The order of the quantum chromodynamics transition predicted by the standard model of particle physics

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.

Conjectures about the Chiral Phase Transition in QCD from Anomalous Multi-Instanton Interactions

To date numerical simulations of lattice QCD have not found a chiral phase transition of first order that is expected to occur for sufficiently light pions. We show how the restoration of an exact global chiral symmetry can strongly decrease the breaking of the approximate, anomalous U_{A}(1) symmetry. This is testable on the lattice through simulations for one through four flavors. In QCD a small breaking of the U_{A}(1) symmetry in the chirally symmetric phase generates novel experimental signals.

Cosmological Background Interpretation of Pulsar Timing Array Data

We discuss the interpretation of the detected signal by pulsar timing array (PTA) observations as a gravitational wave background of cosmological origin. We combine NANOGrav 15-years and EPTA-DR2new datasets and confront them against backgrounds from supermassive black hole binaries (SMBHBs), and cosmological signals from inflation, cosmic (super)strings, first-order phase transitions, Gaussian and non-Gaussian large scalar fluctuations, and audible axions. We find that scalar-induced, and to a lesser extent audible axion and cosmic superstring signals, provide a better fit than SMBHBs. These results depend, however, on modeling assumptions, so further data and analysis are needed to reach robust conclusions. Independently of the signal origin, the data strongly constrain the parameter space of cosmological signals, for example, setting an upper bound on primordial non-Gaussianity at PTA scales as |f_{nl}|≲2.34 at 95% C.L.

Mirror QCD phase transition as the origin of the nanohertz Stochastic Gravitational-Wave Background

Several Pulsar Timing Array (PTA) Collaborations have recently provided strong evidence for a nHz Stochastic Gravitational-Wave Background (SGWB). Here we investigate the implications of a first-order phase transition occurring within the early Universe's dark quantum chromodynamics epoch, specifically within the framework of the mirror twin Higgs dark sector model. Our analysis indicates a distinguishable SGWB signal originating from this phase transition, which can explain the measurements obtained by PTAs. Remarkably, a significant portion of the parameter space for the SGWB signal also effectively resolves the existing tensions in both the H0 and S8 measurements in Cosmology. This intriguing correlation suggests a possible common origin of these three phenomena for 0.2<ΔNeff<0.5, where the mirror dark matter component constitutes less than 30% of the total dark matter abundance. Next-generation CMB experiments such as CMB-S4 can test this parameter region.

Footprints of the QCD Crossover on Cosmological Gravitational Waves at Pulsar Timing Arrays

Pulsar timing arrays (PTAs) have reported evidence for a stochastic gravitational wave (GW) background at nanohertz frequencies, possibly originating in the early Universe. We show that the spectral shape of the low-frequency (causality) tail of GW signals sourced at temperatures around T≳1  GeV is distinctively affected by confinement of strong interactions (QCD), due to the corresponding sharp decrease in the number of relativistic species, and significantly deviates from ∼f^{3} commonly adopted in the literature. Bayesian analyses in the NANOGrav 15 years and the previous international PTA datasets reveal a significant improvement in the fit with respect to cubic power-law spectra, previously employed for the causality tail. While no conclusion on the nature of the signal can be drawn at the moment, our results show that the inclusion of standard model effects on cosmological GWs can have a decisive impact on model selection.

Machine Learning Approach to Analyze the Heavy Quark Diffusion Coefficient in Relativistic Heavy Ion Collisions

The diffusion coefficient of heavy quarks in a deconfined medium is examined in this research using a deep convolutional neural network (CNN) that is trained with data from relativistic heavy ion collisions involving heavy flavor hadrons. The CNN is trained using observables such as the nuclear modification factor RAA and the elliptic flow v2 of non-prompt J/ψ from the B-hadron decay in different centralities, where B meson evolutions are calculated using the Langevin equation and the instantaneous coalescence model. The CNN outputs the parameters, thereby characterizing the temperature and momentum dependence of the heavy quark diffusion coefficient. By inputting the experimental data of the non-prompt J/ψ(RAA,v2) from various collision centralities into multiple channels of a well-trained network, we derive the values of the diffusion coefficient parameters. Additionally, we evaluate the uncertainty in determining the diffusion coefficient by taking into account the uncertainties present in the experimental data (RAA,v2), which serve as inputs to the deep neural network.

QCD Equation of State of Dense Nuclear Matter from a Bayesian Analysis of Heavy-Ion Collision Data

Bayesian methods are used to constrain the density dependence of the QCD equation of state (EOS) for dense nuclear matter using the data of mean transverse kinetic energy and elliptic flow of protons from heavy ion collisions (HICs), in the beam energy range sqrt[s_{NN}]=2-10  GeV. The analysis yields tight constraints on the density dependent EOS up to 4 times the nuclear saturation density. The extracted EOS yields good agreement with other observables measured in HIC experiments and constraints from astrophysical observations both of which were not used in the inference. The sensitivity of inference to the choice of observables is also discussed.

Microscopic Encoding of Macroscopic Universality: Scaling Properties of Dirac Eigenspectra near QCD Chiral Phase Transition

Macroscopic properties of the strong interaction near its chiral phase transition exhibit scaling behaviors, which are the same as those observed close to the magnetic transition in a three-dimensional classical spin system with O(4) symmetry. We show that the universal scaling properties of the chiral phase transition in quantum chromodynamics (QCD) at the macroscale are, in fact, encoded within the microscopic energy levels of its fundamental constituents, the quarks. We establish a connection between the cumulants of the chiral order parameter, i.e., the chiral condensate, and the correlations among the energy levels of quarks, i.e., the eigenspectra of the massless QCD Dirac operator. This relation elucidates how the fluctuations of the chiral condensate arise from the correlations within the infrared part of the energy spectra of quarks, and naturally leads to a generalization of the Banks-Casher relation for the cumulants of the chiral condensate. Then, through (2+1)-flavor lattice QCD calculations with varying light quark masses near the QCD chiral transition, we demonstrate that the correlations among the infrared part of the Dirac eigenvalue spectra exhibit same universal scaling behaviors as expected of the cumulants of the chiral condensate. We find that these universal scaling behaviors extend up to the physical values of the up and down quark masses. Our study reveals how the hidden scaling features at the microscale give rise to the macroscopic universal properties of QCD.

Beam Energy Dependence of Triton Production and Yield Ratio (N_{t}×N_{p}/N_{d}^{2}) in Au+Au Collisions at RHIC

We report the triton (t) production in midrapidity (|y|<0.5) Au+Au collisions at sqrt[s_{NN}]=7.7-200  GeV measured by the STAR experiment from the first phase of the beam energy scan at the Relativistic Heavy Ion Collider. The nuclear compound yield ratio (N_{t}×N_{p}/N_{d}^{2}), which is predicted to be sensitive to the fluctuation of local neutron density, is observed to decrease monotonically with increasing charged-particle multiplicity (dN_{ch}/dη) and follows a scaling behavior. The dN_{ch}/dη dependence of the yield ratio is compared to calculations from coalescence and thermal models. Enhancements in the yield ratios relative to the coalescence baseline are observed in the 0%-10% most central collisions at 19.6 and 27 GeV, with a significance of 2.3σ and 3.4σ, respectively, giving a combined significance of 4.1σ. The enhancements are not observed in peripheral collisions or model calculations without critical fluctuation, and decreases with a smaller p_{T} acceptance. The physics implications of these results on the QCD phase structure and the production mechanism of light nuclei in heavy-ion collisions are discussed.

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.

Equation of State and Energy Loss of Hot and Dense Quark-Gluon matter from Holographic Black Holes

By using gravity/gauge correspondence, we construct a holographic model, constrained to mimic the lattice QCD equation of state at zero density, to investigate the temperature and baryon chemical potential dependence of the equation of state. We also obtained the energy loss of light and heavy partons within the hot and dense plasma represented by the heavy quark drag force, Langevin diffusion coefficients and jet quenching parameter at the critical point and across the first-order transition line predicted by the model.

Lattice QCD equation of state at finite chemical potential from an alternative resummation: Strangeness neutrality and beyond

In this contribution we present a resummation of the Quantum Chromodynamics (QCD) equation of state from lattice simulations at imaginary chemical potentials. We generalize the scheme introduced in a previous work [1], to the case of non-zero strangeness chemical potential. We present continuum extrapolated results for thermodynamic observables in the temperature range 130MeV ≤ T ≤ 280 MeV, for chemical potentials up to μB/T = 3:5, along the strangeness neutral line. Furthermore, we relax the constraint of strangeness neutrality, by extrapolating to small values of the strangeness-to-baryon-number ratio R = nS / nB.

Higher-order moments of net-proton and the QCD phase structure

Higher-order cumulants of the conserved quantities and their ratios are powerful tools to study the properties of QGP and explore the QCD phase structure, such as critical point and/or the first-order phase transition boundary. In this proceedings, we present the recent results of the higher-order cumulants and ratios at different collision energies. We compare the results with hadronic transport model, Hadron Resonance Gas model, and QCD thermodynamic calculations and discuss the physics implications. Additionally, we mention the near future cumulant analyses and an initial volume fluctuation issue.

Seventh and eighth-order cumulants of net-proton multiplicity distributions in heavy-ion collisions at RHIC-STAR

We report the first measurements of seventh and eighth-order cumulants of net-proton distributions in Au+Au collisions at √SNN=27,54.4, and 200 GeV. The measurements are performed at mid-rapidity |y| < 0.5 within 0.4 < pT < 2.0 GeV/c using the Time Projection Chamber and Time-of-Flight detector. Motivation for the measurements comes from lattice-QCD and QCD based model calculations that predict their negative signs for a crossover quark-hadron transition. While 0-40% centrality measurements at √SNN=54.4 and 200 GeV are consistent with zero within large uncertainties, at √SNN=27 GeV, they are negative with ≤ 1.4σ significance. The peripheral 70-80% measurements are either positive or consistent with zero for the three energies.

Constraints on hadron resonance gas interactions via first-principles Lattice QCD susceptibilities

We investigate extensions of the Hadron Resonance Gas (HRG) Model beyond the ideal case by incorporating both attractive and repulsive interactions into the model. When considering additional states exceeding those measured with high confidence by the Particle Data Group, attractive corrections to the overall pressure in the HRG model are imposed. On the other hand, we also apply excluded-volume corrections, which ensure there is no overlap of baryons by turning on repulsive (anti)baryon-(anti)baryon interactions. We emphasize the complementary nature of these two extensions and identify combinations of conserved charge susceptibilities that allow us to constrain them separately. In particular, we find interesting ratios of susceptibilities that are sensitive to one correction and not the other. This allows us to constrain the excluded volume and particle spectrum effects separately. Analysis of the available lattice results suggests the presence of both the extra states in the baryonstrangeness sector and the repulsive baryonic interaction, with indications that hyperons have a smaller repulsive core than non-strange baryons. We note that these results are interesting for heavy-ion-collision systems at both the LHC and RHIC.

Study of Bulk Properties of Strange Particles in Au+Au Collisions at sNN = 54.4 GeV

We analyzed the transverse momentum pT spectra of various strange hadrons KS0, Λ(Λ¯) and Ξ-(Ξ¯+) at mid-rapidity (y) in different centrality intervals from Au+Au collisions at sNN= 54.4 GeV. The pT spectra of these strange hadrons are investigated by the Tsallis-like distribution, which satisfactorily fits the experimental data. The bulk properties of the medium produced in ultra-relativistic heavy-ion collisions at the kinetic freeze-out are reflected by measuring the hadron spectra. The effective temperature T, transverse flow velocity βT, and mean pT along with other parameters that are strongly dependent on centrality and particle specie are extracted. The effective temperature of multi-strange particle (Ξ-(Ξ¯+)) is larger as compared to singly-strange particles Λ(Λ¯) and KS0. Furthermore, the kinetic freeze-out temperature T, transverse flow velocity βT. and mean pT (⟨pT⟩) show a decreasing trend towards lower centrality, while the entropy parameter q increases from central to peripheral collisions. In addition, a positive correlation of ⟨pT⟩ and T and a negative correlation of q and T are also reported.

All Order Resummed Leading and Next-to-Leading Soft Modes of Dense QCD Pressure

The cold and dense QCD equation of state at high baryon chemical potential μ_{B} involves at order α_{s}^{2} an all-loop summation of the soft mode m_{E}∼α_{s}^{1/2}μ_{B} contributions. Recently, the complete soft contributions at order α_{s}^{3} were calculated using the hard thermal loop formalism. By identifying massive renormalization group properties of the hard thermal loop theory, we resum to all orders α_{s}^{p}, p≥3 the leading and next-to-leading logarithmic soft contributions. We obtain compact analytical expressions that show visible deviations from the state-of-the art results, and noticeably reduce residual scale dependence. Our results should help to reduce uncertainties in extending the equation of state in the intermediate μ_{B} regime, relevant in particular for the phenomenology of neutron stars.

Particle Multiplicity Fluctuations and Spatiotemporal Properties of Particle-Emitting Source of Strongly Interacting Matter for NICA and RHIC Energies

The results of the model analysis of hadron femtoscopic correlations and factorial moments of particle multiplicity in heavy ion collisions for the energy range of the Beam Energy Scan (BES) program at RHIC and future NICA collider are presented. For this purpose, the simulation of Au+Au collisions at center-of-mass energies 7.7 and 11.5 GeV per nucleon pair using the UrQMD, vHLLE+UrQMD (with the crossover and first-order equation of states), and HYDJET++ event generators was performed. The sensitivity of pion and kaon correlation radii and the dependence of the factorial moments on heavy ion beam energy to quark–hadron phase transition details was studied. In addition, the possible influence of some relevant detector effects on the corresponding experimental observables is discussed.

Effects of a Finite Volume in the Phase Structure of QCD

Working in the SU(2) flavor version of the NJL model, we study the effect of taking a finite system volume on a strongly interacting system of quarks, and, in particular, the location of the chiral phase transition and the CEP. We consider two shapes for the volume, spherical and cubic regions with different sizes and different boundary conditions. To analyze the QCD phase diagram, we use a novel criterion to study the crossover zone. A comparison between the results obtained from the two different shapes and several boundary conditions is carried out. We use the method of Multiple Reflection Expansion to determine the density of states and three kinds of boundary conditions over the cubic shape. These boundary conditions are: periodic, anti-periodic and stationary boundary conditions on the quark fields.

Thermal Axion Production at Low Temperatures: A Smooth Treatment of the QCD Phase Transition

We study thermal axion production around the confinement scale. At higher temperatures, we extend current calculations to account for the masses of heavy quarks, whereas we quantify production via hadron scattering at lower temperatures. Matching our results between the two opposite regimes provides us with a continuous axion production rate across the QCD phase transition. We employ such a rate to quantify the axion contribution to the effective number of neutrino species.

Cosmology Meets Functional QCD: First-Order Cosmic QCD Transition Induced by Large Lepton Asymmetries

The lepton flavor asymmetries of the Universe are observationally almost unconstrained before the onset of neutrino oscillations. We calculate the cosmic trajectory during the cosmic QCD epoch in the presence of large lepton flavor asymmetries. By including QCD thermodynamic quantities derived from functional QCD methods in our calculation, our work reveals for the first time the possibility of a first-order cosmic QCD transition. We specify the required values of the lepton flavor asymmetries for which a first-order transition occurs for a number of different benchmark scenarios.

Overview of recent lattice QCD results: phase diagram, fluctuations and strangeness

In recent years there has been much progress on the investigation of the QCD phase diagram with lattice QCD. This work will focus on the developments in the last few years with physical parameters and low chemical potential which are obtained by extrapolations from zero or imaginary chemical potential.

QCD Critical Point and Net-Proton Number Fluctuations at RHIC-STAR

In the search of QCD phase boundary and critical point, higher-order cumulants of conserved quantities are proposed as promising observables and have been studied extensively both experimentally and theoretically. In this paper we present cumulant ratios up to 6th-order of net-proton number distributions in Au+Au collisions at √SNN = 7.7 - 200 GeV from STAR Beam Energy Scan program phase I and √S = 200 GeV p + p collisions. The results are compared with various models and Lattice QCD calculations.

Finite chemical potential equation of state for QCD from an alternative expansion scheme

The Taylor expansion approach to the equation of state of QCD at finite chemical potential struggles to reach large chemical potential μB. This is primarily due to the intrinsic diffculty in precisely determining higher order Taylor coefficients, as well as the structure of the temperature dependence of such observables. In these proceedings, we illustrate a novel scheme [1] that allows us to extrapolate the equation of state of QCD without suffering from the poor convergence typical of the Taylor expansion approach. We continuum extrapolate the coefficients of our new expansion scheme and show the thermodynamic observables up to μB/T ≤ 3.5.

Probing Compressed Baryonic Matter

The objective of the compressed baryonic matter (CBM) experiment at the future Facility for Antiproton and Ion Research (FAIR) in Darmstadt, Germany, is the investigation of the fundamental properties of strongly interacting matter. Of particular interest for our understanding of compact stellar objects is the determination of the equation-of-state (EOS) at high baryon densities and the exploration of the microscopic degrees-of-freedom under these conditions. The results of these laboratory experiments will complement astronomical observations, which also constrain the high-density EOS. Recent results of QCD-based calculations suggest that a possible first-order chiral phase transition should be observable in heavy-ion collisions at FAIR energies. This article reviews relevant observables from heavy-ion collisions and describes the detector configuration and the physics performance of the CBM experiment.

Neutron Star Mergers and the Quark Matter Equation of State

As neutron stars merge they can approach very high nuclear density. Here, we summarized recent results for the evolution and gravitational wave emission from binary-neutron star mergers using a a variety of nuclear equations of state with and without a crossover transition to quark matter. We discuss how the late time gravitational wave emission from binary neutron star mergers may possibly reveal the existence of a crossover transition to quark matter.

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.

Accidentally Asymmetric Dark Matter

We study the effect of a first-order phase transition in a confining SU(N) dark sector with heavy dark quarks. The baryons of this sector are the dark matter candidates. During the confinement phase transition the heavy quarks are trapped inside isolated, contracting pockets of the deconfined phase, giving rise to a second stage of annihilation that dramatically suppresses the dark quark abundance. The surviving abundance is determined by the local accidental asymmetry in each pocket. The correct dark matter abundance is obtained for O(1-100)  PeV dark quarks, above the usual unitarity bound.

Lattice Constraints on the QCD Chiral Phase Transition at Finite Temperature and Baryon Density

The thermal restoration of chiral symmetry in QCD is known to proceed by an analytic crossover, which is widely expected to turn into a phase transition with a critical endpoint as the baryon density is increased. In the absence of a genuine solution to the sign problem of lattice QCD, simulations at zero and imaginary baryon chemical potential in a parameter space enlarged by a variable number of quark flavours and quark masses constitute a viable way to constrain the location of a possible non-analytic phase transition and its critical endpoint. In this article I review recent progress towards an understanding of the nature of the transition in the massless limit, and its critical temperature at zero density. Combined with increasingly detailed studies of the physical crossover region, current data bound a possible critical point to μB ≳ 3T.

Degeneracy Patterns of Chiral Companions at Finite Temperature

Chiral symmetry represents a fundamental concept lying at the core of particle and nuclear physics. Its spontaneous breaking in vacuum can be exploited to distinguish chiral hadronic partners, whose masses differ. In fact, the features of this breaking serve as guiding principles for the construction of effective approaches of QCD at low energies, e.g., the chiral perturbation theory, the linear sigma model, the (Polyakov)–Nambu–Jona-Lasinio model, etc. At high temperatures/densities chiral symmetry can be restored bringing the chiral partners to be nearly degenerated in mass. At vanishing baryochemical potential, such restoration follows a smooth transition, and the chiral companions reach this degeneration above the transition temperature. In this work I review how different realizations of chiral partner degeneracy arise in different effective theories/models of QCD. I distinguish the cases where the chiral states are either fundamental degrees of freedom or (dynamically-generated) composed states. In particular, I discuss the intriguing case in which chiral symmetry restoration involves more than two chiral partners, recently addressed in the literature.

The Gamma-ray Window to Intergalactic Magnetism

One of the most promising ways to probe intergalactic magnetic fields (IGMFs) is through gamma rays produced in electromagnetic cascades initiated by high-energy gamma rays or cosmic rays in the intergalactic space. Because the charged component of the cascade is sensitive to magnetic fields, gamma-ray observations of distant objects such as blazars can be used to constrain IGMF properties. Ground-based and space-borne gamma-ray telescopes deliver spectral, temporal, and angular information of high-energy gamma-ray sources, which carries imprints of the intervening magnetic fields. This provides insights into the nature of the processes that led to the creation of the first magnetic fields and into the phenomena that impacted their evolution. Here we provide a detailed description of how gamma-ray observations can be used to probe cosmic magnetism. We review the current status of this topic and discuss the prospects for measuring IGMFs with the next generation of gamma-ray observatories.

Lattice QCD Equation of State at Finite Chemical Potential from an Alternative Expansion Scheme

In this Letter, we introduce a novel scheme for extrapolating the equation of state of QCD to finite chemical potential that features considerably improved convergence properties and allows us to extend its reach to unprecedentedly high baryonic chemical potentials. We present continuum extrapolated lattice results for the new expansion coefficients and show the thermodynamic observables up to μ_{B}/T≤3.5. This novel expansion does not suffer from the shortcomings that characterize the traditional Taylor expansion method, such as difficulties inherent in performing such an expansion with a limited number of coefficients and the poor signal-to-noise ratio that affects Taylor coefficients determined from lattice calculations.

Localization of Dirac Fermions in Finite-Temperature Gauge Theory

It is by now well established that Dirac fermions coupled to non-Abelian gauge theories can undergo an Anderson-type localization transition. This transition affects eigenmodes in the lowest part of the Dirac spectrum, the ones most relevant to the low-energy physics of these models. Here we review several aspects of this phenomenon, mostly using the tools of lattice gauge theory. In particular, we discuss how the transition is related to the finite-temperature transitions leading to the deconfinement of fermions, as well as to the restoration of chiral symmetry that is spontaneously broken at low temperature. Other topics we touch upon are the universality of the transition, and its connection to topological excitations (instantons) of the gauge field and the associated fermionic zero modes. While the main focus is on Quantum Chromodynamics, we also discuss how the localization transition appears in other related models with different fermionic contents (including the quenched approximation), gauge groups, and in different space-time dimensions. Finally, we offer some speculations about the physical relevance of the localization transition in these models.

Probing Dense Nuclear Matter in the Laboratory: Experiments at FAIR and NICA

The poorly known properties of high-density strongly-interacting matter govern the structure of neutron stars and the dynamics of neutron star mergers. New insight has been and will be gained by astronomical observations, such as the measurement of mass and radius of neutron stars, and the detection of gravitational waves emitted from neutron star mergers. Alternatively, information on the Nuclear Matter Equation-of-State (EOS) and on a possible phase transition from hadronic to quark matter at high baryon densities can be obtained from laboratory experiments investigating heavy-ion collisions. Detector systems dedicated to such experiments are under construction at the “Facility for Antiproton and Ion Research” (FAIR) in Darmstadt, Germany, and at the “Nuclotron-based Ion Collider fAcility” (NICA) in Dubna, Russia. In heavy-ion collisions at these accelerator centers, one expects the creation of baryon densities of up to 10 times saturation density, where quark degrees-of-freedom should emerge. This article reviews the most promising observables in heavy-ion collisions, which are used to probe the high-density EOS and possible phase transition from hadronic to quark matter. Finally, the facilities and the experimental setups will be briefly described.

Overview of the QCD phase diagram: Recent progress from the lattice

In recent years there has been much progress on the investigation of the QCD phase diagram with lattice QCD simulations. In this review we focus on the developments in the last two years. Especially the addition of external influences or new parameter ranges yields an increasing number of interesting results. We discuss the progress for small, finite densities from both extrapolation-based methods (Taylor expansion and analytic continuation for imaginary chemical potential) and complex Langevin simulations, for heavy quark bound states (quarkonium), the dependence on the quark masses (Columbia plot) and the influence of a magnetic field. Many of these conditions are relevant for the understanding of both the QCD transition in the early universe and heavy ion collision experiments, which are conducted for example at the LHC and RHIC.

Nonequilibrium Dynamics of the Chiral Quark Condensate under a Strong Magnetic Field

Strong magnetic fields impact quantum-chromodynamics (QCD) properties in several situations; examples include the early universe, magnetars, and heavy-ion collisions. These examples share a common trait—time evolution. A prominent QCD property impacted by a strong magnetic field is the quark condensate, an approximate order parameter of the QCD transition between a high-temperature quark-gluon phase and a low-temperature hadronic phase. We use the linear sigma model with quarks to address the quark condensate time evolution under a strong magnetic field. We use the closed time path formalism of nonequilibrium quantum field theory to integrate out the quarks and obtain a mean-field Langevin equation for the condensate. The Langevin equation features dissipation and noise kernels controlled by a damping coefficient. We compute the damping coefficient for magnetic field and temperature values achieved in peripheral relativistic heavy-ion collisions and solve the Langevin equation for a temperature quench scenario. The magnetic field changes the dissipation and noise pattern by increasing the damping coefficient compared to the zero-field case. An increased damping coefficient increases fluctuations and time scales controlling condensate’s short-time evolution, a feature that can impact hadron formation at the QCD transition. The formalism developed here can be extended to include other order parameters, hydrodynamic modes, and system’s expansion to address magnetic field effects in complex settings as heavy-ion collisions, the early universe, and magnetars.

Nonmonotonic Energy Dependence of Net-Proton Number Fluctuations

Nonmonotonic variation with collision energy (sqrt[s_{NN}]) of the moments of the net-baryon number distribution in heavy-ion collisions, related to the correlation length and the susceptibilities of the system, is suggested as a signature for the quantum chromodynamics critical point. We report the first evidence of a nonmonotonic variation in the kurtosis times variance of the net-proton number (proxy for net-baryon number) distribution as a function of sqrt[s_{NN}] with 3.1  σ significance for head-on (central) gold-on-gold (Au+Au) collisions measured solenoidal tracker at Relativistic Heavy Ion Collider. Data in noncentral Au+Au collisions and models of heavy-ion collisions without a critical point show a monotonic variation as a function of sqrt[s_{NN}].

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.

Mass distribution of magnetized quark-nugget dark matter and comparison with requirements and observations

Quark nuggets are a candidate for dark matter consistent with the Standard Model. Previous models of quark nuggets have investigated properties arising from their being composed of strange, up, and down quarks and have not included any effects caused by their self-magnetic field. However, Tatsumi found that the core of a magnetar star may be a quark nugget in a ferromagnetic state with core magnetic field Bsurface = 1012±1 T. We apply Tatsumi’s result to quark-nugget dark-matter and report results on aggregation of magnetized quark nuggets (MQNs) after formation from the quark-gluon plasma until expansion of the universe freezes out the mass distribution to ~ 10−24 kg to ~ 1014 kg. Aggregation overcomes weak-interaction decay. Computed mass distributions show MQNs are consistent with requirements for dark matter and indicate that geologic detectors (craters in peat bogs) and space-based detectors (satellites measuring radio-frequency emissions after passage through normal matter) should be able to detect MQN dark matter. Null and positive observations narrow the range of a key parameter Bo ~ Bsurface to 1 × 1011 T < Bo ≤ 3 × 1012 T.

Radio frequency emissions from dark-matter-candidate magnetized quark nuggets interacting with matter

Quark nuggets are theoretical objects composed of approximately equal numbers of up, down, and strange quarks. They are also called strangelets, nuclearites, AQNs, slets, Macros, and MQNs. Quark nuggets are a candidate for dark matter, which has been a mystery for decades despite constituting ~ 85% of the universe's mass. Most previous models of quark nuggets have assumed no intrinsic magnetic field; however, Tatsumi found that quark nuggets may exist in magnetars as a ferromagnetic liquid with a magnetic field BS = 1012±1 T. We apply that result to quark nuggets, a dark-matter candidate consistent with the Standard Model, and report results of analytic calculations and simulations that show they spin up and emit electromagnetic radiation at ~ 104 to ~ 109 Hz after passage through planetary environments. The results depend strongly on the value of Bo, which is a parameter to guide and interpret observations. A proposed sensor system with three satellites at 51,000 km altitude illustrates the feasibility of using radio-frequency emissions to detect 0.003 to 1,600 MQNs, depending on Bo, during a 5 year mission.

QCD Crossover at Finite Chemical Potential from Lattice Simulations

We provide the most accurate results for the QCD transition line so far. We optimize the definition of the crossover temperature T_{c}, allowing for its very precise determination, and extrapolate from imaginary chemical potential up to real μ_{B}≈300  MeV. The definition of T_{c} adopted in this work is based on the observation that the chiral susceptibility as a function of the condensate is an almost universal curve at zero and imaginary μ_{B}. We obtain the parameters κ_{2}=0.0153(18) and κ_{4}=0.00032(67) as a continuum extrapolation based on N_{t}=10, 12, 16 lattices with physical quark masses. We also extrapolate the peak value of the chiral susceptibility and the width of the chiral transition along the crossover line. In fact, both of these are consistent with a constant function of μ_{B}. We see no sign of criticality in the explored range.

Searching the QCD critical endpoint with lattice simulations

We discuss the usefulness of various lattice observables especially fluctuations to locate the QCD critical endpoint. We apply different models to interpret our results for the baryon fluctuations up to µ8 from simulations at imaginary chemical potentials.