Finite Baryon Chemical Potential Research Articles

Cold isospin asymmetric baryonic rich matter in nonlocal NJL-like models

We study the features of low energy strong interactions for a system at zero temperature and finite baryon and isospin chemical potentials, in the framework of a Nambu–Jona-Lasinio-like model that includes nonlocal four-point interactions. We analyze the phase transitions corresponding to chiral symmetry restoration and pion condensation, comparing our results with those obtained from local NJL-like models and lattice QCD calculations. Published by the American Physical Society 2024

Polyakov loop models in the large N limit: Correlation function and screening masses

We explore the ’t Hooft-Veneziano limit of the Polyakov loop models at finite baryon chemical potential. Using methods developed by us earlier we calculate the two- and N-point correlation functions of the Polyakov loops. This gives a possibility to compute the various potentials in the confinement phase and to derive the screening masses outside the confinement region. In particular, we establish the existence of complex masses and an oscillating decay of correlations in a certain range of parameters. Furthermore, it is shown that the calculation of the N-point correlation function in the confinement phase reduces to the geometric median problem. This leads to a large N analog of the Y law for the baryon potential. Published by the American Physical Society 2024

Non-Abelian chiral soliton lattice in rotating QCD matter: Nambu-Goldstone and excited modes

The ground state of QCD with two flavors at a finite baryon chemical potential under rapid rotation is a chiral soliton lattice (CSL) of the η meson, consisting of a stack of sine-Gordon solitons carrying a baryon number, due to the anomalous coupling of the η meson to the rotation. In a large parameter region, the ground state becomes a non-Abelian CSL, in which due to the neutral pion condensation each η soliton decays into a pair of non-Abelian sine-Gordon solitons carrying S2 moduli originated from Nambu-Goldstone (NG) modes localized around it, corresponding to the spontaneously broken vector symmetry SU(2)V. There, the S2 modes of neighboring solitons are anti-aligned, and these modes should propagate in the transverse direction of the lattice due to the interaction between the S2 modes of neighboring solitons. In this paper, we calculate excitations including gapless NG modes and excited modes around non-Abelian and Abelian (η) CSLs, and find three gapless NG modes with linear dispersion relations (type-A NG modes): two isospinons (S2 modes) and a phonon corresponding to the spontaneously broken vector SU(2)V and translational symmetries around the non-Abelian CSL, respectively, and only a phonon for the Abelian CSL because of the recovering SU(2)V. We also find in the deconfined phase that the dispersion relation of the isospinons becomes of the Dirac type, i.e. linear even at large momentum.

Self-consistent thermodynamic potential for magnetized QCD matter

Within the two-flavor Nambu--Jona-Lasinio model, we derive a self-consistent thermodynamic potential $\Omega$ for a QCD matter in an external magnetic field $B$. To be consistent with Schwinger's renormalization spirit, counter terms with vacuum quark mass are introduced into $\Omega$ and then the explicit $B$-dependent parts can be regularized in a cutoff-free way. Following that, explicit expressions of gap equation and magnetization can be consistently obtained according to the standard thermodynamic relations. The formalism is able to reproduce the paramagnetic feature of a QCD matter without ambiguity. For more realistic study, a running coupling constant is also adopted to account for the inverse magnetic catalysis effect. It turns out that the running coupling would greatly suppress magnetization at large $B$ and is important to reproduce the temperature enhancement effect to magnetization. The case with finite baryon chemical potential is also explored: no sign of first-order transition is found by varying $B$ for the running coupling and the de Haas-van Alphen oscillation shows up in the small $B$ region.

Probing QCD critical point and induced gravitational wave by black hole physics

Locating the critical endpoint of QCD and the region of a first-order phase transition at finite baryon chemical potential is an active research area for QCD matter. We provide a gravitational dual description of QCD matter at finite baryon chemical potential ${\ensuremath{\mu}}_{B}$ and finite temperature using the nonperturbative approach from gauge/gravity duality. After fixing all model parameters using state-of-the-art lattice QCD data at zero chemical potential, the predicted equations of state and QCD trace anomaly relation are in quantitative agreement with the latest lattice results. We then give the exact location of the critical endpoint as well as the first-order transition line, which is within the coverage of many upcoming experimental measurements. Moreover, using the data from our model at finite ${\ensuremath{\mu}}_{B}$, we calculate the spectrum of the stochastic gravitational wave background associated with the first-order QCD transition in the early Universe, which could be observable via pulsar timing in the future.

Formation of a chiral soliton lattice

The Chiral Soliton Lattice (CSL) is a lattice structure composed of domain walls aligned in parallel at equal intervals, which is energetically stable in the presence of a background magnetic field and a finite (baryon) chemical potential due to the topological term originated from the chiral anomaly. We study its formation from the vacuum state, with describing the CSL as a layer of domain-wall disks surrounded by the vortex or string loop, based on the Nambu-Goto-type effective theory. We show that the domain wall nucleates via quantum tunneling when the magnetic field is strong enough. We evaluate its nucleation rate and determine the critical magnetic field strength with which the nucleation rate is no longer exponentially suppressed. We apply this analysis to the neutral pion in the two-flavor QCD as well as the axion-like particles (ALPs) with a finite (baryon) chemical potential under an external magnetic field. In the former case, even though the CSL state is more energetically stable than the vacuum state and the nucleation rate becomes larger for sufficiently strong magnetic field, it cannot be large enough so that the nucleation of the domain walls is not exponentially suppressed and promoted, without suffering from the tachyonic instability of the charged pion fluctuations. In the latter case, we confirm that the effective interaction of the ALPs generically includes the topological term required for the CSL state to be energetically favored. We show that the ALP CSL formation is promoted if the magnetic field strength and the chemical potential of the system is slightly larger than the scale of the axion decay constant.

Study of quarkonium properties using SUSYQM method with baryonic chemical potential

In this paper, we employed the quasi-particle (QP) Debye mass at finite baryonic chemical potential which can be used in the medium modified heavy quark potential to solve the [Formula: see text]-dimensional Schrödinger equation. The bound state solution of the Schrödinger equation using Cornell potential been obtained by Super-Symmetry Quantum Mechanics (SUSYQM) method. The thermodynamical properties of quark matter are calculated by using baryonic chemical potential ([Formula: see text]). We found that the binding energy of quarkonia dissociates more with QP Debye mass in comparison to nonperturbative and leading order Debye mass. The medium modified form of potential (real part) has been used to study the thermodynamical properties of quark matter with different equation of states (EoSs) (i.e. pressure, energy density and speed of sound) with [Formula: see text]. The mass spectra of quarkonia have been also calculated in the [Formula: see text]-dimensional space and compared with the experimental data at [Formula: see text]. We have also calculated the dissociation temperature ([Formula: see text]) for the ground states of quarkonium using the dissociation criteria of thermal width.

Charmonium dissociation at high baryon chemical potential

We study the charmonium dissociation in the hot medium with finite baryon chemical potential $\mu_B$. Charmonium bound states are dissociated in the medium by the color screening effect and the random scatterings with thermal partons, which are included in the real and imaginary parts of the potential respectively. $J/\psi$ fraction in the $c\bar c$ pair defined to be the quantum overlap between the wave package and the wave function of $J/\psi$ eigenstate decreases with time due to the complex potentials. When $\mu_B$ is large compared with the medium temperature, the Deybe mass is increased evidently. We consider $\mu_B$-dependent Deybe mass in both real and imaginary parts of the potential to calculate the $J/\psi$ survival probability in the static medium and the Bjorken medium. $J/\psi$ survival probability is reduced evidently by the $\mu_B$ effect at low temperatures available in the medium produced in Beam Energy Scan experiments, while this effect becomes not apparent at high temperatures.

Inverse catalysis effect of the quark anomalous magnetic moment to chiral restoration and deconfinement phase transitions at finite baryon chemical potential

The effect of quark anomalous magnetic moment (AMM) to chiral restoration and deconfinement phase transitions in baryon chemical potential-temperature $(\mu_B-T)$ plane under magnetic fields is investigated in frame of a Pauli-Villars regularized PNJL model. It's found that the quark AMM plays the role of inverse catalysis to the phase transitions, and large quark AMM will change the magnetic catalysis phenomena of phase transitions to inverse magnetic catalysis in the whole $\mu_B-T$ plane. For a fixed magnetic field, the critical temperature $T_c$ and critical baryon chemical potential $\mu_B^c$ decreases with quark AMM. The stronger the magnetic field is, the inverse catalysis effect of AMM becomes more important. For a small AMM $\kappa=\kappa_1$, it shows the magnetic catalysis effect for critical temperature $T_c$ at vanishing $\mu_B$ with increasing magnetic field, and (inverse) magnetic catalysis effect for critical baryon chemical potential $\mu_B^c$ at vanishing $T$ under (weak) strong magnetic field. At finite $T$ and $\mu_B$, there exist some crossings of the phase transition lines with different magnetic field. For a large AMM $\kappa=\kappa_2$, we obtain the inverse magnetic catalysis effect in the whole $\mu_B-T$ plane, and no crossings of phase transition lines happen.

Gravitational waves of the QCD phase transition in a 5D soft wall model with Gauss-Bonnet correction

In this paper, we study the gravitational wave energy density spectrum of cosmological de/confinement phase transition at finite baryon chemical potential within a soft wall model of AdS/QCD with Gauss-Bonnet correction. Focusing on the approach of dilaton/radion dominance approximation, we find the dual bounce action and the duration of the phase transition at the nucleation temperature. We also consider the possibility of a supercooling period during the transition, obtain the quantities characterizing the gravitational wave spectrum through this approach, and discuss the detectability prospect of generated gravitational wave signals by gravitational wave experiments.

Polyakov loop models in the large N limit: Phase diagram at finite density

The 't Hooft-Veneziano limit of various U(N) and SU(N) Polyakov loop models is constructed at finite temperature and non-zero baryon chemical potential. In this paper we calculate the free energy, its derivatives, the Polyakov loop expectation values and the baryon density. The phase diagram is described in details.

Three-dimensional QCD phase diagram with a pion condensate in the NJL model

With the isovector coupling constants adjusted to reproduce the physical pion mass and lattice QCD results in baryon-free quark matter, we have carried out rigourous calculations for the pion condensate in the 3-flavor Nambu-Jona-Lasinio model, and studied the 3-dimensional QCD phase diagram. With the increasing isospin chemical potential $\mu_I$, we have observed two nonzero solutions of the pion condensate at finite baryon chemical potentials $\mu_B$, representing respectively the pion superfluid phase and the Sarma phase, and their appearance and disappearance correspond to a second-order (first-order) phase transition at higher (lower) temperatures $T$ and lower (higher) $\mu_B$. Calculations by assuming equal constituent mass of $u$ and $d$ quarks would lead to large errors of the QCD phase diagram within $\mu_B \in (500, 900)$ MeV, and affect the position of the critical end point.

NANOGrav signal from first-order confinement-deconfinement phase transition in different QCD-matter scenarios

Recently, an indicative evidence of a stochastic process, reported by the NANOGrav Collaboration based on the analysis of 12.5-year pulsar timing array data which might be interpreted as a potential stochastic gravitational wave signal, has aroused the keen interest of theorists. The first-order color charge confinement phase transition at the QCD scale could be one of the cosmological sources for the NANOGrav signal. If the phase transition is flavor dependent and happens sequentially, it is important to find that what kind of QCD matter in which the first-order confinement-deconfinement phase transition happens is more likely to be the potential source of the NANOGrav signal during the evolution of the universe. In this paper, we would like to illustrate that the NANOGrav signal could be generated from confinement-deconfinement transition in either heavy static quarks with a zero baryon chemical potential, or quarks with a finite baryon chemical potential. In contrast, the gluon confinement could not possibly be the source for the NANOGrav signal according to the current observation. Future observation will help to distinguish between different scenarios.

Properties of the quark‐gluon plasma created in heavy‐ion collisions

AbstractWe review the properties of the strongly interacting quark‐gluon plasma (QGP) at finite temperature and baryon chemical potential as created in heavy‐ion collisions at ultrarelativistic energies. The description of the strongly interacting (non‐perturbative) QGP in equilibrium is based on the effective propagators and couplings from the Dynamical QuasiParticle Model (DQPM) that is matched to reproduce the equation‐of‐state of the partonic system above the deconfinement temperature from lattice QCD. Based on a microscopic transport description of heavy‐ion collisions, we discuss which observables are sensitive to the QGP creation and its properties.

QCD phase diagram at finite isospin and baryon chemical potentials with the self-consistent mean field approximation * *Supported by National Natural Science Foundation of China (12075117, 11535005, 11775118, 11690030, 11905104) and National Major state Basic Research and Development of China (2016YEF0129300)

The self-consistent mean field approximation of the two-flavor NJL model, with a free parameter to reflect the competition between the "direct" channel and the "exchange" channel, is employed to study the QCD phase structure at finite isospin chemical potential , finite baryon chemical potential and finite temperature T, and especially to study the location of the QCD critical point. Our results show that in order to match the corresponding lattice results of isospin density and energy density, the contributions of the "exchange" channel need to be considered in the framework of the NJL model, and a weighting factor should be taken. It is also found that for fixed isospin chemical potentials, the lower temperature of the phase transition is obtained with increasing in the plane, and the largest difference of the phase transition temperature with different 's appears at . At the temperature of the QCD critical end point (CEP) decreases with increasing , while the critical baryon chemical potential increases. At high isospin chemical potential ( MeV), the temperature of the QCD tricritical point (TCP) increases with increasing , and in the low temperature regions the system will transition from the pion superfluidity phase to the normal phase as increases. At low density, the critical temperature of the QCD phase transition with different 's rapidly increases with at the beginning, and then increases smoothly around MeV. In the high baryon density region, the increase of the isospin chemical potential will raise the critical baryon chemical potential of the phase transition.

Quarkonium dissociation properties at finite chemical potential in relativistic heavy ion collisions

Using the quasi-particle Debye mass we have mapped the quarkonium properties at finite baryonic chemical potential which is obtained by approximated medium modified potential at T = 0 through the dielectric function. We study the dissociation temperature and baryonic chemical potential dependence of binding energy of heavy quarkonia states for full QCD case and estimated the ground state patterns of the J/ψ states.

Correspondence between Israel-Stewart and first-order causal and stable hydrodynamics for Bjorken-expanding baryon-rich systems with vanishing particle masses

We obtain an exact correspondence between the dynamical equations in Israel-Stewart (IS) theory and first-order causal and stable (FOCS) hydrodynamics for a boost-invariant system with an ideal gas equation of state at finite baryon chemical potential. Explicit expressions for the temperature and chemical potential dependence of the regulators in the FOCS theory are given in terms of the kinetic coefficients and constant relaxation time of the IS theory. Using the correspondence between the IS and FOCS theory, stability conditions for a charged fluid which are known in the FOCS approach are applied and one finds that the IS theory considered is unstable.

On the critical endpoint and the first‐order phase transition in the extended Polyakov Nambu Jona‐Lasinio Lagrangian

AbstractThe (Polyakov) Nambu‐ Jona‐Lasinio (PNJL) approach is an effective theory for low energies which shares with Quantumchromodynamics (QCD) the global symmetries. This approach is easy to handle and allows for analytical results for many of the observables which are of interest for the studies of ultrarelativistic heavy‐ion collisions but also for the merger and collisions of neutron stars. It allows in particular to study the density and temperature dependence of quark masses and of the masses of mesons and baryons as well as the chiral phase transition. In recent times, this transition came in the focus of interest because it is expected that the upcoming experiments at the Fair (Germany) and NICA (Russia) facilities will observe a Quark‐Gluon‐Plasma (QGP) at finite baryon chemical potential. In this contribution, we show that the extended PNJL model is able to describe the properties of symmetric matter at vanishing chemical potential, as determined by lQCD calculations.

Equation of state and thermodynamic properties of isospin imbalanced strongly interacting matter

The effects of temperature and baryon chemical potential on equation of state and thermodynamics of isospin imbalanced QCD matter are investigated in the framework of two-flavor Nambu−Jona-Lasinio model. The equation of state at zero temperature and baryon chemical potential as well as the isospin density and normalized pressure at finite temperature are shown to be consistent with the lattice data. We also find that the energy per isospin increases monotonically with the increase of isospin density at vanishing temperature and baryon chemical potential, while it first decreases and then increases with the augment of isospin density, behaving as a non-symmetric parabolic curve. Finally, we compute the sound velocity and find that it is discontinuous at the phase transition point for finite temperature and/or baryon chemical potential. In particular, the sound velocity in the superfluid phase is distinctly larger than that in the ordinary nuclear matter and quark matter, while the temperature and baryon chemical potential included in the superfluid phase makes the equation of state softer and the sound velocity slower.

Polyakov loop eigenvalues in the presence of baryon chemical potential

The eigenvalues of the Polyakov loop are calculated in the strong coupled lattice QCD at finite tempera­ture. This is done both in the pure gauge theory and in the theory with heavy quarks at finite baryon chemical potential. Computations are performed in the mean­field like approach to the effective action. Using the eigenvalues obtained we also evaluate the free energy, real and imaginary parts of the Polyakov loops and the baryon density. The phase diagram of the model and influence of the baryon chemical potential are discussed in details. We underline a similarity between our calculations and continuum derivations of the phenomenon of A0 condensation.