Relativistic Aspects of Nuclear Physics

The following sections are included:

• Organizing Committee
• Acknowledgments
• Welcome Address
• Contents

One of the most important questions in particle physics which has to be answered today by future super colliders is what the mechanism of electroweak symmetry breaking is. If a light Higgs is absent below 1 TeV, longitudinally polarized W’s, i.e., W_L should interact strongly with themselves at high energies, since the theory without a scalar gives a bad high energy behavior. This inevitably leads us to a new strong interactions. To investigate new physics, we use the techniques of strong interactions which had bloomed in 1960’s with new modification. This new method can also be applied to hadron physics.

The relativistic constituent quark model of the nucleon wave-function, obtained from a Faddeev calculation in the null-plane is used to calculate several properties of the nucleon. The effective interaction between the constituent quarks is choosen as a two-body contact force. The formulation of this three-quark model is reviewed and the covariance of the null-plane Faddeev-like equation under kinematical front-form boosts is discussed. It is shown that the proton electric form-factor, obtained by solving the Faddeev equation, reproduces the experimental data for low momentum transfer and qualitatively describes the asymptotic high momentum transfers region. The two-quark density of the nucleon and the constituent quark wave-function at the center of the nucleon are also calculated.

Recent developments in the string model approach to ultrarelativistic nuclear scattering concern the formation and hadronisation of quark matter. We introduce new methods to study ultrarelativistic scattering by providing a link between the string model approach and a thermal description. The string model is used to provide information about fluctuations in energy density. Regions of high energy density are considered to be quark matter droplets and treated macroscopically. At SPS energies, we find mainly medium size droplets — with energies up to few tens of GeV. A key issue is the microcanonical treatment of individual quark matter droplets. Each droplet hadronizes instantaneously according to the available n-body phase space. Due to the huge number of possible hadron configurations, special Monte Carlo techniques have been developed to calculate this disintegration.

The dynamics of an idealized, infinite, MIT-type flux tube is followed in time as the interior evolves from a pure gluon field to a $\overline{q}q$ plasma. We work in color U(l). $\overline{q}q$ pair formation is evaluated according to the Schwinger mechanism using the results of Brink and Pavel. The drift of quarks toward the tube end caps is calculated by a Boltzmann equation including collisions. The tube undergoes damped radial oscillations until the electric field settles down to zero. The electric field stabilizes the tube against pinch instabilities; when the field vanishes, the tube disintegrates into mesons. There is only one free parameter in the problem, namely the initial flux tube radius, to which the results are very sensitive. Among various quantities calculated are the multiplicity and mean energy of the emitted pions.

Relativistic quantum field theory treats the vacuum as a medium, with bulk properties characterized by long-range order parameters. This has led to suggestions that regions of “disoriented vacuum” might be formed in high energy collision processes. The putative phenomenology of such “Disoriented Chiral Condensates” will be reviewed and used to motivate the design of Fermilab experiment T-864 (MiniMax). The status of the experiment at the time of writing is reviewed, as are prospects for future developments.

We discuss the formation of the disoriented chiral condensate both analytically and numerically within the framework of the mean field theory. We show that the effective potential is modified even by classical fluctuation and then that the quench scenario and annealing scenario can be understood in a unified way. We present a detailed description of the time-dependent solutions for the chiral fields in both scenarios. At the end, a brief outlook is presented.

A new hadronization scenario is proposed where a central role is played by the chiral symmetry break-down in the expanding Quark-Gluon Plasma. This mechanism can become effective and dominant when thermal damping ceases after the thermal freeze-out of the quark system. We estimate time scales and spatial characteristics of chiral-symmetry breaking instabilities on the basis of an effective field-theoretical model. The resulting rapid, post-freeze-out hadronization allows the net strange and anti-strange quarks survive hadronization, and thus leads to the observed high abundance of strange antibaryons in heavy ion reactions.

Particle number ratios in high energy heavy ion collisions are considered in the excluded volume hadron gas model. We analyse the role of bask chemical potentials - baryonic μ_b, strange μ_s and electric μ_e - of strongly interacting matter and possible chemical nonequilibrium effects for the pion subsystem (μ_π > 0).

I present work which attempts to describe the intial conditions for matter formed in ultra-relativistic heavy ion collisions. This work is based on a description of a single nucleus, and directly yields the gluon structure functions. The mathematical formalism relies essentially on the determination of non-abelian Weizsacker-Williams fields associated with the valence color charge distribution.

The following sections are included:

• Introduction
• What we learned from the light “heavy” ion era at CERN SPS
• Event by Event Analysis
• Pb on Pb Experiments at 160 GeV per nucleon at CERN SPS
• Energy density and stopping
• Transverse energy spectra and flow
• Strangeness and strange matter
• Interferometry
• ‘Small’ Pb-beam experiments at CERN SPS
• Conclusions
• References
• Discussions

Theoretical considerations show that in the deconfined quark-gluon plasma (QGP) phase high local strange and antistrange particle density is reached. This observation has inspired investigation of strange particle production as a signature of QGP formation in relativistic heavy ion collisions. Currently, the primary experimental interest is centered on otherwise rarely produced strange antibaryons. We present here a self-contained introduction to the subject matter: we describe and justify the model assumptions, present the highlights of the experimental results motivating the theoretical developments, introduce in considerable detail the theoretical calculations of strangeness production and present a comprehensive data interpretation, within the thermal fireball model. Among novel results presented we draw attention to the exploration of the time and temperature evolution of the strangeness and charm phase space occupancy.

Two concepts of coherent particle emission in heavy-ion collisions are compared and contrasted: Symmetrization-induced Bose-Einstein coherence from incoherent sources and emission from coherent sources. Bose induced coherence is modeled for ultrarelativistic collisions. The degree to which a nucleus can act as a source for coherent pion pairs is investigated for intermediate-energy heavy-ion collisions.

We report on charmonium state production in pA and S-U collisions. Experimental data are reviewed. Ther present status of the interpretation of charmonium suppression is discussed. Finally new preliminary results about Pb-Pb collisions are presented.

The familiar cartoon of any talk on Quark Gluon Plasma (QGP), I am afraid, is my first transparency.

Curiously enough, although it is entirely possible to mimick in the laboratory the very early universe scenario, to an extent at least, with no net baryon but only high temperature with a large energy density, (fig.1) it is not possible to envisage a scenario of cold, highly dense system in a laboratory set up. The ideal opportunity of detecting QGP lies in the central region with no net baryon density. To start with I intend to dwell on some of the important and contemporary milestones of lattice QCD…

We study the production of thermal photons and of e⁺e⁻ pairs from thermal resonances in the central rapidity region of S+Au and Pb+Pb collisions at SPS energy. A boost-invariant one-dimensional (cylindrically symmetric) fluid dynamics code is used to incorporate the effects of transverse expansion. The system is assumed to be in thermal equilibrium throughout, while deviations from chemical equilibrium are considered in a parametrized form. We use equations of state with a first-order transition between a massless pion gas and a high-energy phase with transition temperatures in the range 150 MeV ≤ T_c ≤ 200 MeV. The available data loosely constrain the transition temperature, the freeze-out temperature and the thermalization time. Scenarios with no transverse expansion appear to be ruled out. The transverse mass spectrum of e⁺e⁻ pairs is a good thermometer for T_c.

The solution of QCD equations for generating functions of multiplicity distributions reveals new peculiar features of cumulant moments oscillating as functions of their rank. This prediction is supported by experimental data on e⁺e^-, hh, AA collisions. Evolution of the moments at smaller phase space bins leads to intermittency and fractality. The experimentally defined truncated generating functions possess zeros in the complex plane of an auxiliary variable recalling Lee-Yang zeros in statistical mechanics.

The following sections are included:

• Introduction
• Hadron Production in AA collisions
• Summary
• References

A resonance gas model previously proposed is here briefly reviewed in order to illustrate some of the geometrical and dynamical effects that could distort the behavior of the two pion correlation function. The main of these effects — the resonance decaying into pions — has earlier been conceived as a possible means to probe resonance abundances at different energy ranges. However, reinforcing previous studies, we show here that the conventional l-D projection of the correlation function does not allow for clear conclusions. Instead, we propose to use the 2-D projection associated to a 2-D ᵪ² analysis, which substantially enhances the resolving power of interferometry to differentiate decoupling geometries of distinct dynamical models. This result is achieved by studying the variation of the mean ᵪ² per degrees of freedom with respect to the range of the analysis in the (qT, qL) plane. The preliminary E802 data[l, 2] on Si + Au at 14.6 AGeV/c, used here for illustrating the method, seem to rule out dynamical models with high ω, η resonance formation yields.

In this paper we present results from AGS experiment E877. Studies of azimuthal asymmetry in the transverse energy production of Au+Au collisions at 11.4 A GeV per nucleon show evidence of a dipole component. We interpret this component as being the result of directed flow. Correlations of the charged particle spectra with the reaction plane show that the flow is carried primarily by the nucleons.

I examine the current status of the exploration of the nuclear fragmentation phase transition with particular emphasis on the search for the critical point and the determination of the associated critical scaling exponents. In particular, I focus on the application of the percolation model to this phase transition.

We use the Gorkov formalism to develop a Dirac version of the Hartree-Fock-Bogoliubov approximation to the nuclear matter mean field. We analyze the ¹S₀ pairing fields in the model and relate the resulting two-nucleon correlations to those of the ¹S₀ N-N virtual state.

The extension of the Periodic System into hitherto unexplored domains – antimatter and hypermatter – is discussed. Starting from an analysis of hyperon and single hypernuclear properties we investigate the structure of multi-hyperon objects (MEMOs) using an extended relativistic meson field theory. These are contrasted with multi-strange quark states (strangelets). Their production mechanism is studied for relativistic collisions of heavy ions from present day experiments at AGS and SPS to future opportunities at RHIC and LHC. It is pointed out that absolutely stable hypermatter is unlikely to be produced in heavy ion collisions. New attention should be focused on short lived metastable hyperclusters (τ ∝ 10⁻¹⁰s) and on intensity interferometry of multi-strange-baryon correlations.

Calculations of the properties of interacting quark-gluon plasmas are beset by infrared divergences associated with the fact that magnetic interactions, i.e., those occurring through exchange of transverse gluons, are, in the absence of a “magnetic mass” in qcd, not screened. In this lecture we discuss the effects of magnetic interactions on the transport coefficients and the quasiparticle structure of quark-gluon plasmas. We describe how inclusion of dynamical screening effects – corresponding to Landau damping of the virtual quanta exchanged – leads to finite transport scattering rates. In the weak coupling limit, dynamical screening effects dominate over a magnetic mass. We illustrate the breakdown of the quasiparticle structure of degenerate plasmas caused by long-ranged magnetic interactions, describe the structure of fermion quasiparticles in hot relativistic plasmas, and touch briefly on the problem of the lifetime of quasiparticles in the presence of long-ranged magnetic interactions.

The present status of solar neutrino experiments is reviewed. The discrepancy between the experimental results and the theoretical expectations has come to be known as the Solar Neutrino Problem. Possible solutions to this problem are discussed. The next generation of solar neutrino experiments are described.

The contribution of each exchanged meson to spin observables of pn scattering are investigated. The comparison of these results with the corresponding results for pp scattering shows that ($\overrightarrow{p}$, pn) quasi-free reactions might give new information about hadronic scaling laws.

Hyperon radiative decays constitute an interesting class of processes that has been studied intensively, both theoretically and experimentally, for the past 20 years. However, despite these efforts we still lack a global understanding of these processes…

Neutron star models are constructed from a given equation of state by integration of Tolman Oppenheimer- Volkov equation[6, 7]. Most of the calculations are concerned with global quantities such as the resultant gravitational mass and radius for given central densities…

Using simple confining quark models, and a statistical model, we obtain the constituent quark structure function at finite temperatures. This will give us the nucleon structure function once adjusted the corresponding chemical potentials for the up and down quarks. One of the aims of our work is to determine observables that show the asymmetry in the cross sections of the ū(x) and $\overline{d}$(x) distribution, in a given quark potential model. Considering also the observed difficulty in fitting the proton structure function together with other observables obtained in deep inelastic scattering (see ref.[1]) we intend to study the model dependence of such observables. In our first approach, presented here, we use a linear confining potential model. Our work is mainly concerned with deep inelastic observables and the observed flavour assymmetry [2], that implies that the structure functions for proton and neutron violates the Gottfried sum rule [3]…

The traditional approach to the nuclear many body problem where nucleons are structureless particles interacting by means of a static potencial has proven very sucessfull in the description of properties of cold nuclei in general. Nowadays however as the energy limits of accelerators are increasing a description in terms relativistic: field theories is most desirable. The most sucessfull and well explored model in this context is the non-chiral σ-ω model proposted originally by J.D.Walecka[1]. It has proven to be a very effective tool in the sense of an effective theory treated in mean field approximation, for which the inclusion of renormalization effects are qualitatively unimportant[2]. On the other hand the chiral σ-ω model[3] has also been used to explore the consequences of chiral symmetry at zero temperature in nuclear matter[4, 5, 6]. More specifically, in ref[6] it is shown that although the experimental binding energy per nucleon can be obtained within the context of both models, the σ-ω or the chiral σ-ω model, in the former case a too large effective s-wave pion-nucleon scattering length is obtained. One must therefore impose additional constraints on the nonlinear couplings in the model lagrangean in order to minimize these effects. However in the chiral σ-ω model these constraints are shown to be automatically implemented by the symmetry and an s-wave pion-nucleon scattering length may be obtained which egrees with the empirical result, provided the nuclear matter ground state is treated self consistently. Also, recently a self consistent c:aleulation of nucleon, pion and sigma propagators in the chiral σ-ω model has evidentiated the importance of renormalization effects and Ward identities for the quality of results[7]. All these results together seem to suggest that the sense in which the linear chiral σ-ω model represents an effective model is diferent from the nowadays widely accept sense in which the non chiral σ-ω model is used as a effective model for the latter case that the model is expected to work well in mean field approximation and VFC are not qualitatively important. In contrast including chiral symmetry seems to demand a more rigorous field theoretical treatment. The inclusion of renormalization effects is absolutely crucial quantitatively as well as qualitatively…

We study the correlation function describing Bose-Einstein correlations in a multi-particle production picture with several fragmentation processes.

In the name of the international advisory committee I wish to thank the local organizers, Profs. Chung Cheong, Yogiro Hama and Takeshi Kodama, for their effort to host all of us, the students, the teachers, and the meeting. But even such a simple phrase, just a ‘thank you’ needs some elaboration and a brief situation report for others to understand our experiences, to know and appreciate why we all would like to return…

The following sections are included:

• PROGRAM
• LIST OF PARTICIPANTS