Quark Number Susceptibility Research Articles

Properties of strange quark matter under strong rotation

We investigate the rotating quark matter in the three-flavor Nambu--Jona-Lasinio (NJL) model. The chiral condensation, spin polarization, and number susceptibility of the light and strange quarks are carefully studied at finite temperatures without or with finite chemical potential in this model. We find that the rotation suppresses the chiral condensation and enhances the first-order quark spin polarization, however for the second-order quark spin polarization and quark number susceptibility the effect is complicated and interesting. When extending to the situation with finite chemical potential, we find the angular velocity also plays a crucial role, at small angular velocity the chemical potential enhances the susceptibility, however in the middle region of angular velocity the effect of the chemical potential is suppressed by the angular velocity and susceptibility can be changed considerably, it can be observed that at very low temperature in the presence of quark chemical potential the quark number susceptibility has two maxima with increasing angular velocity. Furthermore, it is found that at sufficiently large angular velocity the contributions played by the light quark and the strange quark to these phenomena are almost equal. We also discuss the chiral phase transition of rotating quark matter in the three-flavor NJL model. We expect these studies to be used to understand the chiral symmetry breaking and restoration as well as probe the QCD phase transition.

High order quark number susceptibilities in hot QCD from lattice electrostatic QCD

Building on the experience of [1], we develop a formalism to construct operators for higher derivatives of the pressure in hot QCD with respect to the quark chemical potential $\mu$. We provide formulae for the operators up to the sixth derivative, and obtain continuum-extrapolated results from lattice EQCD at zero and finite $\mu$ and at six different pairs of temperature T and number of massless quark flavors $n_f$. Our data is benchmarked against full-QCD lattice and perturbative results, allowing to judge the quality of the perturbative series expansion in EQCD and the dimensional reduction procedure as a whole.

Melting of heavy vector mesons and quasinormal modes in a finite density plasma from holography

In this work, we investigate, for the first time, the melting of charmonium states within a holographic QCD model in the context of Einstein-Maxwell-dilaton theory. In the dual field theory, the model describes the heavy mesons inside a finite temperature and density medium. First, we calculate the spectrum at zero temperature. Then, at finite temperature, we obtain the spectral functions, where the heavy vector meson are represented by peaks. We show that the charmonium melts down at temperatures above the confinement/deconfinement temperature of the quark-gluon plasma. We also observe that the chemical potential speeds up the melting process. In the gravitational side of the theory, we solve the perturbation equations in the hydrodynamic limit. From this result, we read off the diffusion coefficient, then the quark number susceptibility. We show that the quark number susceptibility computed in this way does not blow up at the critical end point. We interpret this result as the lack of backreaction on the background by the action describing the vector mesons. To get the quasinormal frequencies, we solve the perturbation equations numerically. We report the emergence of a new mode whose real part increases rapidly at a certain value of the chemical potential, while its imaginary part decreases with the increasing of the chemical potential. Finally, by comparing against results obtained in the conformal plasma, we observe that the real part of the frequency increases, while the imaginary part decreases when we consider the nonconformal plasma.

Phase diagram of QCD in a magnetic background

We provide numerical evidence that the thermal QCD crossover turns into a first order transition in the presence of large enough magnetic background fields. The critical endpoint is found to be located between $eB = 4$ GeV$^2$ (where the pseudocritical temperature is $T_c = (98 \pm 3)$ MeV) and $eB = 9$ GeV$^2$ (where the critical temperature is $T_c = (63 \pm 5)$ MeV). Results are based on the analysis of quark condensates and number susceptibilities, determined by lattice simulations of $N_f = 2+1$ QCD at the physical point, discretized with three different lattice spacings, $a = 0.114, 0.086$ and $0.057$ fm, via rooted stout staggered fermions and a Symanzik tree level improved pure gauge action. We also present preliminary results regarding the confining properties of the thermal theory, suggesting that they could change drastically going across the phase transition

Aspects of isentropic trajectories in chiral effective models

The evolution of the fireball in heavy ion collisions is an isentropic process, meaning that it follows a trajectory of constant entropy per baryon in the phase diagram of the strong interaction. The collective acceleration of the system is determined by the speed of sound, while fluctuations of conserved charges are encoded in quark-number susceptibilities: together, they leave their imprint in final observables. Here, this isentropic evolution will be analysed within chiral effective models that account for both chiral and center symmetry breaking, two central aspects of QCD. Our discussion focusses on the impact on the isentropic trajectories of the treatment of high-momentum modes, of the meson contribution to thermodynamics and of the number of quark flavours.

Exploration of the phase diagram and the thermodynamic properties of QCD at finite temperature and chemical potential with the PNJL effective model

The QCD transition from a hadronic to a quark-gluon plasma phase is a cross-over at vanishing/small baryo-chemical potential, while at higher chemical potentials it is argued that it becomes of first order, ending with a critical end-point. The present goal is the determination of the critical line and, possibly, the recognition of the critical endpoint. For this purpose, the effective model (Nambu-Jona-Lasinio model with Polyakov Loop) with 2+1 flavours is used. In Mean Field Approximation it is possible to obtain all thermodynamic quantities (pressure, entropy, energy and quark density) and their fluctuations, in particular, the generalized quark-number susceptibilities. We use the net baryon-number fluctuations and net-strangeness fluctuations to identify the critical line and the order of the phase transition in the chemical potential-temperature plane.

Second-order quark number susceptibility of deconfined QCD matter in the presence of a magnetic field

Considering the strong field approximation we compute the hard thermal loop pressure at finite temperature and chemical potential of hot and dense deconfined QCD matter in lowest Landau level in one-loop order. We consider the anisotropic pressure in the presence of the strong magnetic field i.e., longitudinal and transverse pressure along parallel and perpendicular to the magnetic field direction. As a first effort, we compute and discuss the anisotropic quark number susceptibility of deconfined QCD matter in lowest Landau level. The longitudinal quark number susceptibility is found to increase with the temperature whereas the transverse one decreases with the temperature. We also compute the quark number susceptibility in the weak field approximation. We find that the thermomagnetic correction to the quark number susceptibility is very marginal in the weak field approximation.

Quark mass dependent collective excitations and quark number susceptibilities within the hard thermal loop approximation

We calculate all those QCD $N$-point functions which are relevant for a three-loop QCD thermodynamics calculation with finite quark masses within the hard the thermal loop approximation. Using the effective quark propagator, we also calculate second order quark and baryon number susceptibilities within the hard thermal loop approximation and compare the results with available lattice data.

2 + 1 Flavors QCD Equation of State in NJL Model with Proper Time Regularization

In this paper, we firstly combine the 2 + 1 flavors Nambu-Jona-Lasinio (NJL) model with propertime regularization (PTR) to study the equation of state (EOS) and fix the corresponding parameters in 2 + 1 flavors system. Based on this model, we calculate chiral susceptibility and quark number susceptibility and we find a crossover with chemical potential from 220 to 400 MeV. Then we consider the chemical equilibrium and electric charge neutrality conditions in electroweak reactions, which give some constrains of chemical potentials of different quark flavors. At last, we find that the 2 + 1 flavors system is more stable than 2 flavors system after a comparison and discussion of these two cases.

Holographic estimate of heavy quark diffusion in a magnetic field

We study the influence of a background magnetic field on the $J/\ensuremath{\psi}$ vector meson in a Dirac-Born-Infeld-extension of the soft wall model, building upon our earlier work [Phys. Rev. D 91, 086002 (2015)]. In this specific holographic QCD model, we discuss the heavy quark number susceptibility and diffusion constants of charm quarks and their dependence on the magnetic field by either a hydrodynamic expansion or by numerically solving the differential equation. This allows us to determine the response of these transport coefficients to the magnetic field. The effects of the latter are considered both from a direct as indirect (medium) viewpoint. As expected, we find a magnetic field induced anisotropic diffusion, with a stronger diffusion in the longitudinal direction compared to the transversal one. We backup, at least qualitatively, our findings with a hanging string analysis of heavy quark diffusion in a magnetic field. From the quark number susceptibility we can extract an estimate for the effective deconfinement temperature in the heavy quark sector, reporting consistency with the phenomenon of inverse magnetic catalysis.

Holographic QCD phase diagram with critical point from Einstein–Maxwell-dilaton dynamics

Supplementing the holographic Einstein–Maxwell-dilaton model of [1,2] by input of lattice QCD data for 2+1 flavors and physical quark masses for the equation of state and quark number susceptibility at zero baryo-chemical potential we explore the resulting phase diagram over the temperature-chemical potential plane. A first-order phase transition sets in at a temperature of about 112 MeV and a baryo-chemical potential of 612 MeV. We estimate the accuracy of the critical point position in the order of approximately 5–8% by considering parameter variations and different low-temperature asymptotics for the second-order quark number susceptibility. The critical pressure as a function of the temperature has a positive slope, i.e. the entropy per baryon jumps up when crossing the phase border line from larger values of temperature/baryo-chemical potential, thus classifying the phase transition as a gas–liquid one. The updated holographic model exhibits in- and outgoing isentropes in the vicinity of the first-order phase transition.

Chiral symmetry restoration and the critical end point in QCD

Abstract In a system of quark matter we study the chiral phase transition, the behavior of the chiral and quark number susceptibility and the CEP at finite temperature and chemical potential. This is done within the framework of two-flavor Nambu and Jona-Lasinio model. We have calculated the chiral quark condensate and the quark number density and, with this, we have found the phase transition type. With these quantities we have determined the phase diagram for QCD and the CEP.

Quark number density and susceptibility calculation under one-loop correction in the mean-field potential

We calculate quark number density and susceptibility under one-loop correction in the mean-field potential. The calculation shows continuous increase in the number density and susceptibility up to the temperature $$T=0.4$$ GeV. Then the values of number density and susceptibility approach the very weakly result with higher values of temperature. The result indicates that the calculated values fit well with increase in temperature to match the lattice QCD simulations of the same quantities.

Quark number susceptibilities and equation of state at finite chemical potential in staggered QCD with Nt=8

We report the measurement of quark number susceptibilities (QNS) and their temperature dependence from simulations of QCD with two flavours of light dynamical staggered quarks at finite temperature on 8 * 32^3 lattices. From the radius of convergence of the Taylor expansion we estimate the critical end point. We use a Pade approximant to resum the series expansion and compute the equation of state at finite chemical potential, namely the baryon number density and its contribution to the pressure. We also report the isothermal compressibility of QCD matter at finite baryon density. Finally we explore the freezeout conditions for a measure of fluctuations. We examine some sources of systematic and statistical errors in all of these measurements.

Quark number holonomy and confinement-deconfinement transition

We propose a new quantity which describes the confinement-deconfinement transition based on topological properties of QCD. The quantity which we call the quark number holonomy is defined as the integral of the quark number susceptibility along the closed loop of $\theta$ where $\theta$ is the dimensionless imaginary chemical potential. Expected behavior of the quark number holonomy at finite temperature is discussed and its asymptotic behaviors are shown.

Quark susceptibility in a generalized dynamical quasiparticle model

The quark susceptibility $\chi_q$ at zero and finite quark chemical potential provides a critical benchmark to determine the quark-gluon-plasma (QGP) degrees of freedom in relation to the results from lattice QCD (lQCD) in addition to the equation of state and transport coefficients. Here we extend the familiar dynamical-quasiparticle model (DQPM) to partonic propagators that explicitly depend on the three-momentum with respect to the partonic medium at rest in order to match perturbative QCD (pQCD) at high momenta. Within the extended dynamical-quasi-particle model (DQPM$^*$) we reproduce simultaneously the lQCD results for the quark number density and susceptibility and the QGP pressure at zero and finite (but small) chemical potential $\mu_q$. The shear viscosity $\eta$ and the electric conductivity $\sigma_e$ from the extended quasiparticle model (DQPM$^*$) also turn out in close agreement with lattice results for $\mu_q$ =0. The DQPM$^*$, furthermore, allows to evaluate the momentum $p$, temperature $T$ and chemical potential $\mu_q$ dependencies of the partonic degrees of freedom also for larger $\mu_q$ which are mandatory for transport studies of heavy-ion collisions in the regime 5 GeV $< \sqrt{s_{NN}} <$ 10 GeV.

Dilepton rate and quark number susceptibility with the Gribov action

We use a recently obtained resummed quark propagator at finite temperature which takes into account both the chromoelectric scale gT and the chromomagnetic scale g^2T through the Gribov action. The electric scale generates two massive modes whereas the magnetic scale produces a new massless spacelike mode in the medium. Moreover, the non-perturbative quark propagator is found to contain no discontinuity in contrast to the standard perturbative hard thermal loop approach. Using this non-perturbative quark propagator and self-consistent vertices, we compute the non-perturbative dilepton rate at vanishing three-momentum at one-loop order. The resulting rate has a rich structure at low energies due to the inclusion of the non-perturbative magnetic scale. We also calculate the quark number susceptibility, which is related to the conserved quark number density fluctuation in the deconfined state. Both the dilepton rate and quark number susceptibility are compared with results from lattice quantum chromodynamics and the standard hard thermal loop approach. Finally, we discuss how the absence of a discontinuity in the imaginary part of the non-perturbative quark propagator makes the results for both dilepton production and quark number susceptibility dramatically different from those in perturbative approaches and seemingly in conflict with known lattice data.

Susceptibilities and critical exponents within the Nambu–Jona-Lasinio model

In the mean field approximation of (2 + 1)-flavor Nambu–Jona-Lasinio model, we strictly derive several sets of coupled equations for the chiral susceptibility, the quark number susceptibility, etc. at finite temperature and quark chemical potential. The critical exponents of these susceptibilities in the vicinity of the QCD critical end point (CEP) are presented in SU(2) and SU(3) cases, respectively. It is found that these various susceptibilities share almost the same critical behavior near the CEP. The comparisons between the critical exponents for the order parameters and the theoretical predictions are also included.

Diagonal and off-diagonal quark number susceptibilities at high temperatures

We present continuum extrapolated lattice QCD results for up to fourth-order diagonal and off-diagonal quark number susceptibilities in the high temperature region of 300-700 MeV. Lattice QCD calculations are performed using 2+1 flavors of highly improved staggered quarks with nearly physical quark masses and at four different lattice spacings. Comparisons of our results with recent weak coupling perturbative calculations yield reasonably good agreements for the entire temperature range.

Divergences in the quark number susceptibility: The origin and a cure

Quark number susceptibility on the lattice, obtained by merely adding a μN term with μ as the chemical potential and N as the conserved quark number, has a quadratic divergence in the cut-off a. We show that such a divergence already exists for free fermions with a cut-off regulator. While one can eliminate it in the free lattice theory by suitably modifying the action, as is popularly done, it can simply be subtracted off as well. Computations of higher order susceptibilities, needed for estimating the location of the QCD critical point, then need a lot fewer number of quark propagators at any order. We show that this method of divergence removal works in the interacting theory.