Finite Baryon Density Research Articles

Semivariational approach to QCD at finite temperature and baryon density

Recently a new bosonization method has been used to derive, at zero fermion density, an effective action for relativistic field theories whose partition function is dominated by fermionic composites, chiral mesons in the case of QCD. This approach shares two important features with variational methods: the restriction to the subspace of the composites, and the determination of their structure functions by a variational calculation. But unlike standard variational methods it treats excited states on the same footing as the ground state. I show that this bosonization method is an approximation of an exact procedure in which composites are introduced in the presence of fermionic states with the quantum numbers of the constituents (quasiparticles). This procedure consists of an independent Bogoliubov transformation at each time slice. The time-dependent parameters of the transformation are then associated with composite fields. In this way states of nonvanishing fermion (baryon) number (neglected in the bosonization approach) are retained. By the exact procedure I derive an effective action for QCD at finite temperature and baryon density. I test the result on a four-fermion interaction model.

Density Dependence of Transport Coefficients from Holographic Hydrodynamics

We study the transport coefficients of Quark-Gluon-Plasma in finite temperature and finite baryon density. We use AdS/QCD of charged AdS black hole background with bulk-filling branes identifying the U(1) charge as the baryon number. We calculate the diffusion constant, the shear viscosity and the thermal conductivity to plot their density and temperature dependences. Hydrodynamic relations between those are shown to hold exactly. The diffusion constant and the shear viscosity are decreasing as a function of density for fixed total energy. For fixed temperature, the fluid becomes less diffusible and more viscous for larger baryon density.

On the possibility of P-violation at finite baryon-number densities

We show how the introduction of a finite baryon density may trigger spontaneous parity violation in the hadronic phase of QCD. Since this involves strong interaction physics in an intermediate energy range we approximate QCD by a σ model that retains the two lowest scalar and pseudoscalar multiplets. We propose a novel mechanism based on interplay between lightest and heavy meson states which cannot be realized solely in the Goldstone boson (pion) sector and thereby is unrelated to the one advocated by Migdal some time ago. Our approach is relevant for dense matter in an intermediate regime of few nuclear densities where quark percolation does not yet play a significant role.

Holographic vector mesons from spectral functions at finite baryon or isospin density

We consider gauge/gravity duality with flavor for the finite-temperature field theory dual of the AdS-Schwarzschild black hole background with embedded D7-brane probes. In particular, we investigate spectral functions at finite baryon density in the black hole phase. We determine the resonance frequencies corresponding to meson-mass peaks as function of the quark mass over temperature ratio. We find that these frequencies have a minimum for a finite value of the quark mass. If the quotient of quark mass and temperature is increased further, the peaks move to larger frequencies. At the same time the peaks narrow, in agreement with the formation of nearly stable vector meson states which exactly reproduce the meson-mass spectrum found at zero temperature. We also calculate the diffusion coefficient, which has finite value for all quark mass to temperature ratios, and exhibits a first-order phase transition. Finally we consider an isospin chemical potential and find that the spectral functions display a resonance peak splitting, similar to the isospin meson-mass splitting observed in effective QCD models.

Two-pion interferometry for a partially coherent evolution source**Supported by National Natural Science Foundation of China (10575024)

We give the formulas of two-pion Hanbury-Brown-Twiss (HBT) correlation function for a partially coherent evolution pion-emitting source, using quantum probability amplitudes in a path-integral formalism. The multiple scattering of the particles in the source is taken into consideration based on Glauber scattering theory. Two-pion interferometry with effects of the multiple scattering and source collective expansion is examined for a partially coherent source of hadronic gas with a finite baryon density and evolving hydrodynamically. We do not find observable effect of either the multiple scattering or the source collective expansion on HBT chaotic parameter.

Axial anomaly and magnetism of nuclear and quark matter

We consider the response of the QCD ground state at finite baryon density to a strong magnetic field $B$. We point out the dominant role played by the coupling of neutral Goldstone bosons, such as ${\ensuremath{\pi}}^{0}$, to the magnetic field via the axial triangle anomaly. We show that, in vacuum, above a value of $B\ensuremath{\sim}{m}_{\ensuremath{\pi}}^{2}/e$, a metastable object appears---the ${\ensuremath{\pi}}^{0}$ domain wall. Because of the axial anomaly, the wall carries a baryon number surface density proportional to $B$. As a result, for $B\ensuremath{\gtrsim}{10}^{19}\text{ }\text{ }\mathrm{G}$ a stack of parallel ${\ensuremath{\pi}}^{0}$ domain walls is energetically more favorable than nuclear matter at the same density. Similarly, at higher densities, somewhat weaker magnetic fields of order $B\ensuremath{\gtrsim}{10}^{17}--{10}^{18}\text{ }\text{ }\mathrm{G}$ transform the color-superconducting ground state of QCD into new phases containing stacks of axial isoscalar ($\ensuremath{\eta}$ or ${\ensuremath{\eta}}^{\ensuremath{'}}$) domain walls. We also show that a quark-matter state known as ``Goldstone current state,'' in which a gradient of a Goldstone field is spontaneously generated, is ferromagnetic due to the axial anomaly. We estimate the size of the fields created by such a state in a typical neutron star to be of order ${10}^{14}--{10}^{15}\text{ }\text{ }\mathrm{G}$.

The chiral model of Sakai-Sugimoto at finite baryon density

In the context of holographic QCD we analyze Sakai-Sugimoto's chiral model at finite baryon density and zero temperature. The baryon number density is introduced through compact D4 wrapping S^4 at the tip of D8-\bar{D8}. Each baryon acts as a chiral point-like source distributed uniformly over R^3, and leads a non-vanishing U(1)_V potential on the brane. For fixed baryon charge density n_B we analyze the bulk energy density and pressure using the canonical formalism. The baryonic matter with point like sources is always in the spontaneously broken phase of chiral symmetry, whatever the density. The point-like nature of the sources and large N_c cause the matter to be repulsive as all baryon interactions are omega mediated. Through the induced DBI action on D8-\bar{D8}, we study the effects of the fixed baryon charge density n_B on the pion and vector meson masses and couplings. Issues related to vector dominance in matter in the context of holographic QCD are also discussed.

Anomaly Mediated Neutrino-Photon Interactions at Finite Baryon Density

We propose new physical processes based on the axial vector anomaly and described by the Wess-Zumino-Witten term that couples the photon, Z-boson, and the omega-meson. The interaction takes the form of a pseudo-Chern-Simons term, approximately E(munurhosigma)omega(mu)ZnuFrhosigma. This term induces neutrino-photon interactions at finite baryon density via the coupling of the Z-boson to neutrinos. These interactions may be detectable in various laboratory and astrophysical arenas. The new interactions may account for the excess observed at the Fermilab Booster Neutrino Experiment MiniBooNE. They also produce a competitive contribution to neutron star cooling at temperatures greater, similar10(9) K. These processes and related axion-photon interactions at finite baryon density appear to be relevant in many astrophysical regimes.

Holographic thermodynamics at finite baryon density: some exact results

We use the AdS/CFT correspondence to study the thermodynamics of massive N=2 supersymmetric hypermultiplets coupled to N=4 supersymmetric SU(Nc) Yang-Mills theory in the limits of large Nc and large 't Hooft coupling. In particular, we study the theory at finite baryon number density. At zero temperature, we present an exact expression for the hypermultiplets' leading-order contribution to the free energy, and in the supergravity description we clarify which D-brane configuration is appropriate for any given value of the chemical potential. We find a second-order phase transition when the chemical potential equals the mass. At finite temperature, we present an exact expression for the hypermultiplets' leading-order contribution to the free energy at zero mass.

Abelian two-Higgs model of strongly correlated electrons: Phase structure, strengthening of phase transition, and QCD at finite density

We investigate nonperturbative features of a three-dimensional Abelian Higgs model with singly and doubly charged scalar fields coupled to a single compact Abelian gauge field. The model is pretending to describe various planar systems of strongly correlated electrons such as high-T{sub c} superconductivity in the overdoped regime and exotic materials possessing excitations with fractionalized quantum numbers. The complicated phase structure of the model is studied thoroughly using numerical tools and analytical arguments. In the three-dimensional space of coupling parameters we identify the Fermi liquid, the spin gap, the superconductor and the strange metallic phases. The behavior of three kinds of topological defects--holon, spinon vortices, and monopoles--is explored in various phases. We also observe an effect, the strong enhancement of the phase transition strength reflected in a lower order of the transition: at sufficiently strong gauge coupling the two second-order phase transitions--corresponding to spinon pair and holon condensation lines--join partially in the phase diagram and become a first-order phase transition in that region. The last observation may have an analog in quantum chromodynamics at nonzero temperature and finite baryon density. We argue that at sufficiently large baryon density the finite-temperature transition between the (three-flavor paired) color superconducting phase and the quark-gluonmore » plasma phases should be much stronger compared with the transition between two-flavor paired and three-flavor paired superconducting phases.« less

Hall conductivity of flavor fields from AdS/CFT correspondence

We use the AdS/CFT correspondence to compute a conductivity associated with massive $\mathcal{N}=2$ supersymmetric hypermultiplet fields at finite baryon density, propagating through an $\mathcal{N}=4$ supersymmetric $SU({N}_{c})$ Yang-Mills plasma in the large ${N}_{c}$, large 't Hooft coupling limit. We do so by introducing external electric and magnetic fields coupled to baryon number and computing the resulting induced current, from which we extract the conductivity tensor. At large hypermultiplet mass we compute the drag force on the charge carriers. We also compute the product of the drag coefficient with the kinetic mass, and find that the answer is unchanged from the zero-density case. The gravitational dual is a probe D7-brane, with a nontrivial world volume gauge field configuration, in an AdS-Schwarzschild background. We identify an effective horizon on the D7-brane world volume analogous to the world sheet horizon observed for strings moving in the same background. We generalize our results to a class of theories described by probe D-branes in various backgrounds.

Baryon-Number-Induced Chern-Simons Couplings of Vector and Axial-Vector Mesons in Holographic QCD

We show that holographic models of QCD predict the presence of a Chern-Simons coupling between vector and axial-vector mesons at finite baryon density. In the Anti de Sitter/Conformal Field Theory dictionary, the coefficient of this coupling is proportional to the baryon number density and is fixed uniquely in the five-dimensional holographic dual by anomalies in the flavor currents. For the lightest mesons, the coupling mixes transverse rho and a1 polarization states. At sufficiently large baryon number densities, it produces an instability, which causes the rho and a1 mesons to condense in a state breaking both rotational and translational invariance.

ASPECTS OF HADRONS AT FINITE BARYONIC DENSITY

The linear sigma model at finite baryonic density with a massive classical vector field is investigated considering that all the bosonic fields develop non zero expected classical values, eventually corresponding to dynamical symmetry breakings. The densities involving baryons are calculated using the solutions of the Dirac equation coupled to the classical vector and scalar field. The stability and ground state conditions are analyzed with particular (variational-like) prescriptions. Some aspects of relevance for states containing anti-hadrons and also for the restoration of chiral symmetry are discussed.

Influence of finite baryon density on hadronization in nucleus–nucleus collisions via recombination

In this paper, the influence of net baryon density on baryon and meson yields in relativistic nucleus–nucleus collisions is investigated on the basis of the recombination model for hadronization. Unitarity condition is used as a constraint on the model. Three cases with different assumptions on the expansion of the partonic system are considered and the baryon-to-meson ratio is calculated for those situations.

Evolution and photons of a chemically equilibrating quark–gluon plasma at finite baryon density

We study the evolution of a chemically equilibrating quark–gluon plasma in a (3+1)-dimensional spacetime at finite baryon density and its photon production. We find that the photon production is a strongly decreasing function of the ratio of quark chemical potential to temperature.

Phase structure in a hadronic chiral model

We study the phase diagram of a hadronic chiral flavour-SU(3) model. Heavy baryon resonances can induce a phase structure that matches current results from lattice-QCD calculations at finite temperature and baryon density. Furthermore, we determine trajectories of constant entropy per net baryon in the phase diagram.

Susceptibilities and the phase structure of a chiral model with Polyakov loops

In an extension of the Nambu--Jona-Lasinio model where the quarks interact with the temporal gluon field, represented by the Polyakov loop, we explore the relation between the deconfinement and chiral phase transitions. The effect of Polyakov loop dynamics on thermodynamic quantities, on the phase structure at finite temperature and baryon density and on various susceptibilities is presented. Particular emphasis is put on the behavior and properties of the fluctuations of the (approximate) order parameters and their dependence on temperature and net-quark number density. We also discuss how the phase structure of the model is influenced by the coupling of the quarks to the Polyakov loop.

Phase Structure of Color Superconductivity and Chiral Restoration

We investigate color superconductivity and chiral symmetry restoration at finite temperature and baryon density in the frame of standard two flavor Nambu–Jona-Lasinio model. We derive the diquark mass in RPA, discuss its constraint on the coupling constant in the diquark channel, and find a strong competition between the two phase transitions when the coupling constant is large enough.

Linear sigma model at finite baryonic density and symmetry breakings

The linear sigma model at finite baryonic density with a massive vector field is investigated considering that all the bosonic fields develop non zero expected classical values, eventually associated with condensates and corresponding to dynamical symmetry breakings which might occur in the QCD phase diagram. A modified equation for the classical vector field is proposed with its respective solution. Some in medium properties of the model (mainly masses) are investigated within reasonable prescriptions. In particular the behavior of the in medium pion and sigma masses and a particular way of calculating in medium coupling to baryons is investigated. A symmetry radius for finite baryonic densities is proposed and calculated in different ways in terms of the other variables of the model and these different ways of calculating it agree quite well. However, assuming that the pion and sigma masses go to zero close to the restoration of chiral symmetry a too high value for the critical density is obtained rhoc <FONT FACE=Symbol>@</FONT> 4.3 rho0.

Thermal dimuon yields: Comparison with NA60 results at 158 GeV/nucleon

Dilepton emission rates from a hadronic gas at finite temperature and baryon density are completely constrained by broken chiral symmetry in a density expansion. The rates can be expressed in terms of vacuum correlations which are measured in ${e}^{+}{e}^{\ensuremath{-}}$ annihilation, \ensuremath{\tau} decays, and photoreactions on nucleons and nuclei [1--3]. In this paper, the theoretical results are summarized and the total dimuon yield is calculated by integrating the dimuon rates over the space-time history of a fireball based on hydrodynamic calculations with CERN Super Proton Synchrotron (SPS) conditions. We compare the resulting dimuon yield with the recent measurements reported by NA60 [4].