Edward Shuryak

Instantons in QCD

The authors review the theory and phenomenology of instantons in quantum chromodynamics (QCD). After a general overview, they provide a pedagogical introduction to semiclassical methods in quantum mechanics and field theory. The main part of the review summarizes our understanding of the instanton liquid in QCD and the role of instantons in generating the spectrum of light hadrons. The authors also discuss properties of instantons at finite temperature and how instantons can provide a mechanism for the chiral phase transition. They give an overview of the role of instantons in some other models, in particular low-dimensional sigma models, electroweak theory, and supersymmetric QCD.

Quantum Chromodynamics and the Theory of Superdense Matter

Abstract At high enough density and/or temperature ordinary matter undergoes a transition into a plasma-like phase, consisting of quarks and gluons rather than of separate hadrons. Due to asymptotic freedom, the asymptotic properties of such matter can be calculated perturbatively, while in the discussion of phase transitions one should concentrate on nonperturbative effects. Recent progress in this theory is reviewed, as well as its applications to such topics as hadronic structure, neutron stars, high energy collisions of hadrons, etc.

Flow at the SPS and RHIC as a Quark-Gluon Plasma Signature

D. Teaney, 2 J. Lauret, and E.V. Shuryak 1 Department of Physics and Astronomy, State University of New York, Stony Brook, NY 11794 2 Department of Physics, Brookhaven National Laboratory Upton, NY 11973 (Dated: February 5, 2008) A hydrodynamic + cascade model of relativistic heavy ion collisions is presented and compared to available hadronic data from the SPS to RHIC. The model consistently reproduces the radial and elliptic flow data for different particles, collision energies, and impact parameters. Three ingredients are essential to the success: (a) a reasonable EOS exhibiting the hard and soft features of the QCD phase transition, (b) thermal hadronization at the phase boundary, and (c) subsequent hadronic rescattering. Some features of the RHIC data are readily explained: (i) the observed elliptic flow and its dependence on pT and mass, (ii) the anomalous p̄/π − ratio for pT ≈ 2.0 GeV, (iii) the difference in the slope parameters measured by the STAR and PHENIX collaborations, and (iv) the respectively strong and weak impact parameter dependence of the p̄ and φ slope parameters. For an EOS without the hard and soft features of the QCD phase transition, the broad consistency with the data is lost.Radial and elliptic flow in noncentral heavy-ion collisions can constrain the effective equation of state (EOS) of the excited nuclear matter. To this end, a model combining relativistic hydrodynamics and a hadronic transport code [Sorge, Phys. Rev. C 52, 3291 (1995)] is developed. For an EOS with a first-order phase transition, the model reproduces both the radial and elliptic flow data at the SPS. With the EOS fixed from SPS data, we quantify predictions at RHIC where the quark-gluon plasma (QGP) pressure is expected to drive additional radial and elliptic flows. Currently, the strong elliptic flow observed in the first RHIC measurements does not conclusively signal this nascent QGP pressure.

Signatures of the Tricritical Point in QCD

Several approaches to QCD with two {ital massless} quarks at finite temperature T and baryon chemical potential {mu} suggest the existence of a tricritical point on the boundary of the phase with spontaneously broken chiral symmetry. In QCD with {ital massive} quarks there is then a critical point at the end of a first order transition line. We discuss possible experimental signatures of this point, which provide information about its location and properties. We propose a combination of event-by-event observables, including suppressed fluctuations in T and {mu} and, simultaneously, enhanced fluctuations in the multiplicity of soft pions. {copyright} {ital 1998} {ital The American Physical Society }

THE ROLE OF INSTANTONS IN QUANTUM CHROMODYNAMICS (I). Physical vacuum

Abstract We argue that the physical QCD vacuum is similar to the “instanton liquid” with density d n /d ϱ = n c ( gd ( ϱ − ϱ c ), where n c ⋍ 8 · 10 −4 GeV 4 and ϱ c ⋍ 1 600 GeV . Instantons occupy only about 1 20 th of space-time, which can be traced to the presence of several light quark flavours. Several predictions of the vacuum properties ( e.g. 〈 ψ ψ〉 ⋍ − 1 · 10 −2 GeV 3 ) are in agreement with phenomenology.

Random matrix theory and spectral sum rules for the Dirac operator in QCD

Abstract We construct a random matrix model that, in the large- N limit, reduces to the low-energy limit of the QCD partition function put forward by Leutwyler and Smilga. This equivalence holds for an arbitrary number of flavors and any value of the QCD vacuum angle. In this model, moments of the inverse squares of eigenvalues of the Dirac operator obey sum rules, which we conjecture to be universal. In other words, the validity of the sum rules depends only on the symmetries of the theory but not on its details. To illustrate this point we show that the sum rules hold for an interacting liquid of instantons. The physical interpretations is that the way the thermodynamic limit of the spectral density near zero is approached is universal. However, its value, i.e. the chiral condensate, is not.

Quark-Gluon Plasma and Hadronic Production of Leptons, Photons and Psions

Abstract QCD calculations of the production rate in a quark-gluon plasma and account of the space-time picture of hadronic collisions lead to estimates of the dilepton mass spectrum, p⊥ distributions of e±, μ±, γ, π±, production cross sections of charm and psions.

Why does the quark–gluon plasma at RHIC behave as a nearly ideal fluid?

Abstract This article gives a brief review in the following areas. (i) Collective flow phenomena in heavy ion collisions. The data from RHIC indicate robust collective flows, well described by hydrodynamics with the expected equation of state. The transport properties turned out to be unexpected, with very small viscosity. (ii) The physics of highly excited matter produced in heavy ion collisions at T c T T c , different from that of weakly coupled quark–gluon plasma because of the relatively strong coupling generating bound states of quasiparticles. (iii) Wider discussion of other “strongly coupled systems”, including strongly coupled supersymmetric theories studied via Maldacena duality, as well as recent progress as regards trapped atoms with very large scattering lengths.

Screening of the topological charge in a correlated instanton vacuum

Screening of the topological charge due to fermion-induced interactions is an important phenomenon, closely related with the resolution of the strong {ital CP} and U(1) problems. We study the mechanism of such screening in a ``correlated instanton vacuum,`` as opposed to the ``random`` one. Both scalar and pseudoscalar gluonic correlators are analyzed by means of an observable that minimizes finite size effects. Screening of the topological charge is established. This allows us to calculate the {eta}{prime} mass without having to invert the Dirac operator. We suggest that this method might be used in lattice QCD calculations as well. Our results for the screening of the topological charge are in agreement with the chiral Ward identities, and the scalar gluonic correlator satisfies a low energy theorem first derived by Novikov {ital et} {ital al}. We also propose a modified Witten-Veneziano formula, in which the topological susceptibility is not defined for an {ital infinite} box in a world {ital without} fermions, but for a {ital small} box in the real world.

Hadrons Containing a Heavy Quark and QCD Sum Rules

Masses and other parameters of mesons and baryons containing one heavy (c,b,...) quark are calculated by the QCD sum rule method developed by Shifman, Vainshtein and Zakharov. In our case the calculations are greatly simplified because the heavy quark acts like a static centre similar to the proton in a hydrogen atom. Analysis of the sum rules is more difficult, because the continuum contribution is more important. A brief discussion of ordinary baryons, the nucleon and its isobar, is also given.