Quark-Gluon Plasma and Heavy Ion Collisions

CONTENTS.

PREFACE.

No abstract received.

The Large Hadron Collider (LHC) under construction at CERN will deliver ion beams up to centre of mass energies of the order of 5.5 TeV per nucleon, in case of lead. If compared to the available facilities for the study of nucleus–nucleus collisions (SpS and RHIC), this represents a huge step forward in terms of both volume and energy density that can be attained in nuclear interactions. ALICE (A Large Ion Collider Experiment) is the only detector specifically designed for the physics of nuclear collisions at LHC, even though it can also study high cross section processes occurring in proton–proton collisions. The main goal of the experiment is to observe and study the phase transition from hadronic matter to deconfined partonic matter (Quark Gluon Plasma — QGP). ALICE is conceived as a general–purpose detector and will address most of the phenomena related to the QGP formation at LHC energies: to this purpose, a large fraction of the hadrons, leptons and photons produced in each interaction will be measured and identified.

We discuss how hard processes can be used as probes for the hot deconfined state of matter predicted by QCD. Hard processes are first defined in hadronic collisions; next, modifications due to known normal nuclear matter are obtained from pA collisions. This then allows the search for additional effects caused by the new medium produced in high energy AA collisions.

The physics of heavy ion collisions with regard the soft probes of the Quark-Gluon Plasma is reviewed.

This contribution is short discussion of hard probes in nuclear collisions, in particular of photon and dilepton production.

We show that non–conventional statistical effects (due to the presence of long range forces, memory effects, correlations and fluctuations) can be very relevant in the interpretation of the experimental observables in relativistic heavy-ions collisions. Transverse mass spectrum, transverse momentum fluctuations and rapidity spectra are analysed in the framework of the non-extensive statistical mechanics.

We develop a model to calculate strangeness production in both elementary and heavy ion collisions, within the framework of a statistical approach to hadronisation. Calculations are based on the canonical partition function of the thermal Nambu-Jona-Lasinio model with exact conservation of flavor and color. It turns out that the growth of strange quarks production in heavy ion collisions is due to the initial excess of non-strange matter over antimatter, whereas a suppression occurs for elementary collisions, owing to the constraint of exact quantum charges conservation over small volumes.

Multiple parton collisions play an increasingly important role in high energy hadronic and nuclear interactions. The rates of double parton scatterings in heavy quark production at LHC are estimated while a few interesting features, peculiar of hadron-nucleus interactions, are outlined.

The behaviour of quarkonium states in a strongly interacting medium can be studied through non-relativistic potential theory in a static picture, by using the heavy-quark potential provided by lattice QCD calculations. That leads to a sequential suppression pattern: higher excited states may decay into open charm/beauty even below the deconfinement temperature, due to in-medium modifications of the open charm/beauty threshold, whereas tightly bound states, like the J/ψ or ϒ, can be dissolved only in a deconfined medium, due to colour screening.

Recent results on charged particle pseudo-rapidity densities from RHIC are analysed in the framework of the Dual String Model, in particular when including string fusion.

The issue of averaging randomness is addressed, mostly in nuclear physics, but shortly also in QCD. The Feshbach approach, so successful in dealing with the continuum spectrum of the atomic nuclei (optical model), is extended to encompass bound states as well (shell model). Its relationship with the random-matrix theory is discussed and the bearing of the latter on QCD, especially in connection with the spectrum of the Dirac operator, is briefly touched upon. Finally the question of whether Feshbach's theory can cope with the averaging required by QCD is considered.

We briefly review the Auxiliary Field Diffusion Monte Carlo (AFDMC) method, recently developed to perform quantum simulations of medium size nucleon systems. This quantum Monte Carlo method generalizes the well established Diffusion Monte Carlo method, largely used in condensed matter, and includes auxiliary fields of the Hubbard–Stratonovich type to linearize the spin–isospin dependence of the NN interaction. The AFDMC method has significatively improved the possibility of performing ab initio calculations on nuclear and neutron matter, as well as on medium–heavy nuclei. The results of recent calculations of the equation of state and the compressibilty of a neutron matter model, characterized by the Argonne two–nucleon potential plus the Urbana IX three-nucleon force, are presented and discussed. Other properties of astrophysical interest such as the spin susceptibility of neutron matter and the symmetry energy are also discussed. Of particular interest for the mean free path of a neutrino in hadronic matter is the finding that NN correlations reduce by about a factor 3 the spin susceptibility of neutron matter.

I review the available empirical information on the equation of state of cold strongly interacting matter, as well as the prospects for obtaining new insights from the experimental study of gravitational waves emitted by neutron stars.

We study equilibrium and collective response properties of Asymmetric Nuclear Matter (ANM) within a Quantum-Hadro-Dynamics effective field picture of the hadronic sector. We focus our attention on the effects of the interplay between scalar and vector channel contributions. The introduction of an explicit coupling to the scalar-isovector channel of the nucleon-nucleon interaction is strongly supported. This coupling (to a δ-meson-like effective field) leads to a larger repulsion of the symmetry term at high baryon density and to new features of the collective response. Interesting contributions are found on the propagation of isovector-like modes at normal density and on an expected smooth transition to isoscalar-like oscillations at high baryon density. Important “chemical” effects on the neutron-proton structure of the mode are shown. For dilute ANM we have the isospin distillation mechanism of the unstable isoscalar-like oscillations, while at high baryon density we predict an almost pure neutron wave structure of the propagating sounds. Using the same hadronic EOS's we finally support, from collision simulations, the possibility of an “early” transition to a mixed hadron-deconfined phase in charge asymmetric heavy ion reactions at intermediate energies.

We propose the use of a dynamical model to describe relativistic heavy ion collisions starting from quark degrees of freedom with colors. As a preliminary step, we calculate the equation of state of a system interacting through a Coulomb and a linear term. The Fermionic nature of the system is enforced. An analytical estimate is discussed.

The microscopic many-body theory of the Nuclear Equation of State is discussed in the framework of the Bethe-Brueckner-Goldstone method. The expansion is extended up to the three hole-line diagrams contribution. In order to study neutron stars static properties, the theory is extended to include strangeness, and the possible quark-gluon plasma component is described in the simplified MIT bag model. The results for the mass and radius of neutron stars are discussed. It is shown that the value of the neutron star maximum mass can be used as a direct test of the quark-gluon plasma Equation of State.

We explore the dependence of the critical density, separating hadronic matter from a mixed phase of quarks and hadrons, on the ratio Z/A. We use both the MIT bag model and the Color Dielectric Model to describe the quark dynamics, while for the hadronic phase we employ various relativistic equations of state. We find that, if the parameters of quark models are fixed so that the existence of quark stars is allowed, then the critical density drops dramatically in the range Z/A ~ 0.3–0.4. Moreover, for Z/A ~ 0.3 the critical density is only slightly larger than the saturation density of symmetric nuclear-matter. This open the possibility to verify Witten-Bodmer hypothesis on absolute stability of quark matter using ground-based experiments in which neutron-rich nuclei are tested.

The equations of state of spin-polarized nuclear matter and pure neutron matter are studied in the framework of the Brueckner-Hartree-Fock theory including a three-body force. The energy per nucleon E_A(δ) calculated in the full range of spin polarization δ = (ρ_↑ − ρ_↓)/ρ for symmetric nuclear matter and pure neutron matter fulfills a parabolic law. In both cases the spin-symmetry energy is calculated as a function of the baryonic density along with the related quantities such as the magnetic susceptibility and the Landau parameter G₀. The main effect of the three-body force is to strongly reduce the degenerate Fermi gas magnetic susceptibility even more than the value with only two body force. The EOS is monotonically increasing with the density for all spin-aligned configurations studied here so that no any signature is found for a spontaneous transition to a ferromagnetic state.

An overview aimed at non specialists who wish to follow the current literature: a brief outline of field theory thermodynamics is followed by a survey of the main theoretical idea and results on the QCD phase diagram. The lattice approach is then discussed, with emphasys on nonzero baryon density.

In the high density, low temperature limit, Quantum Chromodynamics exhibits a transition to phases characterized by color superconductivity and energy gaps in the fermion spectra. We review some fundamental results obtained in this area and in particular we describe the low energy effective lagrangian describing the motion of the quasi-particles in the high density medium (High Density Effective Theory).

I briefly review some aspects of the Quantum Chromo Dynamics phase diagram at non zero temperature and quark chemical potential. I then suggest new possible phases which can appear in strongly interacting theories at non zero chemical potential. Finally I describe the phase diagram as function of the number of flavors and colors at zero quark chemical potential and zero temperature.

We discuss the role of the U(1) axial symmetry for the phase structure of QCD at finite temperature. We expect that, above a certain critical temperature, also the U(1) axial symmetry will be restored. We will try to see if this transition has (or has not) anything to do with the usual chiral transition: various possible scenarios are discussed. In particular, we analyse a scenario in which the U(1) axial symmetry is still broken above the chiral transitions. We will show that this scenario can be consistently reproduced using an effective Lagrangian model. A new order parameter is introduced for the U(1) axial symmetry.

We discuss current proposals for the mechanism of color confinement in QCD. The role of topological excitations like vortices and monopoles is analyzed, starting from the numerical evidence produced by Monte Carlo simulations. Trying to characterize the deconfinement phase transition in terms of symmetry, we argue that the confined phase can be characterized as a dual superconducting phase, i.e. a phase where a dual magnetic symmetry is spontaneously broken à la Higgs. We discuss the definition of a disorder parameter that is capable of monitoring dua superconductivity and present numerical data in favour of a deconfining phase transition in pure gluodynamics driven by monopole condensation. This picture can be naturally extended to the case of QCD with dynamical fermions: in this case, the disorder parameter becomes a unique tool to identify the phase transition.

We discuss a few topics from our ongoing investigation of the phase diagram of SU (2) Lattice Gauge Theory: we analyse a first set of results for vector mesons and diquarks, we discuss long distance screening, inferred from the behaviour of interquark potential at large separation, and we contrast and compare features at high temperature and density.

We use a gauge-invariant effective action defined in terms of the lattice Schrödinger functional to investigate vacuum dynamics and confinement in pure lattice gauge theories. After a brief introduction to the method, we report some numerical results.

After presenting a brief review of how simulations of QCD with imaginary chemical potential can be used to extract physical results, we analyse the phase structure of QCD with four flavours of dynamical fermions in the finite temperature - imaginary chemical potential plane, and discuss perspectives for realistic calculations.

We present an effective field theory for the crystalline color superconductivity phase of QCD. It is kown that at high density and at low temperature QCD exhibits a transition to a color superconducting phase characterized by energy gaps in the fermion spectra. Under specific circumstances the gap parameter has a crystalline pattern, breaking translational and rotational invariance. The corresponding phase is the crystalline color superconductive phase (or LOFF phase). We compute the parameters of the low energy effective lagrangian describing the motion of the free phonon in the high density medium and derive the phonon dispersion law.

This paper is organized in two parts. In the first one, I present a recent determination of the critical exponent ν of the correlation length in 3D SU(3) and in 4D SU(2) pure gauge theories at finite temperature, by a new approach inspired by-universality and based on finite size scaling. Moreover, I discuss possible implications of universality on the spectrum of screening masses in 4D SU(2) just above the critical temperature. In the second part, I propose two topics, well known in the literature, to be investigated by numerical simulations on the lattice, namely the Polyakov loop model by Pisarski for the high temperature phase of 4D SU(N) pure gauge theories and the Roberge-Weiss formulation of 4D SU(N) gauge theories with fermions and with imaginary chemical potential.

We discuss the condensation of relativistic spin-one fields at high chemical potential. This phenomenon leads to the spontaneous breaking of rotational invariance, together with the breaking of internal symmetries.