Pion scalar density and chiral symmetry restoration at finite temperature and density

This paper is devoted to the evaluation of the pionic scalar density at finite temperature and baryonic density. We express the latter effect in terms of the nuclear response evaluated in the random phase approximation. We discuss the density and temperature evolution of the pionic density which governs the quark condensate evolution. Numerical evaluations are performed. Received: 7 December 1999 / Accepted: 8 May 2000     

Nucleon sigma term and quark condensate in nuclear matter

We study the bound-nucleon sigma term and the quark condensate in nuclear matter. In the quark-meson coupling (QMC) model the nuclear correction to the sigma term is small and negative, i.e., it decelerates the decrease of the quark condensate in nuclear matter. However, the quark condensate in nuclear matter is controlled primarily by the scalar-isoscalar σ field. Compared to the leading term, it moderates the decrease more than that of the nuclear sigma term alone at densities around and larger than the normal nuclear-matter density.     

QCD susceptibilities and nuclear-matter saturation in a relativistic chiral theory

We investigate the evolutions with density of the QCD scalar susceptibility and of the sigma mass in a chiral relativistic theory of nuclear matter, in the mean-field approximation. In order to reach saturation we need to introduce the scalar response of the nucleons. The consequences are a quite mild density dependence of the sigma mass and the progressive decoupling of the quark density fluctuations from the nucleonic ones at large densities.     

Model independent constraints from vacuum and in-medium QCD Sum Rules

We discuss QCD sum rule constraints based on moments of vector meson spectral distributions in the vacuum and in a nuclear medium. Sum rules for the two lowest moments of these spectral distributions do not suffer from uncertainties related to QCD condensates of dimension higher than four. We exemplify these relations for the case of the ω meson and discuss the issue of in-medium mass shifts from this viewpoint. Received: 22 December 1998 / Revised version: 13 January 1999     

Mixing and decays of ρ- and ω-mesons

Isospin-violating mixing of ρ- and ω-mesons is reconsidered in terms of propagators. Its influence on various pairs of (ρ,ω)-decays to the same final states is demonstrated. Some of them, (ρ,ω)↦π⁺π^- and (ρ,ω)↦πγ, have been earlier discussed in the literature, others (e.g., (ρ,ω)↦ηγ and (ρ,ω)↦e ⁺ e ^-) are new in this context. Changes in partial widths for all the decay pairs are shown to be correlated. The set of present experimental data, though yet inconclusive, provides some limits for the direct (ρω)-coupling and indirectly supports enhancement of ρ↦πγ in comparison with ρ^±↦π^±γ, though not so large as in some previous estimates. Received: 16 September 2002 / Accepted: 23 September 2002 / Published online: 4 February 2003 RID="a" ID="a"e-mail: azimov@pa1400.spb.edu Communicated by V.V. Anisovich     

The quark condensate in relativistic nucleus-nucleus collisions

We compute the modification of the quark condensate <ˉq q> in relativistic nucleus-nucleus collisions and estimate the 4-volume, where the quark condensate is small (<ˉqq>/<ˉqq>⁰≤ 0.1–0.3) using hadron phase-space distributions obtained with the quark-gluon string model. As a function of the beam energy the 4-volume rises sharply at a beam energy E^lab/A ≃ (2–5) GeV, remains roughly constant up to beam energies ≃ 20 GeV and rises at higher energies. At low energies the reduction of the condensate is mainly due to baryons, while at higher energies the rise of the 4-volume is due to the abundant mesons produced. Based on our results we expect that moderate beam energies on the order of 10 GeV per nucleon are favourable for studying the restoration of chiral symmetry in a baryon-rich environment in nucleus-nucleus collisions. Received: 4 December 1997 / Revised version: 31 July 1998     

Fluctuations of the quark densities in nuclei

We study the static scalar susceptibility of the nuclear medium, i.e., the change of the quark condensate for a small modification of the quark mass. In the linear sigma model it is linked to the in-medium sigma propagator and its magnitude increases due to the mixing with the softer modes of the nucleon-hole excitations. We show that the pseudoscalar susceptibility, which is large in the vacuum, owing to the smallness of the pion mass, follows the density evolution of the quark condensate and thus decreases. At normal nuclear matter density the two susceptibilities become much closer, a partial chiral symmetry restoration effect as they become equal when the full restoration is achieved. Received: 20 July 2002 / Accepted: 14 September 2002 / Published online: 21 January 2003 RID="a" ID="a"e-mail: chanfray@ipnl.in2p3.fr Communicated by A. Molinari     

Molecular dynamics simulation for the baryon-quark phase transition at finite baryon density

We study the baryon-quark phase transition in the molecular dynamics (MD) of the quark degrees of freedom at finite baryon density. The baryon state at low baryon density, and the deconfined quark state at high baryon density are reproduced. We investigate the equations of state of matters with different u-d-s compositions. It is found that the baryon-quark transition is sensitive to the quark width.     

QCD at high baryon density in a random matrix model

A high-density diquark phase seems to be a generic feature of QCD. If so it should also be reproduced by random matrix models. We discuss a specific one in which the random matrix elements of the Dirac operator are supplemented by a finite chemical potential and by non-random elements which model the formation of instanton-anti-instanton molecules. Comparing our results to those found in a previous investigation by Vanderheyden and Jackson we find additional support for our starting assumption, namely that the existence of a high-density diquark phase is common to all QCD-like model. Received: 20 February 2001 / Accepted: 24 April 2001     

Effective-field theory and the nuclear many-body problem

We review many-body calculations of the equation of state of dilute neutron matter in the context of effective-field theories of the nucleon-nucleon interaction.     

Low-energy photoproduction of Φ-mesons

Photoproduction of Φ-vector-mesons has been studied from reaction threshold up to W = 2.4 GeV with the SAPHIR spectrometer at the Bonn electron stretcher ring ELSA. Total cross-sections, differential cross-sections and decay angular distributions were measured. We find evidence for strong non-diffractive contributions to Φ photoproduction. Received: 12 December 2002 / Accepted: 13 March 2003 / Published online: 20 May 2003     

Scalar and axial-vector mesons

Almost thirty years ago, Penny G. Estabrooks asked “Where and what are the scalar mesons?” (P. Estabrooks, Phys. Rev. D 19, 2678 (1979)). The first part of her question can now be confidently responded (E. van Beveren et al., Z. Phys. C 30, 615 (1986)). However, with respect to the “What” many puzzles remain unanswered. Scalar and axial-vector mesons form part of a large family of mesons. Consequently, though it is useful to pay them some extra attention, there is no point in discussing them as isolated phenomena. The particularity of structures in the scattering of --basically-- pions and kaons with zero angular momentum is the absence of the centrifugal barrier, which allows us to “see” strong interactions at short distances. Experimentally observed differences and similarities between scalar and axial-vector mesons on the one hand, and other mesons on the other hand, are very instructive for further studies. Nowadays, there exists an abundance of theoretical approaches towards the mesonic spectrum, ranging from confinement models of all kinds, i.e., glueballs, and quark-antiquark, multiquark and hybrid configurations, to models in which only mesonic degrees of freedom are taken into account. Nature seems to come out somewhere in the middle, neither preferring pure bound states, nor effective meson-meson physics with only coupling constants and possibly form factors. As a matter of fact, apart from a few exceptions, like pions and kaons, Nature does not allow us to study mesonic bound states of any kind, which is equivalent to saying that such states do not really exist. Hence, instead of extrapolating from pions and kaons to the remainder of the meson family, it is more democratic to consider pions and kaons mesonic resonances that happen to come out below the lowest threshold for strong decay. Nevertheless, confinement is an important ingredient for understanding the many regularities observed in mesonic spectra. Therefore, excluding quark degrees of freedom is also not the most obvious way of describing mesons in general, and scalars and axial-vectors in particular.     

Effective potential of the O(N) linear sigma-model at finite temperature

We study the O(N) symmetric linear sigma-model at finite temperature as the low-energy effective models of quantum chromodynamics (QCD) using the Cornwall-Jackiw-Tomboulis (CJT) effective action for composite operators. It has so far been claimed that the Nambu-Goldstone theorem is not satisfied at finite temperature in this framework unless the large-N limit in the O(N) symmetry is taken. We show that this is not the case. The pion is always massless below the critical temperature, if one determines the propagator within the form such that the symmetry of the system is conserved, and defines the pion mass as the curvature of the effective potential. We use a regularization for the CJT effective potential in the Hartree approximation, which is analogous to the renormalization of auxiliary fields. A numerical study of the Schwinger-Dyson equation and the gap equation is carried out including the thermal and quantum loops. We point out a problem in the derivation of the sigma meson mass without quantum correction at finite temperature. A problem about the order of the phase transition in this approach is also discussed. Received: 21 June 2000 / Accepted: 13 September 2000     

Mind the gap

In this summary of the application of Dyson-Schwinger equations to the theory and phenomenology of hadrons, some deductions following from a nonperturbative, symmetry-preserving truncation are highlighted, notable amongst which are results for pseudoscalar mesons. We also describe inferences from the gap equation relating to the radius of convergence of a chiral expansion, applications to heavy-light and heavy-heavy mesons, and quantitative estimates of the contribution of quark orbital angular momentum in pseudoscalar mesons; and recapitulate upon studies of nucleon electromagnetic form factors.     

Statistical properties at the spectrum edge of the QCD Dirac operator

The statistical properties of the spectrum of the staggered Dirac operator in an SU(2) lattice gauge theory are analyzed both in the bulk of the spectrum and at the spectrum edge. Two commonly used statistics, the number variance and the spectral rigidity, are investigated. While the spectral fluctuations at the edge are suppressed to the same extent as in the bulk, the spectra are more rigid at the edge. To study this effect, we introduce a microscopic unfolding procedure to separate the variation of the microscopic spectral density from the fluctuations. For the unfolded data, the number variance shows oscillations of the same kind as before unfolding, and the average spectral rigidity becomes larger than the one in the bulk. In addition, the short-range statistics at the origin is studied. The lattice data are compared to predictions of chiral random-matrix theory, and agreement with the chiral Gaussian Symplectic Ensemble is found. Received: 6 November 1997 / Revised version: 19 January 1998     

Diffraction at HERA, Color Opacity and Nuclear Shadowing in DIS off nuclei

The QCD factorization theorem for diffractive processes in DIS is used to derive formulae for the leading twist contribution to the nuclear shadowing of parton distributions in the low thickness limit (due to the coherent projectile (photon) interactions with two nucleons). Based on the current analyzes of diffraction at HERA we find that the average strength of the interactions which govern diffraction in the gluon sector at x≤ 10⁻³, Q ₀= 2 GeV is ∼50mb. This is three times larger than in the quark sector and suggests that applicability of DGLAP approximation requires significantly larger Q ₀ in the gluon sector. We use this information on diffraction to estimate the higher order shadowing terms due to the photon interactions with N≥ 3 nucleons which are important for the scattering of heavy nuclei and to calculate nuclear shadowing and Q ² dependence of gluon densities. For the heavy nuclei the amount of the gluon shadowing: G _A(x,Q ₀ ²) /AG _N(x,Q ₀ ²)_{|x ≤ 10−3}∼ 0.25–0.4 is sensitive to the probability of the small size configurations within wave function of the gluon “partonometer” at the Q ₀ scale. At this scale for A∼ 200 the nonperturbative contribution to the gluon density is reduced by a factor of 4–5 at x≤ 10⁻³ unmasking PQCD physics in the gluon distribution of heavy nuclei. We point out that the shadowing of this magnitude would strongly modify the first stage of the heavy ion collisions at the LHC energies, and also would lead to large color opacity effects in eA collisions at HERA energies. In particular, the leading twist contribution to the cross section of the coherent J/ψ production off A≥ 12 nuclei at s ⁻²≥ 70 GeV is strongly reduced as compared to the naive color transparency expectations. The Gribov black body limit for F _2A(x,Q ²) is extended to the case of the gluon distributions in nuclei and shown to be relevant for the HERA kinematics of eA collisions. Properties of the final states are also briefly discussed. Received: 12 March 1999     

Self-consistent treatment of the quark condensate and hadrons in nuclear matter

We calculate the contribution of pions to the $\bar qq$-expectation value κ(ρ) =<M|ˉq q|M> in symmetric nuclear matter. We employ exact pion propagator renormalized by nucleon-hole and isobar-hole excitations. Conventional straightforward calculation leads to the “pion condensation” at unrealistically small values of densities, causing even earlier restoration of chiral symmetry. This requires a self-consistent approach, consisting in using the models, which include direct dependence of in-medium mass values on κ(ρ), e.g. the Nambu–Jona-Lasinio–model. We show, that in the self-consistent approach the ρ-dependence of the condensate is described by a smooth curve. The “pion condensate” point is removed to much higher values of density. The chiral restoration does not take place at least while ρ < 2.8ρ₀ with ρ₀ being the saturation value. Validity of our approach is limited by possible accumulation of heavier baryons (delta isobars) in the ground state of nuclear matter. For the value of effective nucleon mass at the saturation density we found m ^*(ρ₀) = 0.6m, consistent with nowadays results of other authors. Received: 8 October 1998     

Latest results on the hot dense partonic matter at RHIC

At the Relativistic Heavy-Ion Collider (RHIC) collisions of heavy ions at nucleon-nucleon energies of 200GeV appear to have created a new form of matter thought to be a deconfined state of the partons that ordinarily are bound in nucleons. We discuss the evidence that a thermalized partonic medium, usually called a Quark Gluon Plasma (QGP), has been produced. Then, we discuss the effect of this high-density medium on the production of jets and their pair correlations. Next, we look at direct photons as a clean electro-magnetic probe to constrain the initial hard scatterings. Finally, we review the developing picture for the effect of this medium on the production of open heavy quarks and on the screening by the QGP of heavy-quark bound states.     

OZI rule violation in p¯p annihilation into φππ by two step processes

The φπ⁺π⁻ production in pˉp annihilation at rest is strongly enhanced by a two step mechanism with intermediate KˉKππ states. The relative yield of the φ production due to the resonant final state interaction decreases with increasing total energy of the pˉp system. Received: 4 August 1997