diagram of Quantum Chromodynamics. Putting side by side the evolution of both systems, we find that laboratory heavy-ion collisions at the energy range of $E_{\mathrm{lab}}=0.4 - 0.6\ A$ MeV probe (thermodynamic) states of matter that are very similar to those created in binary neutron-star mergers. These results can inform future low-energy heavy-ion collisions probing this regime.

Intermittency of charged particles in the hybridUrQMD+CMCmodel at energies available at the BNL Relativistic Heavy Ion Collider

Within the framework of intermittency analysis, a search for critical fluctuations is ongoing to locate the possible critical point in the quantum chromodynamics phase diagram. In this study, self-similar critical fluctuations from a critical Monte Carlo (CMC) model have been incorporated into the cascade ultrarelativistic quantum molecular dynamics (UrQMD) model. This hybrid UrQMD+CMC model exhibits a clear power-law behavior of scaled factorial moment for charged particles in Au+Au collisions at $\sqrt{s_\mathrm{NN}}$ = 7.7-200 GeV. By comparing the UrQMD+CMC model results with those from the STAR experiment, it is found that the value of a calculated scaling exponent falls in the range of the experimental measurement when 1-2 \% signal of intermittency fluctuations is added into the UrQMD sample.

Dilepton signature of a first-order phase transition

The search for a first-order phase transition in strongly interacting matter is one of the major objectives in the exploration of the phase diagram of Quantum Chromodynamics (QCD). In the present work we investigate dilepton radiation from the hot and dense fireballs created in Au-Au collisions at projectile energies of 1-2 $A$GeV for potential signatures of a first-order transition. Toward this end, we employ a hydrodynamic simulation with two different equations of state, with and without a phase transition. The latter is constrained by susceptibilities at vanishing chemical potential from lattice-QCD as well as neutron star properties, while the former is implemented via modification of the mean-fields in the quark phase. We find that the latent heat involved in the first-order transition leads to a substantial increase in the low-mass thermal emission signal, by about a factor of two above the cross-over scenario.

Color-flavor dependence of the Nambu-Jona-Lasinio model and QCD phase diagram

We study the dynamical chiral symmetry breaking/restoration for various numbers of light quarks flavors and colors using the Nambu-Jona-Lasinio (NJL) model of quarks in the Schwinger-Dyson equation framework, dressed with a color-flavor dependence of effective coupling. For fixed and varying , we observe that the dynamical chiral symmetry is broken when exceeds its critical value . For a fixed and varying , we observe that the dynamical chiral symmetry is restored when reaches its critical value . Strong interplay is observed between and , i.e., larger values of tend to strengthen the dynamical generated quark mass and quark-antiquark condensate, while higher values of suppress both parameters. We further sketch the quantum chromodynamics (QCD) phase diagram at a finite temperature T and quark chemical potential μ for various and . At finite T and μ, we observe that the critical number of colors is enhanced, whereas the critical number of flavors is suppressed as T and μ increase. Consequently, the critical temperature , , and co-ordinates of the critical endpoint in the QCD phase diagram are enhanced as increases and suppressed when increases. Our findings agree with the lattice QCD and Schwinger-Dyson equations predictions.

QCD phase diagram in a finite volume in the PNJL model

Abstract In this work, we study the quantum chromodynamics phase diagram at finite temperature and non-zero chemical potential in the framework of the SU(2) flavor of the Polyakov–Nambu – Jona–Lasinio model (PNJL). Applying multiple reflection expansion to cubic and spherical finite volumes of different sizes and boundary conditions, the chiral phase transition and deconfinement of strongly interacting matter are analyzed. We give special attention to find and locate the critical endpoint and locating the critical endpoint, if it exists, as a function of the volume size and its shape, and its dependence of chemical potential and temperature.

Competition of chiral soliton lattice and Abrikosov vortex lattice in QCD with isospin chemical potential

We investigate the thermodynamics of two-flavor quark matter in presence of nonzero isospin chemical potential and external magnetic field. It is known that at sufficiently high isospin chemical potential, charged pions undergo Bose–Einstein condensation (BEC). The condensate behaves as a superconductor, exhibiting Meissner effect in weak external magnetic fields. Stronger fields stress the superconducting state, turning it first into an Abrikosov lattice of vortices, and eventually destroying the condensate altogether. On the other hand, for sufficiently strong magnetic fields and low-to-moderate isospin chemical potential, the ground state of quantum chromodynamics (QCD) is expected to be a spatially modulated condensate of neutral pions, induced by the chiral anomaly: the chiral soliton lattice (CSL). We map the phase diagram of QCD as a function of isospin chemical potential and magnetic field in the part of the parameter space accessible to a low-energy effective field theory description of QCD. Our main result is an explicit account of the competition between the CSL and the Abrikosov vortex lattice. This is accomplished by adopting a fast numerical algorithm for finding the vortex lattice solution of the equation of motion and the corresponding Gibbs energy. We find that the Abrikosov vortex lattice phase persists in the phase diagram, separating the uniform charged pion BEC phase from the CSL phase. The precise layout of the phase diagram depends sensitively on the choice of the vacuum pion mass.

Limits of thermalization in relativistic heavy ion collisions

The goal of collider programs of high energy heavy-ion collisions is to produce a form of matter that can test non-perturbative aspects of Quantum Chromodynamics (QCD), the theory of strong interactions. One of the primary predictions from a computational approach to this quantum field theory is the existence of distinct thermodynamic states of QCD, particularly a state of deconfined quarks and gluons. An important step in establishing changes of state of QCD matter is to demonstrate that femto-scale system created in the laboratory can attain thermodynamic equilibrium. We present such a demonstration by checking that event-to-event fluctuations of several different conserved quantities have a consistent treatment in a grand canonical ensemble through a common temperature and chemical potentials. A key component of this work is that we used cumulants of up to third order in the net proton number, charge, and strangeness. We found a clear indication that the femto-scale fireball is thermalized when the collision energy in the centre of mass, sNN, is high enough. Also, the use of higher order cumulants, within the framework of grand canonical ensemble, reveals for the first time that the fireballs created at lower sNN are not in thermodynamic equilibrium. This opens the door to further studies of the approach to equilibrium, and the effects that a critical point in the phase diagram of QCD could have on such phenomena.

Gravitational wave signatures of phase transition from hadronic to quark matter in isolated neutron stars and binaries

The fundamental constituent of matter at high temperature and density has intrigued physicists for quite some time. Recent results from heavy-ion colliders have enriched the Quantum Chromodynamics phase diagram at high temperatures and low baryon density. However, the phase at low temperatures and finite (mostly intermediate) baryon density remain unexplored. Theoretical Quantum Chromodynamics calculation predicts phase transition from hadronic matter to quark matter at such densities. Presently, the best laboratories available to probe such densities lie at the core of neutron stars. Recent results of how such phase transition signatures can be probed using gravitational waves both in isolated neutron stars and neutron star in binaries. The isolated neutron star would probe the very low-temperature regime, whereas neutron stars in binaries would probe finite baryon density in the intermediate temperature regime. We would also discuss whether the gravitational wave signature of such phase transition is unique and the detector specification needed to detect such signals.

Dynamic modeling for heavy-ion collisions

Recent theory progress in (3+1)D dynamical descriptions of relativistic nuclear collisions at finite baryon density are reviewed. Heavy-ion collisions at different collision energies produce strongly coupled nuclear matter to probe the phase structure of Quantum Chromodynamics (QCD). Dynamical frameworks serve as a quantitative tool to study properties of hot QCD matter and map collisions to the QCD phase diagram. Outstanding challenges are highlighted when confronting theoretical models with the current and forthcoming experimental measurements from the RHIC beam energy scan program.

Chiral soliton lattice phase in warm QCD

We analyze the phase diagram of quantum chromodynamics at low-to-moderate temperature, baryon chemical potential and external magnetic field within chiral perturbation theory at next-to-leading order of the derivative expansion. Our main result is that the anomaly-induced chiral soliton lattice (CSL) phase is stabilized by thermal fluctuations. As a consequence, the CSL state may survive up to temperatures at which chiral symmetry is restored.

Chiral symmetry restoration and deconfinement in the contact interaction model of quarks with parallel electric and magnetic fields

We study the impact of steady, homogeneous, and external parallel electric and magnetic field strengths ( ) on the chiral symmetry breaking-restoration and confinement-deconfinement phase transition. We also sketch the phase diagram of quantum chromodynamics (QCD) at a finite temperature T and in the presence of background fields. The unified formalism for this study is based on the Schwinger-Dyson equations, symmetry preserving vector-vector contact interaction model of quarks, and an optimal time regularization scheme. At , in the purely magnetic case (i.e., ), we observe the well-known magnetic catalysis effect. However, in a pure electric field background ( ), the electric field tends to restore the chiral symmetry and deconfinement above the pseudo-critical electric field . In the presence of both and , we determine the magnetic catalysis effect in the particular region where dominates over , whereas we observe the chiral inhibition (or electric chiral rotation) effect when overshadows eB. At finite T, in the pure electric field case, the phenomenon of inverse electric catalysis appears to exist in the proposed model. Conversely, for a pure magnetic field background, we observe the magnetic catalysis effect in the mean-field approximation and inverse magnetic catalysis with -dependent coupling. The combined effects of and on the pseudo-critical yields an inverse electromagnetic catalysis, with and without an -dependent effective coupling of the model. The findings of this study agree well with the already predicted results obtained via lattice simulations and other reliable effective models of QCD.

Flavor, temperature and magnetic field dependence of the QCD phase diagram: magnetic catalysis and its inverse

We study dynamical chiral symmetry breaking for quarks in the fundamental representation of SU(N c) for the N f number of light quark flavors. We also investigate the phase diagram of quantum chromodynamics at finite temperature T and/or in the presence of a constant external magnetic field eB. The unified formalism for this analysis is provided by a symmetry-preserving Schwinger–Dyson equation treatment of a vector × vector contact interaction model which encodes several well-established features of quantum chromodynamics to mimic the latter as closely as possible. Deconfinement and chiral symmetry restoration are triggered above a critical value of N f at T = 0 = eB. On the other hand, increasing temperature itself screens strong interactions, thus ensuring that a smaller value of N f is sufficient to restore chiral symmetry at higher temperatures. We also observe the well-known phenomenon of magnetic catalysis for a strong enough magnetic field. However, we note that if the effective coupling strength of the model decreases as a function of magnetic field, it can trigger inverse magnetic catalysis in a certain window of this functional dependence. Our model allows for the simultaneous onset of dynamical chiral symmetry breaking and confinement for each case. Qualitative as well as quantitative predictions of our simple but effective model are in reasonably satisfactory agreement with lattice results and other reliable and refined predictions based upon intricate continuum studies of quantum chromodynamics.