Finite Baryon Density Research Articles

QCD equation of state and cosmological parameters in the early universe

The time evolution of cosmological parameters in the early Universe at the deconfinement transition is studied by an equation of state (EoS) which takes into account the finite baryon density and the background magnetic field. The nonperturbative dynamics is described by the field correlator method which gives, with a small number of free parameters, a good fit of lattice data. The entire system has two components, i.e., the quark-gluon plasma and the electroweak sector, and the solutions of the Friedmann equation show that the scale factors $a(t)$ and $H(t)=(1/a)da/dt$ are weakly dependent on the EoS, but the deceleration parameter $q(t)$ and the jerk $j(t)$ are strongly modified above the critical temperature ${T}_{c}$, corresponding to a critical time ${t}_{c}\ensuremath{\simeq}20--25\text{ }\text{ }\ensuremath{\mu}\mathrm{s}$. The time evolution of the cosmological parameters suggests that above and around ${T}_{c}$, there is a transient state of acceleration typical of a matter-dominated universe; this is entailed by the QCD strong interaction. The effect of the hadronic matter below ${T}_{c}$ does not qualitatively change the previous behavior and one can consistently follow the cosmological evolution up to $100\text{ }\text{ }\ensuremath{\mu}\mathrm{s}$.

A 3d effective lattice theory for phase transitions in Yang-Mills and heavy dense QCD

QCD thermodynamics is crucial for the physics of the early universe, heavy ion collisions and compact stars. However, predictions by lattice simulations are very costly or, in the case of finite baryon density, even impossible because of a sign problem. Starting from Yang- Mills theory, I review how to use strong coupling methods to construct a 3d effective theory which reproduces the deconfinement phase transition to about 10% accuracy. The generalisation to QCD, which is valid for heavy quarks, has only a mild sign problem in the case of finite density and can be simulated efficiently. Moreover, it allows to address the nuclear liquid gas transition in the cold and dense regime for the first time directly from QCD.

Effective model for the QCD phase transitions at finite baryon density

We introduce an effective quark-meson-nucleon model for the QCD phase transitions at finite baryon density. The nucleon and the quark degrees of freedom are described within a unified framework of a chiral linear sigma model. The deconfinement transition is modeled through a simple modification of the distribution functions of nucleons and quarks, where an additional auxiliary field, the bag field, is introduced. The bag field plays a key role in converting between the nucleon and the quark degrees of freedom. The model predicts that the chiral and the deconfinement phase transitions are always separated. Depending on the model parameters, the chiral transition occurs in the baryon density range of $(1.5-15.5)n_0$, while the deconfinement transition occurs above $5 n_0$, where $n_0$ is the saturation density.

Holographic Skyrmions

Skyrmions are topological solitons that describe baryons within a nonlinear theory of pions. In holographic QCD, baryons correspond to topological solitons in a bulk theory with an extra spatial dimension. Thus, the three-dimensional Skyrmion lifts to a four-dimensional holographic Skyrmion in the bulk. We begin this review with a description of the simplest example of this correspondence, where the holographic Skyrmion is exactly the self-dual Yang–Mills instanton in flat space. This places an old result of Atiyah and Manton within a holographic framework and reveals that the associated Skyrme model extends the nonlinear pion theory to include an infinite tower of vector mesons, with specific couplings for a BPS theory. We then describe the more complicated curved space version that arises from the string theory construction of Sakai and Sugimoto. The basic concepts remain the same but the technical difficulty increases as the holographic Skyrmion is a curved space version of the Yang–Mills instanton, so self-duality and integrability are lost. Finally, we turn to a low-dimensional analog of holographic Skyrmions, where aspects such as multi-baryons and finite baryon density are amenable to both numerical computation and an approximate analytic treatment.

Taming the pion condensation in QCD at finite baryon density: a numerical test in a random matrix model

In the Monte Carlo study of QCD at finite baryon density based upon the phase reweighting method, the pion condensation in the phase-quenched theory and associated zero-mode prevent us from going to the low-temperature high-density region. We propose a method to circumvent them by a simple modification of the density of state method. We first argue that the standard version of the density of state method, which is invented to solve the overlapping problem, is effective only for a certain ‘good’ class of observables. We then modify it so as to solve the overlap problem for ‘bad’ observables as well. While, in the standard version of the density of state method, we usually constrain an observable we are interested in, we fix a different observable in our new method which has a sharp peak at some particular value characterizing the correct vacuum of the target theory. In the finite-density QCD, such an observable is the pion condensate. The average phase becomes vanishingly small as the value of the pion condensate becomes large, hence it is enough to consider configurations with π+ ≃ 0, where the zero mode does not appear. We demonstrate an effectiveness of our method by using a toy model (the chiral random matrix theory) which captures the properties of finite-density QCD qualitatively. We also argue how to apply our method to other theories including finite-density QCD. Although the example we study numerically is based on the phase reweighting method, the same idea can be applied to more general reweighting methods and we show how this idea can be applied to find a possible QCD critical point.

Bulk and shear viscosities of hot and dense hadron gas

We estimate bulk and shear viscosity at finite temperature and baryon densities of hadronic matter within hadron resonance gas model. For bulk viscosity we use low energy theorems of QCD for the energy momentum tensor correlators. For shear viscosity coefficient, we estimate the same using molecular kinetic theory to relate the shear viscosity coefficient to average momentum of the hadrons in the hot and dense hadron gas. The bulk viscosity to entropy ratio increases with chemical potential and is related to the reduction of velocity of sound at nonzero chemical potential. The shear viscosity to entropy ratio on the other hand, shows a nontrivial behavior with the ratio decreasing with chemical potential for small temperatures but increasing with chemical potential at high temperatures and is related to decrease of entropy density with chemical potential at high temperature due to finite volume of the hadrons.

Heavy dense QCD and nuclear matter from an effective lattice theory

A three-dimensional effective lattice theory of Polyakov loops is derived from QCD by expansions in the fundamental character of the gauge action, u, and the hopping parameter, \kappa, whose action is correct to \kappa^n u^m with n+m=4. At finite baryon density, the effective theory has a sign problem which meets all criteria to be simulated by complex Langevin as well as by Monte Carlo on small volumes. The theory is valid for the thermodynamics of heavy quarks, where its predictions agree with simulations of full QCD at zero and imaginary chemical potential. In its region of convergence, it is moreover amenable to perturbative calculations in the small effective couplings. In this work we study the challenging cold and dense regime. We find unambiguous evidence for the nuclear liquid gas transition once the baryon chemical potential approaches the baryon mass, and calculate the nuclear equation of state. In particular, we find a negative binding energy per nucleon causing the condensation, whose absolute value decreases exponentially as mesons get heavier. For decreasing meson mass, we observe a first order liquid gas transition with an endpoint at some finite temperature, as well as gap between the onset of isospin and baryon condensation.

Beam energy scan using a viscous hydro+cascade model

Following the experimental program at BNL RHIC, we perform a similar "energy scan" using 3+1D viscous hydrodynamics coupled to the UrQMD hadron cascade, and study the collision energy dependence of pion and kaon rapidity distributions and mT-spectra, as well as charged hadron elliptic flow. To this aim the equation of state for finite baryon density from a Chiral model coupled to the Polyakov loop is employed for hydrodynamic stage. 3D initial conditions from UrQMD are used to study gradual deviation from boost-invariant scaling flow. We find that the inclusion of shear viscosity in the hydrodynamic stage of evolution consistently improves the description of the data for Pb-Pb collisions at CERN SPS, as well as of the elliptic flow measurements for Au-Au collisions in the Beam Energy Scan (BES) program at BNL RHIC. The suggested value of shear viscosity is η/s ≥ 0.2 for = 6.3... 39 GeV.

3+1 dimensional viscous hydrodynamics at high baryon densities

We apply a 3+1D viscous hydrodynamic + cascade model to heavy ion collision reactions with = 6.3... 39 GeV. To accommodate the model for a given collision energy range, the initial conditions for the hydrodynamic phase are taken from UrQMD, and the equation of state at finite baryon density is based on a Chiral model coupled to the Polyakov loop.We study the collision energy dependence of pion and kaon rapidity distributions and mT-spectra, as well as charged hadron elliptic flow and how shear viscosity affects them. The model calculations are compared to the data for Pb-Pb collisions at CERN SPS, as well as for Au-Au collisions in the Beam Energy Scan (BES) program energies at BNL RHIC. The data favours the value of shear viscosity η/s ≳ 0.2 for this collision energy range.

Holographic zero sound at finite temperature in the Sakai-Sugimoto model

In this paper, we study the fate of the holographic zero sound mode at finite temperature and non-zero baryon density in the deconfined phase of the Sakai-Sugimoto model of holographic QCD. We establish the existence of such a mode for a wide range of temperatures and investigate the dispersion relation, quasi-normal modes, and spectral functions of the collective excitations in four different regimes, namely, the collisionless quantum, collisionless thermal, and two distinct hydrodynamic regimes. For sufficiently high temperatures, the zero sound completely disappears, and the low energy physics is dominated by an emergent diffusive mode. We compare our findings to Landau-Fermi liquid theory and to other holographic models.

Sign problem and the chiral spiral on the finite density lattice

We investigate the sign problem of the fermion determinant at finite baryon density in (1+1) dimensions, in which the ground state in the chiral limit should be free from the sign problem by forming a chiral spiral. To confirm it, we evaluate the fermion determinant in the continuum theory at the one-loop level and find that the determinant becomes real as expected. The conventional lattice formulation to implement a chemical potential is, however, not compatible with the spiral transformation. We discuss an alternative of the finite-density formulation and numerically verify the chiral spiral on the finite-density lattice.

BCS–BEC CROSSOVER IN RELATIVISTIC FERMI SYSTEMS

We review the BCS–BEC crossover in relativistic Fermi systems, including the QCD matter at finite density. In the first part, we study the BCS–BEC crossover in a relativistic four-fermion interaction model and show how the relativistic effect affects the BCS–BEC crossover. In the second part, we investigate both two-color QCD at finite baryon density and pion superfluid at finite isospin density, by using an effective Nambu–Jona–Lasinio model. We will show how the model describes the weakly interacting diquark and pion condensates at low density and the BEC–BCS crossover at high density.

Bulk viscosity of quark-gluon matter in a magnetic field

On the basis of low-energy QCD theorems, the bulk viscosity ζ(T, µ, H) is expressed in terms of basic thermodynamic quantities that characterizes quark-gluon matter at finite temperature and a finite baryon density in a magnetic field. Various limiting cases are considered.

The density in the density of states method

It has been suggested that for QCD at finite baryon density the distribution of the phase angle, i.e. the angle defined as the imaginary part of the logarithm of the fermion determinant, has a simple Gaussian form. This distribution provides the density in the density of states approach to the sign problem. We calculate this phase angle distribution using i) the hadron resonance gas model; and ii) a combined strong coupling and hopping parameter expansion in lattice gauge theory. While the former model leads only to a Gaussian distribution, in the latter expansion we discover terms which cause the phase angle distribution to deviate, by relative amounts proportional to powers of the inverse lattice volume, from a simple Gaussian form. We show that despite the tiny inverse-volume deviation of the phase angle distribution from a simple Gaussian form, such non-Gaussian terms can have a substantial impact on observables computed in the density of states/reweighting approach to the sign problem.

Inverse magnetic catalysis induced by sphalerons

The recently discovered inverse magnetic catalysis around the critical temperature indicates that some important information is missing in our current understanding of conventional chiral dynamics of QCD, which is enhanced by the magnetic field. In this work, we provide a mechanism to explain that the inverse magnetic catalysis around the critical temperature is induced by sphalerons. At high temperatures, sphaleron transitions between distinct classical vacua cause an asymmetry between the number of right- and left-handed quarks due to the axial anomaly of QCD. In the presence of a strong magnetic field, the chiral imbalance is enhanced and destroys the right- and left-handed pairings, which naturally induces a decreasing critical temperature of the chiral phase transition for increasing magnetic field. The inverse magnetic catalysis at finite baryon density, and the critical end point in the presence of a strong magnetic field is also explored in this work.

The shear viscosity of a chemically equilibrating quark-gluon plasma at finite baryon density

Taking account of elastic and bremsstrahlung processes, as well as quark elastic scattering, we calculated the shear viscous coefficient of a chemically equilibrating quark-gluon plasma at finite baryon density. We found that the inelastic bremsstrahlung processes make the shear viscosity remarkably lower, and the ratio of shear viscosity to entropy density increases with increasing initial quark chemical potential. Considering the effect of shear viscosity the evolution of the QGP system was investigated. We found that the evolution of the system becomes slower owing to viscosity compared to the one in the ideal case, and the inelastic bremsstrahlung processes make the slower rate of the system not as much as in our previous calculations.

Ultracold quantum gases and lattice systems: quantum simulation of lattice gauge theories

Abelian and non‐Abelian gauge theories are of central importance in many areas of physics. In condensed matter physics, Abelian U(1) lattice gauge theories arise in the description of certain quantum spin liquids. In quantum information theory, Kitaev's toric code is a lattice gauge theory. In particle physics, Quantum Chromodynamics (QCD), the non‐Abelian gauge theory of the strong interactions between quarks and gluons, is non‐perturbatively regularized on a lattice. Quantum link models extend the concept of lattice gauge theories beyond the Wilson formulation, and are well suited for both digital and analog quantum simulation using ultracold atomic gases in optical lattices. Since quantum simulators do not suffer from the notorious sign problem, they open the door to studies of the real‐time evolution of strongly coupled quantum systems, which are impossible with classical simulation methods. A plethora of interesting lattice gauge theories suggests itself for quantum simulation, which should allow us to address very challenging problems, ranging from confinement and deconfinement, or chiral symmetry breaking and its restoration at finite baryon density, to color superconductivity and the real‐time evolution of heavy‐ion collisions, first in simpler model gauge theories and ultimately in QCD.

Dissipative hydrodynamic effects on the quark-gluon plasma at finite baryon density

The quark-gluon plasma behaves as a relativistic viscous fluid in high-energy heavy ion collisions. I develop a causal dissipative hydrodynamic model at finite baryon density for RHIC and LHC to estimate the net baryon rapidity distribution. The net baryon number is found to be carried to forward rapidity by the flow, effectively enhancing the transparency of the collisions. This suggests that the energy available for the production of a hot medium could be larger than that naively implied from experimental data. Also the distribution can be sensitive to baryon dissipation as much as to shear and bulk viscosity.

Hydrodynamics of anisotropic quark and gluon fluids

The recently developed framework of anisotropic hydrodynamics is generalized to describe the dynamics of coupled quark and gluon fluids. The quark and gluon components of the fluids are characterized by different dynamical anisotropy parameters. The dynamical equations describing such mixtures are derived from kinetic theory, with the collisional kernel treated in the relaxation-time approximation, allowing for different relaxation times for quarks and gluons. Baryon number conservation is enforced in the quark and antiquark components of the fluid, but overall parton number nonconservation is allowed in the system. The resulting equations are solved numerically in the ($0+1$)--dimensional boost-invariant case at zero and finite baryon density.

Probing the QCD chiral cross-over transition in heavy ion collisions

Abstract We argue that by measuring higher moments of the net proton number fluctuations in heavy ion collisions (HIC) one can probe the QCD chiral cross-over transition experimentally. We discuss the properties of fluctuations of the net baryon number in the vicinity of the chiral cross-over transition within the Polyakov loop extended quark-meson model at finite temperature and baryon density. The calculation includes non-perturbative dynamics implemented within the functional renormalization group approach. We find a clear signal for the chiral cross-over transition in the fluctuations of the net baryon number. We address our theoretical findings to experimental data of the STAR Collaboration on energy and centrality dependence of the net proton number fluctuations and their probability distributions in HIC.