Nonzero Baryon Chemical Potential Research Articles

Energy loss, equilibration, and thermodynamics of a baryon rich strongly coupled quark-gluon plasma

Lattice data for the QCD equation of state and the baryon susceptibility near the crossover phase transition (at zero baryon density) are used to determine the input parameters of a 5-dimensional Einstein-Maxwell-Dilaton holographic model that provides a consistent holographic framework to study both equilibrium and out-of-equilibrium properties of a hot and {\it baryon rich} strongly coupled quark-gluon plasma (QGP). We compare our holographic equation of state computed at nonzero baryon chemical potential, $\mu_B$, with recent lattice calculations and find quantitative agreement for the pressure and the speed of sound for $\mu_B \leq 400$ MeV. This holographic model is used to obtain holographic predictions for the temperature and $\mu_B$ dependence of the drag force and the Langevin diffusion coefficients associated with heavy quark jet propagation as well as the jet quenching parameter $\hat{q}$ and the shooting string energy loss of light quarks in the baryon dense plasma. We find that the energy loss of heavy and light quarks generally displays a nontrivial, fast-varying behavior as a function of the temperature near the crossover. Moreover, energy loss is also found to generally increase due to nonzero baryon density effects even though this strongly coupled liquid cannot be described in terms of well defined quasiparticle excitations. Furthermore, to get a glimpse of how thermalization occurs in a hot and baryon dense QGP, we study how the lowest quasinormal mode of an external massless scalar disturbance in the bulk is affected by a nonzero baryon charge. We find that the equilibration time associated with the lowest quasinormal mode decreases in a dense medium.

Thermal photon, dilepton production, and electric charge transport in a baryon rich strongly coupled QGP from holography

We obtain the thermal photon and dilepton production rates in a strongly coupled quark-gluon plasma (QGP) at both zero and nonzero baryon chemical potential using a bottom-up Einstein-Maxwell-Dilaton (EMD) holographic model that is in good quantitative agreement with the thermodynamics of $(2+1)$-flavor lattice QCD around the crossover transition for baryon chemical potentials up to 400 MeV, which may be reached in the beam energy scan (BES) at RHIC. We find that increasing the temperature $T$ and the baryon chemical potential $\mu_B$ enhances the peak present in both spectra. We also obtain the electric charge susceptibility, the DC and AC electric conductivities and the electric charge diffusion as functions of $T$ and $\mu_B$. We find that electric diffusive transport is suppressed as one increases $\mu_B$. At zero baryon density, we compare our results for the DC electric conductivity and the electric charge diffusion with the latest lattice data available for these observables and find reasonable agreement around the crossover transition. Therefore, our holographic results may be used to constraint the magnitude of the thermal photon and dilepton production rates in a strongly coupled QGP, which we found to be at least one order of magnitude below perturbative estimates.

Chiral phase transition and Schwinger mechanism in a pure electric field

We systematically study the chiral symmetry breaking and restoration in the presence of a pure electric field in the Nambu--Jona-Lasinio (NJL) model at finite temperature and baryon chemical potential. In addition, we also study the effect of the chiral phase transition on the charged pair production due to the Schwinger mechanism. For these purposes, a general formalism for parallel electric and magnetic fields is developed at finite temperature and chemical potential for the first time. In the pure electric field limit $B\rightarrow0$, we compute the order parameter, the transverse-to-longitudinal ratio of the Goldstone mode velocities, and the Schwinger pair production rate as functions of the electric field. The inverse catalysis effect of the electric field to chiral symmetry breaking is recovered. And the Goldstone mode is find to disperse anisotropically such that the transverse velocity is always smaller than the longitudinal one, especially at nonzero temperature and baryon chemical potential. As expected, the quark-pair production rate is greatly enhanced by the chiral symmetry restoration.

Lattice simulation study of SU(2) QCD with a nonzero baryon density

The lattice simulation of SU(2) QCD with two quark dynamical flavors and a nonzero baryon chemical potential has been performed. The dependence of the Polyakov loop and chiral condensate on the chemical potential has been studied. It has been shown that the chemical potential reduces the chiral condensate, thus weakening the breaking of the chiral symmetry.

Color path integral equation of state of the quark–gluon plasma at nonzero chemical potential

Based on the constituent quasiparticle model of the quark–gluon plasma (QGP), a color quantum path-integral Monte-Carlo (PIMC) method for calculation of the thermodynamic properties of the QGP is developed. We show that the PIMC method can be used for calculations of the equation of state at zero and non-zero baryon chemical potential not only above but also below the QCD critical temperature. Our results agree with lattice QCD calculations based on a Taylor expansion around zero baryon chemical potential. In our approach the QGP partition function is presented in the form of a color path integral with a relativistic measure replacing the Gaussian one traditionally used in the Feynman–Wiener path integrals. A procedure of sampling color variables according to the SU(3) group Haar measure is used for integration over the color variables. We expect that this approach will be useful to predict additional properties of the QGP that are still unaccesible in lattice QCD.

Recent lattice QCD results and phase diagram of strongly interacting matter

I review recent lattice QCD results on a few selected topics which are relevant to the heavy ion physics community. Special emphasis is put on the QCD equation of state at vanishing and nonzero baryon chemical potential, the onset of deconfinement of open strange and charmed hadrons, the contribution from experimentally not yet observed hadrons to the thermodynamics of the hadronic gas and their influence on freeze-out conditions of strange and light-quark hadrons.

Critical line of2+1flavor QCD

We determine the curvature of the (pseudo)critical line of QCD with ${n}_{f}\text{ }=\text{ }2\text{ }+\text{ }1$ staggered fermions at nonzero temperature and quark density by analytic continuation from imaginary chemical potentials. Monte Carlo simulations are performed by adopting the highly improved staggered quarks /tree action discretization, as implemented in the code by the MILC Collaboration, suitably modified to include a nonzero imaginary baryon chemical potential. We work on a line of constant physics, as determined in Ref. [1], adjusting the couplings so as to keep the strange quark mass ${m}_{s}$ fixed at its physical value, with a light to strange mass ratio of ${m}_{l}/{m}_{s}=1/20$. In the present investigation, we set the chemical potential at the same value for the three quark species, ${\ensuremath{\mu}}_{l}={\ensuremath{\mu}}_{s}\ensuremath{\equiv}\ensuremath{\mu}$. We explore lattices of different spatial extensions, ${16}^{3}\ifmmode\times\else\texttimes\fi{}6$ and ${24}^{3}\ifmmode\times\else\texttimes\fi{}6$, to check for finite size effects, and present results on a ${32}^{3}\ifmmode\times\else\texttimes\fi{}8$ lattice, to check for finite cutoff effects. We discuss our results for the curvature $\ensuremath{\kappa}$ of the (pseudo)critical line at $\ensuremath{\mu}=0$, which indicate $\ensuremath{\kappa}=0.018(4)$, and compare them with previous lattice determinations by alternative methods and with experimental determinations of the freeze-out curve.

Probing the QCD phase diagram with fluctuations

The relevance of higher order cumulants of conserved charges for the analysis of freeze-out and critical conditions in heavy ion collisions at LHC and RHIC is discussed. Using properties of $O(4)$ scaling functions, the generic structure of these higher cumulants at vanishing baryon chemical potential is discussed. Chiral model calculations are then used to study their properties at non-zero baryon chemical potential. It is argued that the rapid variation of sixth and higher order cumulants at the phase boundary may be used to explore the QCD phase diagram in experiment. Moreover, results for the Polyakov loop susceptibilities in SU(3) lattice gauge theory as well as in (2+1) flavor lattice QCD are discussed. An analysis of the ratios of susceptibilities indicates that the deconfinement transition is reflected in characteristic modifications of these ratios.

Magnetic properties of four dimensional fermions

We investigate the Sakai-Sugimoto model at nonzero baryon chemical potential in a background magnetic field in the chiral symmetric phase. We find that a new form of baryonic matter shows up, and we investigate its properties. We find a generated axial current, a reduction in the amount of charge participating in dissipative interactions and a metamagnetic like phase transition at low temperature.

Magnetic properties of confined holographic QCD

We investigate the Sakai-Sugimoto model at nonzero baryon chemical potential in a background magnetic field in the confined phase where chiral symmetry is broken. The D8-brane Chern-Simons term holographically encodes the axial anomaly and generates a gradient of the η' meson, which carries a non-vanishing baryon charge. Above a critical value of the chemical potential, there is a second-order phase transition to a mixed phase which includes also ordinary baryonic matter. However, at fixed baryon charge density, the matter is purely η'-gradient above a critical magnetic field.

Hydrodynamics of a quark droplet II: Implications of a non-zero baryon chemical potential

We present an extended version of the dynamical model for a multi-quark droplet evolution described in our proceeding paper. The model includes collective expansion of the droplet, effects of the vacuum pressure and surface tension, and now a non-zero baryon number. The hadron emission from the droplet is described following Weisskopf's statistical model. We consider evolutions of droplets with different initial temperatures and net baryon number. It is found that the introduction of a non-zero net baryon number does not change the lifetime of the droplets significantly. Only when we consider an initially very baryon-rich, low-temperature droplets is the lifetime is decreased significantly. We have, furthermore, found a convergence of both baryon chemical potential and temperature toward the values $\mu_{\rm B} \approx$ 450 MeV and $T \approx 150$ MeV. This convergence is linked to the competing emission of baryons versus mesons.

A Random Walk with Heavy Flavours

We focus on evaluating transport coefficients like drag and diffusion of heavy quarks (HQ) passing through Quark Gluon Plasma using perturbative QCD (pQCD). Experimental observable like nuclear suppression factor (RAA) of HQ is evaluated for both zero and non-zero baryonic chemical potential ({\mu}_B) scenarios using Fokker- Planck equation. Theoretical estimates of RAA are contrasted with experiments.

Center-symmetric effective theory for two-color quark matter

Abstract We revisit the center-symmetric dimensionally reduced effective theory for two-color Yang-Mills theory at high temperature. This effective theory includes an order parameter for deconfinement and thus allows to broaden the range of validity of the conventional three-dimensional effective theory (EQCD) towards the confining phase transition. We extend the previous results by including the effects of massive quarks with nonzero baryon chemical potential. The parameter space of the theory is constrained by leading-order matching to the Polyakov loop effective potential of two-color QCD. Once all the parameters are fixed, the effective theory can provide model-independent predictions for the physics above the deconfinement transition, thus bridging the gap between large-scale numerical simulations and semi-analytical calculations within phenomenological models.

Holographic realization of large-N c orbifold equivalence with non-zero chemical potential

Recently, it has been suggested that large-Nc orbifold equivalences may be applicable to certain theories with chemical potentials, including QCD, in certain portions of their phase diagram. When valid, such an equivalence offers the possibility of relating large-Nc QCD at non-zero baryon chemical potential, a theory with a complex fermion determinant, to a related theory whose fermion determinant is real and positive. In this paper, we provide a test of this large Nc equivalence using a holographic realization of a supersymmetric theory with baryon chemical potential and a related theory with isospin chemical potential. We show that the two strongly-coupled, large-Nc theories are equivalent in a large region of the phase diagram.

Fluctuations as probe of the QCD phase transition and freeze-out in heavy ion collisions at LHC and RHIC

We discuss the relevance of higher order moments of net baryon number fluctuations for the analysis of freeze-out and critical conditions in heavy ion collisions at LHC and RHIC. Using properties of O(4) scaling functions, we discuss the generic structure of these higher moments at vanishing baryon chemical potential and apply chiral model calculations to explore their properties at non-zero baryon chemical potential. We show that the ratios of the sixth to second and eighth to second order moments of the net baryon number fluctuations change rapidly in the transition region of the QCD phase diagram. Already at vanishing baryon chemical potential they deviate considerably from the predictions of the hadron resonance gas model which reproduce the second to fourth order moments of the net proton number fluctuations at RHIC. We point out that the sixth order moments of baryon number and electric charge fluctuations remain negative at the chiral transition temperature. Thus, they offer the possibility to probe the proximity of the thermal freeze-out to the crossover line.

Fluctuations and correlations of conserved charges near the QCD critical point

We study the fluctuations and correlations of conserved charges, such as the baryon number, the electric charge and the strangeness, at the finite temperature and the nonzero baryon chemical potential in an effective model. The fluctuations are calculated up to the fourth-order and the correlations to the third-order. We find that the second-order fluctuations and correlations have a peak or valley structure when the chiral phase transition takes place with the increase of the baryon chemical potential; the third-order fluctuations and correlations change their signs during the chiral phase transition; and the fourth-order fluctuations have two maxima and one minimum. We also depict contour plots of various fluctuations and correlations of conserved charges in the plane of temperature and the baryon chemical potential. It is found that higher-order fluctuations and correlations of conserved charges are superior to the second-order ones to be used to search for the critical point in heavy ion collision experiments.

Evaluating the phase diagram at finite isospin and baryon chemical potentials in the Nambu–Jona-Lasinio model

We study the phase diagram of two-flavor dense QCD at finite isospin and baryon chemical potentials in the framework of the Nambu--Jona-Lasinio model. We focus on the case with arbitrary isospin chemical potential ${\ensuremath{\mu}}_{\mathrm{I}}$ and small baryon chemical potential ${\ensuremath{\mu}}_{\mathrm{B}}\ensuremath{\le}{\ensuremath{\mu}}_{\mathrm{B}}^{\ensuremath{\chi}}$ where ${\ensuremath{\mu}}_{\mathrm{B}}^{\ensuremath{\chi}}$ is the critical chemical potential for the first-order chiral phase transition to happen at ${\ensuremath{\mu}}_{\mathrm{I}}=0$. The ${\ensuremath{\mu}}_{\mathrm{I}}\ensuremath{-}{\ensuremath{\mu}}_{\mathrm{B}}$ phase diagram shows a rich phase structure since the system undergoes a crossover from a Bose-Einstein condensate of charged pions to a BCS superfluid with condensed quark-antiquark Cooper pairs when ${\ensuremath{\mu}}_{\mathrm{I}}$ increases at ${\ensuremath{\mu}}_{\mathrm{B}}=0$, and a nonzero baryon chemical potential serves as a mismatch between the pairing species. We observe a gapless pion condensation phase near the quadruple point $({\ensuremath{\mu}}_{\mathrm{I}},{\ensuremath{\mu}}_{\mathrm{B}})=({m}_{\ensuremath{\pi}},{M}_{\mathrm{N}}\ensuremath{-}1.5{m}_{\ensuremath{\pi}})$ where ${m}_{\ensuremath{\pi}}$, ${M}_{\mathrm{N}}$ are the vacuum masses of pions and nucleons, respectively. The first-order chiral phase transition becomes a smooth crossover when ${\ensuremath{\mu}}_{\mathrm{I}}>0.82{m}_{\ensuremath{\pi}}$. At very large isospin chemical potential, ${\ensuremath{\mu}}_{\mathrm{I}}>6.36{m}_{\ensuremath{\pi}}$, an inhomogeneous Larkin-Ovchinnikov-Fulde-Ferrell superfluid phase, appears in a window of ${\ensuremath{\mu}}_{\mathrm{B}}$, which should in principle exist for arbitrary large ${\ensuremath{\mu}}_{\mathrm{I}}$. Between the gapless and the Larkin-Ovchinnikov-Fulde-Ferrell phases, the pion superfluid phase and the normal quark matter phase are connected by a first-order phase transition. In the normal phase above the superfluid domain, we find that charged pions are still bound states even though ${\ensuremath{\mu}}_{\mathrm{I}}$ becomes very large, which is quite different from that at finite temperature. Our phase diagram is in good agreement with that found in imbalanced cold atom systems.

Symmetries and symmetry breaking patterns in QCD: chiral and deconfinement transitions

The symmetry breaking pattern of QCD features two seemingly disconnected phenomena: the spontaneous breakdown of the Z ( 3 ) center symmetry in the deconfinement transition of pure-gauge QCD, and the spontaneous breaking of chiral S U ( N f ) × S U ( N f ) symmetry in the limit of N f massless quark flavours. The dynamical entanglement of these symmetries is displayed in the framework of a schematic model (the PNJL model) in comparison with results from Lattice QCD. Extensions to non-zero baryon chemical potential are discussed.

Nuclear suppression at low energy in relativistic heavy ion collisions

The effects of non-zero baryonic chemical potential on the drag and diffusion coefficients of heavy quarks propagating through a baryon rich quark gluon plasma have been studied. The nuclear suppression factor, $R_{\mathrm AA}$ for non-photonic single electron spectra resulting from the semileptonic decays of hadrons containing heavy flavours have been evaluated for low energy collisions. The role of non-zero baryonic chemical potential on $R_{\mathrm AA}$ has been highlighted.

Emergent quantum near-criticality from baryonic black branes

We find new black 3-brane solutions describing the “conifold gauge theory” at nonzero temperature and baryonic chemical potential. Of particular interest is the lowtemperature limit where we find a new kind of weakly curved near-horizon geometry; it is a warped product $$AdS_{2} \times \mathbb{R}^{3} \times T^{1,1} $$ with warp factors that are powers of the logarithm of the AdS radius. Thus, our solution encodes a new type of emergent quantum near-criticality. We carry out some stability checks for our solutions. We also set up a consistent ansatz for baryonic black 2-branes of M-theory that are asymptotic to AdS 4 × Q 1,1,1.