Baryon Chemical Potential Research Articles

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.

Bulk viscosity in strong and electroweak matter

For temperatures [Formula: see text] ranging from a few MeV up to TeV and energy density [Formula: see text] up to [Formula: see text][Formula: see text]GeV/fm3, the bulk viscosity [Formula: see text] is calculated in nonperturbation (up, down, strange, charm and bottom) and perturbation theories with up, down, strange, charm, bottom and top quark flavors, at vanishing baryon-chemical potential. To these calculations, results deduced from the effective QCD-like model, the Polyakov linear-sigma model (PLSM), are also integrated in. The PLSM merely comes up with essential contributions for the vacuum and thermal condensations of the gluons and the quarks (up, down, strange and charm flavors). Furthermore, the thermal contributions of the photons, neutrinos, charged leptons, electroweak particles and scalar Higgs boson are found very significant along the entire range of [Formula: see text] and [Formula: see text] and therefore could be well integrated in. We present the dimensionless quantity [Formula: see text], where [Formula: see text] is a perturbative scale and [Formula: see text] is the entropy density and conclude that [Formula: see text] exponentially decreases with increasing [Formula: see text]. We also conclude that the resulting [Formula: see text] with the nonperturbative and perturbative QCD contributions nonmonotonically increases with increasing [Formula: see text]. But with nearly-entire standard model contributions considered in this study, [Formula: see text] almost-linearly increases with increasing of [Formula: see text]. Apparently, these results offer a great deal to explore in astrophysics, cosmology and nuclear collisions.

Shocks and quark-meson scatterings at large density

We discuss the phase structure of the two-flavour quark-meson model including quantum, thermal, density and critical fluctuations with the functional renormalisation group. This study combines two technical advances in the literature, that are also chiefly important for the quantitative access of the phase boundary of QCD at large density or baryon chemical potential. Specifically we allow for the formation and propagation of shocks as well as a fully self-consistent computation of the order parameter potential for chiral symmetry breaking.

Neutron stars with a crossover equation of state

The question of whether quark matter exists in neutron stars is a long standing one. Generally one finds that a first order phase transition from baryons to quarks softens the equation of state so much that the star would collapse into a black hole. We consider a crossover equation of state, similar to the crossover that is found in lattice QCD studies at finite temperature and zero or small baryon chemical potentials. We find that with reasonable parameters it may be possible to support neutron stars up to about 2.2 solar masses. In that case 1 to 10% of the pressure would be contributed by quark matter in the central core of the highest mass stars.

Modified equilibrium distributions for Cooper-Frye particlization

We introduce a positive definite single-particle distribution that is suitable for describing the transition from a macroscopic hydrodynamic to a microscopic kinetic description during the late stages of heavy-ion collisions in the presence of moderately large viscous corrections. The modified equilibrium distribution function can be constructed with hydrodynamic input from either relativistic viscous fluid dynamics or anisotropic fluid dynamics. We test the modified equilibrium distribution's hydrodynamic output for a stationary hadron resonance gas subject to either shear stress, bulk pressure, or baryon diffusion current at a given freeze-out temperature and baryon chemical potential. While it does not reproduce all components of the net baryon current and energy-momentum tensor exactly, it significantly improves upon the customary linearized approximations for the non-equilibrium correction $\delta f_n$ which typically lead to unphysical negative distribution functions at large particle momenta. A comparison of particle spectra and $p_T$-differential elliptic flow coefficients from the Cooper-Frye formula computed with the modified equilibrium distribution and with linearized $\delta f_n$ corrections is presented, for two different (2+1)-dimensional hypersurfaces corresponding to central and non-central Pb+Pb collisions at the Large Hadron Collider (LHC).

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.

Strangeness-neutral equation of state for QCD with a critical point

We present a strangeness-neutral equation of state for QCD that exhibits critical behavior and matches lattice QCD results for the Taylor-expanded thermodynamic variables up to fourth order in $$\mu _B/T$$ . It is compatible with the SMASH hadronic transport approach and has a range of temperatures and baryonic chemical potentials relevant for phase II of the Beam Energy Scan at RHIC. We provide an updated version of the software BES-EoS, which produces an equation of state for QCD that includes a critical point in the 3D Ising model universality class. This new version also includes isentropic trajectories and the critical contribution to the correlation length. Since heavy-ion collisions have zero global net-strangeness density and a fixed ratio of electric charge to baryon number, the BES-EoS is more suitable to describe this system. Comparison with the previous version of the EoS is thoroughly discussed.

An Approach of Statistical Corrections to Interactions in Hadron Resonance Gas

We propose a new model for hadrons with quantum mechanical attractive and repulsive interactions sensitive to some spatial correlation length parameter inspired by the Beth-Uhlenbeck quantum mechanical nonideal gas model (Uhlenbeck and Beth, 1937). We confront the thermodynamics calculated using our model with a corresponding recent lattice data at four different values of the baryon chemical potential, μ b = 0 , 170 , 340 , 425 MeV over temperatures ranging from 130 MeV to 200 MeV and for five values for the correlation length ranging from 0 to 0.2 fm. For equilibrium temperatures up to the vicinity of the chiral phase transition temperature ≃160 MeV, a decent fitting between the model and the lattice data is observed for different values of r , especially at μ b , r = 170 , 0.05 , 340 , 0.1 , and 340 , 0.15 , where μ b is in MeV and r is in fm. For the vanishing chemical potential, the uncorrelated model r = 0 , which corresponds to the ideal hadron resonance gas model, seems to offer the best fit. The quantum hadron correlations seem to be more probable at nonvanishing chemical potentials, especially within the range μ b ∈ 170 , 340 MeV .

Chiral phase transitions of helical matter

We study the thermodynamics of helical matter, namely quark matter in which a net helicity, $n_H$, is in equilibrium. Interactions are modeled by the renormalized quark-meson model with two flavors of quarks. Helical density is described within the grand-canonical ensemble formalism via a chemical potential, $\mu_H$. We study the transitions from the normal quark matter and hadron gas to the helical matter, drawing the phase diagram at zero temperature. We study the restoration of chiral symmetry at finite temperature and show that the net helical density softens the transition, moving the critical endpoint to lower temperature and higher baryon chemical potential. Finally, we discuss briefly the effect of a rigid rotation on the helical matter, in particular on the fluctuations of $n_H$, and show that these are enhanced by the rotation.

Phase diagram of helically imbalanced QCD matter

We discuss the influence of a helicity imbalance on the phase diagram of dense QCD at finite temperature. We argue that the helical chemical potential is a thermodynamically relevant quantity in theories with the mass gap generation. Using the linear sigma model coupled to quarks, we show that the presence of the helical density substantially affects the phase diagram of dense quark matter. A moderate helical density makes the chiral phase transition softer while shifting the critical endpoint towards lower temperatures and higher baryon chemical potentials. As the helical density increases, the segment of the first-order transition disappears, and the chiral transition becomes a soft crossover. At even higher helical chemical potentials, the first-order transition reappears again at the zero-density finite-temperature transition and extends into the interior of the phase diagram. This evolution of the chiral transition reflects the existence of a thermodynamic duality between helical and vector (baryonic) chemical potentials. We also show that the presence of the helicity imbalance of quark matter increases the curvature of the chiral pseudocritical line in QCD.

Probing Dense QCD Matter: Muon Measurements with the CBM Experiment at FAIR

The Compressed Baryonic Matter (CBM) experiment at the future Facility for Antiproton and Ion Research (FAIR) in Darmstadt is designed to investigate the properties of high-density QCD matter with multi-differential measurements of hadrons and leptons, including rare probes such as multi-strange anti-hyperons and charmed particles. The research program covers the study of the high-density equation-of-state of nuclear matter and the exploration of the QCD phase diagram at large baryon chemical potentials, including the search for quark matter and the critical endpoint of a hypothetical 1st order phase transition. The CBM setup comprises detector systems for the identification of charged hadrons, electrons, and muons; for the determination of collision centrality and the orientation of the reaction plane; and a free-streaming data read-out and acquisition system, which allows online reconstruction and selection of events up to reaction rates of 10 MHz. In this article, emphasis is placed on the measurement of muon pairs in Au-Au collisions at FAIR beam energies, which are unique probes used to determine the temperature of the fireball, and hence to search for a caloric curve of QCD matter. Simultaneously, the subthreshold production of charmonium can be studied via its dimuon decay in order to shed light on the microscopic structure of QCD matter at high baryon densities. The CBM setup with focus on dimuon measurements and the results of the corresponding physics performance studies will be presented.

Influence of correlations between yields on the chemical freeze-out temperature

A statistical (thermal) model is applied to the description of hadron yields measured at central nucleus-nucleus collisions at the top RHIC energy sNN=200 GeV and the LHC energy sNN=2.76 TeV. In contrast to the previous analyzes a more general form of the least squares test statistic is used, which takes into account also possible correlations between different species of yields. In addition to hadrons also light nuclei are included in the fits. Because of the lack of data, a toy model is constructed where the correlation coefficients are just free parameters. Because of this the presented considerations are speculative and should be treated as an imperfect illustration of the problem. Within these limitations it is impossible to formulate any definite conclusion, it might be only mentioned that for the considered examples the dependence of the freeze-out temperature and baryon chemical potential on correlations turned out to be weak.

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.

Universality driven analytic structure of the QCD crossover: Radius of convergence in the baryon chemical potential

Recent lattice QCD calculations strongly indicate that the chiral crossover of QCD at zero baryon chemical potential \mu_B is a remnant of the second-order chiral phase transition. Universal properties of this second-order phase transition can be mapped to QCD temperature T and \mu_B using non-universal parameters determined by lattice QCD recently. Motivated by these results, first, we discuss the analytic structure of the partition function in the QCD crossover regime - the so-called Yang-Lee edge singularity - solely based on universal properties. Next, utilizing the lattice QCD results for non-universal parameters we map this singularity to the real T and complex \mu_B plane, leading to the determination of the radius of convergence is in \mu_B in the QCD crossover regime. These universality- and QCD-based results provide tight constraints on the range of validity of the lattice QCD calculations at \mu_B. Implication of this result on the location of the conjectured QCD critical point is discussed.

Effects of hadronic repulsive interactions on the fluctuations of conserved charges

We investigate the effects of repulsive interaction between hadrons on the fluctuations of the conserved charges. We calculate the baryon,the electric charge and the strangeness susceptibilities within the ambit of hadron resonance gas model extended to include the short range repulsive interactions.The repulsive interactions are included through a mean-field approach where the single particle energy gets modified due to mean field interactions between hadrons proportional to the number density of hadrons.We assume different mean-field interactions for mesons and baryons. It is shown that the repulsive interactions play a very crucial role to describe hadronic matter near transition temperature. We also show that in order to consistently describe higher order conserved charge fluctuations mesonic repulsive interactions cannot be neglected. Further, we demonstrate that the repulsive interaction of baryons are essential to describe the lattice simulation results at finite baryonchemical potential for higher order fluctuations.

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.

Dual simulation of a Polyakov loop model at finite baryon density: Phase diagram and local observables

Many Polyakov loop models can be written in a dual formulation which is free of sign problem even when a non-vanishing baryon chemical potential is introduced in the action. Here, results of numerical simulations of a dual representation of one such effective Polyakov loop model at finite baryon density are presented. We compute various local observables such as energy density, baryon density, quark condensate and describe in details the phase diagram of the model. The regions of the first order phase transition and the crossover, as well as the line of the second order phase transition, are established. We also compute several correlation functions of the Polyakov loops.

Hadron–Quark Phase Transition in the SU (3) Local Nambu–Jona-Lasinio (NJL) Model with Vector Interaction

We study the hadron–quark hybrid equation of state (EOS) of compact-star matter. The Nambu–Jona-Lasinio (NJL) local SU (3) model with vector-type interaction is used to describe the quark matter phase, while the relativistic mean field (RMF) theory with the scalar-isovector δ-meson effective field is adopted to describe the hadronic matter phase. It is shown that the larger the vector coupling constant GV, the lower the threshold density for the appearance of strange quarks. For a sufficiently small value of the vector coupling constant, the functions of the mass dependence on the baryonic chemical potential have regions of ambiguity that lead to a phase transition in nonstrange quark matter with an abrupt change in the baryon number density. We show that within the framework of the NJL model, the hypothesis on the absolute stability of strange quark matter is not realized. In order to describe the phase transition from hadronic matter to quark matter, Maxwell’s construction is applied. It is shown that the greater the vector coupling, the greater the stiffness of the EOS for quark matter and the phase transition pressure. Our results indicate that the infinitesimal core of the quark phase, formed in the center of the neutron star, is stable.

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.

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.