Finite Baryon Density Research Articles

Thermodynamic equation of state of magnetized PNJL model of $$2+1$$ flavor at finite baryonic density

Thermodynamic equation of state of magnetized PNJL model of $$2+1$$ flavor at finite baryonic density

Spatially oscillating correlation functions in ( 2+1 )-dimensional four-fermion models: The mixing of scalar and vector modes at finite density

In this work, we demonstrate that the mixing of scalar and vector condensates produces spatially oscillating, but exponentially damped correlation functions in fermionic theories at finite density and temperature. We find a regime exhibiting this oscillatory behavior in a Gross-Neveu-type model that also features vector interactions within the mean-field approximation. The existence of this regime aligns with expectations based on symmetry arguments that are also applicable to QCD at finite baryon density. We compute the phase diagram including both homogeneous phases and regions with spatially oscillating, exponentially damped correlation functions at finite temperature and chemical potential for different strengths of the vector coupling. Furthermore, we find that inhomogeneous condensates are disfavored compared to homogeneous ones akin to previous findings without vector interactions. We show that our results are valid for a broad class of (2+1)-dimensional models with local four-fermion interactions. Published by the American Physical Society 2024

Polarization dynamics in the paramagnet of a charged quark-gluon plasma

It is commonly understood that the strong magnetic field produced in heavy ion collisions is short-lived. The electric conductivity of the quark-gluon plasma is unable to significantly extend the lifetime of the magnetic field. We propose an alternative scenario to achieve this: with finite baryon density and spin polarization by the initial magnetic field, the quark-gluon plasma behaves as a paramagnet, which may continue to polarize the quark after fading of the initial magnetic field. We confirm this picture by calculations in both quantum electrodynamics and quantum chromodynamics. In the former case, we find a splitting in the damping rates of probe fermions with an opposite spin component along the magnetic field. In the latter case, we find a similar splitting in damping rate of the probe quark in quark-gluon plasma in both high and low density limits. The splitting provides a way of polarizing strange quarks by the quark-gluon plasma paramagnet consisting of light quarks, which effectively extends the lifetime of the magnetic field in heavy ion collisions. Published by the American Physical Society 2024

Ordered Patterns of (3+1)-Dimensional Hadronic Gauged Solitons in the Low-Energy Limit of Quantum Chromodynamics at a Finite Baryon Density, Their Magnetic Fields and Novel BPS Bounds

In this paper, we will review two analytical approaches to the construction of non-homogeneous Baryonic condensates in the low-energy limit of QCD in (3+1) dimensions. In both cases, the minimal coupling with the Maxwell U(1) gauge field can be taken explicitly into account. The first approach (which is related to the generalization of the usual spherical hedgehog ansatz to situations without spherical symmetry at a finite Baryon density) allows for the construction of ordered arrays of Baryonic tubes and layers. When the minimal coupling of the Pions to the U(1) Maxwell gauge field is taken into account, one can show that the electromagnetic field generated by these inhomogeneous Baryonic condensates is of a force-free type (in which the electric and magnetic components have the same size). Thus, it is natural to wonder whether it is also possible to analytically describe magnetized hadronic condensates (namely, Hadronic distributions generating only a magnetic field). The idea of the second approach is to construct a novel BPS bound in the low-energy limit of QCD using the theory of the Hamilton–Jacobi equation. Such an approach allows us to derive a new topological bound which (unlike the usual one in the Skyrme model in terms of the Baryonic charge) can actually be saturated. The nicest example of this phenomenon is a BPS magnetized Baryonic layer. However, the topological charge appearing naturally in the BPS bound is a non-linear function of the Baryonic charge. Such an approach allows us to derive important physical quantities (which would be very difficult to compute with other methods), such as how much one should increase the magnetic flux in order to increase the Baryonic charge by one unit. The novel results of this work include an analysis of the extension of the Hamilton–Jacobi approach to the case in which Skyrme coupling is not negligible. We also discuss some relevant properties of the Dirac operator for quarks coupled to magnetized BPS layers.

Relaxation time for the alignment between quark spin and angular velocity in a rotating QCD medium

We compute the relaxation times for massive quarks and antiquarks to align their spins with the angular velocity in a rigidly rotating medium at finite temperature and baryon density. The rotation effects are implemented using a fermion propagator immersed in a cylindrical rotating environment. The relaxation time is computed as the inverse of the interaction rate to produce an asymmetry between the quark (antiquark) spin components along and opposite to the angular velocity. For conditions resembling heavy-ion collisions, the relaxation times for quarks are smaller than for antiquarks. For semicentral collisions, the relaxation time for quarks is within the possible lifetime of the QGP for all collision energies. However, for antiquarks, this happens only for collision energies sNN≳50 GeV. The results are quantified in terms of the intrinsic quark and antiquark polarizations, namely, the probability to build the spin asymmetry as a function of time. Our results show that these intrinsic polarizations tend to 1 with time at different rates given by the relaxation times with quarks reaching a sizable asymmetry at a faster pace. These are key results to further elucidate the mechanisms of hyperon polarization in relativistic heavy-ion collisions. Published by the American Physical Society 2024

Cold and dense perturbative QCD in a very strong magnetic background

We compute the pressure from first principles within perturbative QCD at finite baryon density and very high magnetic fields up to two-loops and with physical quark masses. The region of validity for our framework is given by ms≪μq≪eB, where ms is the strange quark mass, μq is the quark chemical potential, e is the fundamental electric charge, and B is the magnetic field strength. We include the effects of the renormalization scale in the running coupling, αs(μq,eB), and running strange quark mass. We also discuss the simplifications that come about in the chiral limit. The effectively negligible contribution of the exchange diagram allows for building a simple analytic model for the equation of state for pure quark magnetars and computing their mass and radius at very large values of B. These results provide constraints on the behavior of the maximum mass and associated radius from perturbative QCD. We also discuss the magnetic bag model for extreme magnetic fields. Published by the American Physical Society 2024

Pearcey integrals, Stokes lines and exact baryonic layers in the low energy limit of QCD

The first analytic solutions representing baryonic layers living at finite baryon density within a constant magnetic field in the gauged Skyrme model are constructed. A remarkable feature of these configurations is that, if the Skyrme term is neglected, then these baryonic layers in the constant magnetic background cannot be found analytically and their energies grow very fast with the magnetic field. On the other hand, if the Skyrme term is taken into account, the field equations can be solved analytically and the corresponding solutions have a smooth limit for large magnetic fields. Thus, the Skyrme term discloses the universal character of these configurations living at finite Baryon density in a constant magnetic field. The classical gran-canonical partition function of these configurations can be expressed explicitly in terms of the Pearcey integral. This fact allows us to determine analytically the Stokes lines of the partition function and the corresponding dependence on the baryonic chemical potential as well as on the external magnetic field. In this way, we can determine various critical curves in the (μB−Bext) plane which separates different physical behaviors. These families of inhomogeneous baryonic condensates can be also dressed with chiral conformal excitations of the solutions representing modulations of the layers themselves. Some physical consequences are analyzed.

Correlations of conserved quantities at finite baryon density

Correlations of conserved quantities at finite baryon density

Equation of state of a hot-and-dense quark gluon plasma: Lattice simulations at real μB vs. extrapolations

The equation of state of the quark gluon plasma is a key ingredient of heavy ion phenomenology. In addition to the traditional Taylor method, several novel approximation schemes have been proposed with the aim of calculating it at finite baryon density. In order to gain a pragmatic understanding of the limits of these schemes, we compare them to direct results at μB > 0, using reweighting techniques free from an overlap problem. We use 2stout improved staggered fermions with 8 time-slices and cover the entire RHIC BES range in the baryochemical potential, up to μB/T = 3. This work is based on Ref. [1].

QCD equation of state with improved precision from lattice simulations

The equation of state of Quantum Chromodynamics has been in recent years the focus of intense effort from first principle methods, mostly lattice simulations, with particular interest to the finite baryon density regime. Because of the sign problem, various extrapolation methods have been used to reconstruct bulk properties of the theory up to as far as μB=T ≃ 3:5. However, said efforts rely on the equation of state at vanishing baryon density as an integration constant, which up to μB=T ≃ 2 - 2:5 proves to be the dominant source of uncertainty at the level of precision currently available. In this contribution we present the update of our equation of state at zero net baryon density from 2014, performing a continuum limit from lattices with Nτ = 8; 10; 12; 16. We show how the improved precision is translated in a lower uncertainty on the extrapolated equation of state at finite chemical potential.

Dual simulation of a Polyakov loop model at finite baryon density: Correlations and screening masses

Computations of screening masses in finite-temperature QCD at finite density are plagued by the sign problem and have been performed so far with an imaginary chemical potential. Here, we use a dual formulation of a Polyakov-loop model which allows the determination of screening masses at real baryon chemical potential. This is a second paper in a series devoted to a detailed study of dual Polyakov-loop models at finite density. While the first paper was mainly devoted to establishing the phase diagram of the model, here we compute correlation functions of the Polyakov loops and the second-moment correlation length at non-zero chemical potential. This enables us to evaluate numerically the screening masses from correlations of the real and imaginary parts of the Polyakov loops. We also compute these masses in the mean-field approximation and compare with numerical results. In addition, we provide a quantitative improvement of the general phase diagram presented in the first paper.

Holographic neutrino transport in dense strongly-coupled matter

A (toy) model for cold and luke-warm strongly-coupled nuclear matter at finite baryon density, is used to study neutrino transport. The complete charged current two-point correlators are computed in the strongly-coupled medium and their impact on neutrino transport is analyzed. The full result is compared with various approximations for the current correlators and the distributions, including the degenerate approximation, the hydrodynamic approximation as well as the diffusive approximation and we comment on their successes. Further improvements are discussed.

Phase Diagram of Dense Two-Color QCD at Low Temperatures

This review is devoted to the modern understanding of the two-color QCD phase diagram at finite baryon density and low temperatures. First, we consider the theoretical picture of this phase diagram. It is believed that at low baryon density, two-color QCD can be described by chiral perturbation theory (ChPT), which predicts a second-order phase transition with Bose-Einstein condensation of diquarks at μ=mπ/2. At larger baryon chemical potentials, the interactions between baryons become important, and ChPT is not applicable anymore. At sufficiently large baryon chemical potential, the Fermi sphere composed of quarks is formed, and diquarks are condensed on the surface of this sphere. In this region, two-color baryon matter reveals properties similar to those of the Quarkyonic phase. Particular attention in this review is paid to lattice studies of dense two-color QCD phase diagram. In the low-density region, the results of lattice studies are in agreement with ChPT predictions. At sufficiently large baryon densities, lattice studies observe a Fermi sphere composed of quarks and condensation of diquarks on its surface. Thus, available lattice studies support most of the theoretical predictions. Finally, we discuss the status of the deconfinement in cold dense two-color matter, which was observed in lattice simulation with staggered fermions.

Equation of state of a hot-and-dense quark gluon plasma: Lattice simulations at real μB vs extrapolations

The equation of state of the quark gluon plasma is a key ingredient of heavy ion phenomenology. In addition to the traditional Taylor method, several novel approximation schemes have been proposed with the aim of calculating it at finite baryon density. In order to gain a pragmatic understanding of the limits of these schemes, we compare them to direct results at $\mu_B>0$, using reweighting techniques free from an overlap problem. We use 2stout improved staggered fermions with 8 time-slices and cover the entire RHIC BES range in the baryochemical potential, up to $\mu_B/T=3$.

Skyrmions at finite density

In this paper, we will describe recent advances in analytical methods to construct exact solutions of the Skyrme model (and its generalizations) representing inhomogeneous Hadronic condensates living at finite Baryon density. Such novel analytical tools are based on the idea to generalize the well-known spherical hedgehog ansatz to situations (relevant for the analysis of finite density effects) in which there is no spherical symmetry anymore. Besides the intrinsic mathematical interest to find exact solutions with nonvanishing Baryonic charge confined to a finite volume, this framework opens the possibility to compute important physical quantities which would be difficult to compute otherwise.

Light Nuclei and Hyper Nuclei Collectivity Measurements at High Baryon Density Region

High energy heavy-ion collisions produce large amounts of light nuclei and hype nuclei, especially at high baryon density around collision energy of several GeV. These light nuclei and hyper nuclei carry the information of nucleon-nucleon and hyperon-nucleon interactions and affect the chemical composition and properties of the collision system. This proceeding is a brief review for the recent measurements on light nuclei collective flow, including directed flow v1, elliptic flow v2, and high order flow coefficients, at finite and high baryon densities from different experiments. The light nuclei production mechanism is discussed based on comparisons of the measurements and model calculations. The first measurement for hyper nuclei v1 at 3 GeV by STAR is also reported, which may imply the hyper nuclei are formed via the coalescence of nucleons and hyperon.

Complex Langevin approach to interacting Bose gases

Quantitative numerical analyses of interacting dilute Bose-Einstein condensates are most often based on semiclassical approximations. Since the complex-valued field-theoretic action of the Bose gas does not offer itself to standard Monte Carlo techniques, simulations beyond their scope almost exclusively rely on quantum-mechanical techniques, which are inherently limited to small particle numbers. Here we explore an alternative approach based on a Langevin-type sampling in an extended state space, known as complex Langevin (CL) algorithm. While the use of the CL technique has a long-standing history in high-energy physics, in particular in the simulation of QCD at finite baryon density, applications to ultracold atoms are still in their infancy. Here we examine the applicability of the CL approach for a one- and two-component, three-dimensional non-relativistic Bose gas in thermal equilibrium, below and above the Bose-Einstein phase transition. By comparison with analytic descriptions at the Gaussian level, including Bogoliubov and Hartree-Fock theory, we find that the method allows computing reliably and efficiently observables in the regime of experimentally accessible parameters. Close to the transition, quantum corrections lead to a shift of the critical temperature which we reproduce within the numerical range known in the literature. With this work, we aim to provide a first test of CL as a potential out-of-the-box tool for the simulation of experimentally realistic situations, including trapping geometries and multicomponent/-species models.

Strangeness thermodynamic instabilities in hot and dense nuclear matter

We explore the presence of thermodynamic instabilities and, consequently, the realization of a pure hadronic phase transition in the hot and finite baryon density nuclear matter. The analysis is performed by means of an effective relativistic mean-field model with the inclusion of hyperons, varDelta -isobars, and the lightest pseudoscalar and vector meson degrees of freedom. The Gibbs conditions on the global conservation of baryon number and zero net strangeness in symmetric nuclear matter are required. Similarly to the liquid–gas phase transition, we show that a phase transition, characterized by mechanical instabilities (due to fluctuations on the baryon number) and chemical-diffusive instabilities (due to fluctuations on the strangeness number), can take place for a finite range of varDelta -meson coupling constants, compatible with different experimental constraints. The hadronic phase transition, which presents similar features to the quark-hadron phase transition, is characterized by different strangeness content during the mixed phase and, consequently, by a sensible variation of the strange anti-particle to particle ratios.

Comprehensive simulation of heavy-ion collisions at nonzero baryon chemical potential

We present results of hydrodynamic modelling of Au-Au collisions from $\sqrt{s_{NN}}$ = 7.7 to 200 GeV. Our simulations have three novel components. Firstly, we use a Linear EXtrapolation of Ultrarelativistic nucleon-nucleon Scattering to nucleus-nucleus collisions (LEXUS) inspired Monte-Carlo initial state model. Secondly, we use a crossover equation of state at finite baryon densities without a critical point. Finally, we use departure functions derived from the quasiparticle theory of transport coefficients for hadronic matter at non-zero baryon densities.

A study of the elastic πN scattering at finite baryon density

In this work, we investigate the elastic [Formula: see text] scattering for the [Formula: see text] channel dominated by the [Formula: see text] resonance at finite baryon density for the symmetric nuclear matter, employing the effective Lagrangian approach at the tree-level Born approximation. The quark-meson coupling (QMC) model is employed to describe the medium modifications for the in-medium baryon properties that are constructed at the quark level, such as the nucleon and [Formula: see text] masses, and [Formula: see text] full decay width. We first reproduce the experimental data of the cross-section in a vacuum and we then analyze various physical observables including the total and differential cross-sections and proton-spin asymmetry in a medium. It turns out that suppression and broadening on the peak of the in-medium cross-section becomes more significant at higher baryon density due to the increase of the decay width in the nuclear medium. Also, we find that beyond the [Formula: see text]-resonance region [Formula: see text] GeV, the elastic cross-section scattering is almost independent of the density. Results for the in-medium [Formula: see text] resonance will be relevant and useful for the relativistic heavy-ion collisions (RHICs).