We review the predictions of the theory of a color glass condensate for a gluon production cross section in p(d)A collisions. We demonstrate that, at moderate energies, when the gluon production cross section can be calculated in the framework of the McLerran-Venugopalan model, it has only a partonic level Cronin effect in it. At higher energies or rapidities corresponding to smaller values of the Bjorken x, quantum evolution becomes important. The effect of quantum evolution at higher energies or rapidities is to introduce the suppression of high-p T gluons slightly decreasing the Cronin enhancement. At still higher energies or rapidities quantum evolution leads to the suppression of produced gluons at all values of p T .

We calculate the cross section of a single inclusive gluon production in deep inelastic scattering at very high energies in the saturation regime, where the parton densities inside hadrons and nuclei are large and the evolution of structure functions with energy is nonlinear. The expression we obtain for the inclusive gluon production cross section is generated by this nonlinear evolution. We analyze the rapidity distribution of the produced gluons as well as their transverse momentum spectrum given by the derived expression for the inclusive cross section. We propose an ansatz for the multiplicity distribution of gluons produced in nuclear collisions which includes the effects of nonlinear evolution in both colliding nuclei.

We extract the bulk viscosity of hot quark-gluon matter in the presence of light quarks from the recent lattice data on the QCD equation of state. For that purpose we extend the sum rule analysis by including the contribution of light quarks. We also discuss the universal properties of bulk viscosity in the vicinity of a second order phase transition, as it might occur in the chiral limit of QCD at fixed strange quark mass and most likely does occur in two-flavor QCD. We point out that a chiral transition in the O(4) universality class at zero baryon density as well as the transition at the chiral critical point which belongs to the Z(2) universality class both lead to the critical behavior of bulk viscosity. In particular, the latter universality class implies the divergence of the bulk viscosity, which may be used as a signature of the critical point. We discuss the physical picture behind the dramatic increase of bulk viscosity seen in our analysis, and devise possible experimental tests of related phenomena.Comment: 14 pages, 2 figure

I review the origin and properties of electromagnetic fields produced in heavy-ion collisions. The field strength immediately after a collision is proportional to the collision energy and reaches ~mπ2at RHIC and ~10mπ2at LHC. I demonstrate by explicit analytical calculation that after dropping by about one-two orders of magnitude during the first fm/c of plasma expansion, it freezes out and lasts for as long as quark-gluon plasma lives as a consequence of finite electrical conductivity of the plasma. Magnetic field breaks spherical symmetry in the direction perpendicular to the reaction plane, and therefore all kinetic coefficients are anisotropic. I examine viscosity of QGP and show that magnetic field induces azimuthal anisotropy on plasma flow even in spherically symmetric geometry. Very strong electromagnetic field has an important impact on particle production. I discuss the problem of energy loss and polarization of fast fermions due to synchrotron radiation, consider photon decay induced by magnetic field, elucidateJ/ψdissociation via Lorentz ionization mechanism, and examine electromagnetic radiation by plasma. I conclude thatallprocesses in QGP are affected by strong electromagnetic field and call for experimental investigation.

In this paper a solution is given to the nonlinear equation which describes the evolution of the parton cascade in the case of the high parton density. The related physics is discussed as well as some applications to heavy ion-ion collisions. *

Kubo's formula relates bulk viscosity to the retarded Green's function of the trace of the energy-momentum tensor. Using low energy theorems of QCD for the latter we derive the formula which relates the bulk viscosity to the energy density and pressure of hot matter. We then employ the available lattice QCD data to extract the bulk viscosity as a function of temperature. We find that close to the deconfinement temperature bulk viscosity becomes large, with viscosity-to-entropy ratio ζ/s ∼ 1. Abstract: Kubo's formula relates bulk viscosity to the retarded Green's function of the trace of the energy-momentum tensor. Using low energy theorems of QCD for the latter we derive the formula which relates the bulk viscosity to the energy density and pressure of hot matter. We then employ the available lattice QCD data to extract the bulk viscosity as a function of temperature. We find that close to the deconfinement temperature bulk viscosity becomes large, with viscosity-to-entropy ratio ζ/s ∼ 1. Keywords

ForewordThe study of the fundamental structure of nuclear matter is a central thrust of physics research in the United States. As indicated in Frontiers of Nuclear Science, the 2007 Nuclear Science Advisory Committee long range plan, consideration of a future Electron-Ion Collider (EIC) is a priority and will likely be a significant focus of discussion at the next long range plan. We are therefore pleased to have supported the ten week program in fall 2010 at the Institute of Nuclear Theory which examined at length the science case for the EIC. This program was a major effort; it attracted the maximum allowable attendance over ten weeks.This report summarizes the current understanding of the physics and articulates important open questions that can be addressed by an EIC. It converges towards a set of "golden" experiments that illustrate both the science reach and the technical demands on such a facility, and thereby establishes a firm ground from which to launch the next phase in preparation for the upcoming long range plan discussions. We thank all the participants in this productive program. In particular, we would like to acknowledge the leadership and dedication of the five co-organizers of the program who are also the co-editors of this report.David Kaplan, Director, National Institute for Nuclear Theory Hugh Montgomery, Director, Thomas Jefferson National Accelerator Facility Steven Vigdor, Associate Lab Director, Brookhaven National Laboratory iii Preface This volume is based on a ten-week program on "Gluons and the quark sea at high energies", which took place at the Institute for Nuclear Theory (INT) in Seattle from September 13 to November 19, 2010. The principal aim of the program was to develop and sharpen the science case for an Electron-Ion Collider (EIC), a facility that will be able to collide electrons and positrons with polarized protons and with light to heavy nuclei at high energies, offering unprecedented possibilities for in-depth studies of quantum chromodynamics. Guiding questions were• What are the crucial science issues?• How do they fit within the overall goals for nuclear physics?• Why can't they be addressed adequately at existing facilities?• Will they still be interesting in the 2020's, when a suitable facility might be realized?The program started with a five-day workshop on "Perturbative and Non-Perturbative Aspects of QCD at Collider Energies", which was followed by eight weeks of regular program and a concluding four-day workshop on "The Science Case for an EIC".More than 120 theorists and experimentalists took part in the program over ten weeks. It was only possible to smoothly accommodate such a large number of participants because of the extraordinary efforts of the INT staff, to whom we extend our warm thanks and appreciation. We thank the INT Director, David Kaplan, for his strong support of the program and for covering a significant portion of the costs for printing this volume. We gratefully acknowledge additional financial support provided by BNL and JLab.The program w...

We propose a new thermalization scenario for heavy ion collisions which at sufficiently high energies implies the phase transition to the quark-gluon plasma. The key ingredient of our approach is the Hawking-Unruh effect: an observer moving with an acceleration a experiences the influence of a thermal bath with an effective temperature T = a/2π, similar to the one present in the vicinity of a black hole horizon. For electric charges moving in external electromagnetic fields of realistic strength, the resulting temperature appears too small to be detected. However for partons in strong color fields the effect should be observable: in the Color Glass Condensate picture, the strength of the color-electric field is E ∼ Q 2 s /g (Q s is the saturation scale, and g is the strong coupling), the typical acceleration is a ∼ Q s , and the heat bath temperature is T = Q s /2π ∼ 200 MeV. In nuclear collisions at sufficiently high energies the effect can induce a rapid thermalization over the time period of τ ≃ 2π/Q s ≃ 1 fm accompanied by phase transitions. We consider a specific example of chiral symmetry restoration induced by a rapid deceleration of the colliding nuclei. We argue that parton saturation in the initial nuclear wave functions is a necessary pre-condition for the formation of quark-gluon plasma. We discuss the implications of our "black hole thermalization" scenario for various observables in relativistic heavy ion collisions.2