These two lectures concern the Color Glass Condensate and the Glasma. These are forms of matter which might be studied in high energy hadronic collisions. The Color Glass Condensate is high energy density gluonic matter. It constitutes the part of a hadron wavefunction important for high energy processes. The Glasma is matter produced from the collision of two high energy hadrons. Both types of matter are associated with coherent fields. The Color Glass Condensate is static and related to a hadron wavefunction where the glasma is transient and evolves quickly after a collision. I present the properties of such matter, and some aspects of what is known of their properties.
I discuss the ridge phenomena observed in heavy ion collisions at RHIC. I argue that the ridge may be due to flux tubes formed from the Color Glass Condensate in the early Glasma phase of matter produced in such collisions
These lectures concern the theory of the Color Glass Condensate (CGC) and the Glasma. These are forms of matter that control the earliest times in hadronic collisions. I will motivate the CGC and Glasma from simple physical considerations, and provide a sketchy derivation from QCD. There will be some discussion of experimental tests of these ideas.
We review the Color Glass Condensate effective theory, that describes the gluon content of a high energy hadron or nucleus, in the saturation regime. The emphasis is put on applications to high energy heavy ion collisions. After describing initial state factorization, we discuss the Glasma phase, that precedes the formation of an equilibrated quark-gluon plasma. We end this review with a presentation of recent developments in the study of the isotropization and thermalization of the quark-gluon plasma.
We consider two-gluon production in dilute-dense collisions within the Color Glass Condensate framework, applicable to both proton-nucleus and heavy-light ion collisions. We go beyond the glasma graph approximation which is valid in the dilute-dilute limit and show the correspondence between the glasma graphs and the $k_T$-factorized approach that we use in our calculation. We then identify the classical uncorrelated, and the Hanbury-Brown-Twiss (HBT) and Bose enhancement correlated contributions, with the Bose enhancement contribution being suppressed by the number of degrees of freedom with …
We discuss high energy hadronic collisions within the theory of the Color Glass Condensate. We point out that the initial electric and magnetic fields produced in such collisions are longitudinal. This leads to a novel string like description of the collisions, and a large Chern-Simons charge density made immediately after the collision. The presence of the longitudinal magnetic field suggests that essential to the description of these collisions is the decay of Chern-Simons charge.
The collinear color electric and magnetic fields have been discussed to be produced immediately after high energy heavy ion collisions. We discuss anomalous gluon production under the background gauge fields. The gluons are Nielsen-Olesen unstable modes. The production rate of the modes by Schwinger mechanism has recently been found to be anomalously larger than the rate of quarks or other stable gluons. Analyzing classical evolutions of the modes with initial conditions given by vacuum fluctuations, we find that their production makes the color electric field decay very rapidly. The life time…
In the Color Glass Condensate (CGC) effective field theory, colliding sheets of Colored Glass form a strongly interacting, non-equilibrium state called the Glasma. How Colored Glass shatters to form the Glasma, the properties of the Glasma, and how the Glasma thermalizes into a Quark Gluon Plasma(QGP) are questions of central interest in understanding the properties of the strongly interacting matter produced in heavy ion collisions. We argue that these questions can be addressed in the framework of field theories with strong time dependent external sources. Albeit such field theories are non-…
When two sheets of Color Glass Condensate collide in a high energy heavy ion collision, they form matter with very high energy densities called the Glasma. We describe how this matter is formed, its remarkable properties and its relevance for understanding thermalization of the Quark Gluon Plasma in heavy ion collisions. Long range rapidity correlations contained in the near side ridge measured in heavy ion collisions may allow one to directly infer the properties of the Glasma.
We study the gluon distribution in nucleus-nucleus collisions in the framework of the Color-Glass-Condensate. Approximate analytical solutions are compared to numerical solutions of the non-linear Yang-Mills equations. We find that the full numerical solution can be well approximated by taking the full initial condition of the fields in Coulomb gauge and using a linearized solution for the time evolution. We also compare kt-factorized approximations to the full solution.
The initial energy density produced in an ultrarelativistic heavy ion collision can, in the color glass condensate framework, be factorized into a product of the integrated gluon distributions of the nuclei. Although this energy density is well defined without any infrared cutoff besides the saturation scale, it is apparently logarithmically ultraviolet divergent. We argue that this divergence is not physically meaningful and does not affect the behavior of the system at any finite proper time.
We compute initial conditions in heavy-ion collisions within the Color Glass Condensate (CGC) framework by combining the impact parameter dependent saturation model (IP-Sat) with the classical Yang-Mills description of initial Glasma fields. In addition to fluctuations of nucleon positions, this IP-Glasma description includes quantum fluctuations of color charges on the length-scale determined by the inverse nuclear saturation scale Q_s. The model naturally produces initial energy fluctuations that are described by a negative binomial distribution. The ratio of triangularity to eccentricity is…
Relativistic nuclear collisions offer a unique way to study strong interactions at very high energy. The collision process can be described within the gluon saturation framework as the interaction of two colored glasses, and because of this interaction strong longitudinal gluon fields, namely the Glasma, are produced immediately after the collision. Besides, heavy quarks are also produced in the very early stage and because of their large mass and small concentration, their motion does not affect the evolution of the Glasma, thus behaving as ideal probes of the Glasma itself. We study the evol…
The similarities between string percolation and Glasma results are emphasized, special attention being paid to rapidity long range correlations, ridge structure and elliptic flow. As the string density of high multiplicity pp collisions at LHC energies has similar value as the corresponding to Au-Au semi-central collisions at RHIC we also expect in pp collisions long rapidity correlations and ridge structure, extended more than 8 units in rapidity.
We present our work on the simulation of the early stages of heavy-ion collisions with finite longitudinal thickness in the laboratory frame in 3+1 dimensions. In particular we study the effects of nuclear thickness on the production of a glasma state in the McLerran-Venugopalan model within the color glass condensate framework. A finite thickness enables us to describe nuclei at lower energies, but forces us to abandon boost-invariance. As a consequence, random classical color sources within the nuclei have to be included in the simulation, which is achieved by using the colored particle-in-c…
I argue that the physics of the scattering of very high energy strongly interacting particles is controlled by a new, universal form of matter, the Color Glass Condensate. This matter is the dominant contribution to the low x part of a hadron wavefunction. In collisions, this matter almost instantaneously turns into a Glasma. The Glasma initially has strong longitudinal color electric and magnetic fields, with topological charge. These fields melt into gluons. Due to instabilities, quantum noise is converted into classical turbulence, which may be responsible for the early thermalization seen …
I discuss forms of high energy density matter in QCD. These include the Color Glass Condensate, the Glasma and the Quark Gluon Plasma. They all might be studied in ultra-relativistic heavy ion collisions, nd the Color Glass Condensate might also be probed in electron-hadron collisions. I present the properties of such matter and some aspects of what is known of their properties.
These lectures concern the properties of strongly interacting matter at very high energy density. I begin with the Color Glass Condensate and the Glasma, matter that controls the earliest times in hadronic collisions. I then describe the Quark Gluon Plasma, matter produced from the thermalized remnants of the Glasma. Finally, I describe high density baryonic matter, in particular Quarkyonic matter. The discussion will be intuitive and based on simple structural aspects of QCD. There will be some discussion of experimental tests of these ideas.
We investigate the consequences of long range rapidity correlations in the Glasma. Particles produced locally in the transverse plane are correlated by approximately boost invariant flux tubes of longitudinal color electric and magnetic fields that are formed when two sheets of Colored Glass Condensate pass through one another, each acquiring a modified color charge density in the collision. We argue that such long range rapidity correlations persist during the evolution of the Quark Gluon Plasma formed later in the collision. When combined with transverse flow, these correlations reproduce ma…
I introduce the concept of the Color Glass Condensate. I review data from HERA and RHIC which suggest that such a universal form of matter has been found.
I briefly review the physical picture of the saturated gluons at small-x as a Colour Glass Condensate, and the effective theory which forms the basis of this picture.
We simulate the 3+1 D classical Yang-Mills dynamics of the collisions of longitudinally extended nuclei, described by eikonal color charges in the Color Glass Condensate framework. By varying the longitudinal thickness of the colliding nuclei, we discuss the violations of boost invariance and explore how the boost invariant high-energy limit is approached. Subsequently, we develop a more realistic model of the three dimensional color charge distributions that connects longitudinal and transverse fluctuations to the $x$ and $k_\bot$ dependence of transverse momentum dependent parton distributio…
The Color Glass Condensate provides a systematic power counting of initial state effects in high energy QCD. We briefly discuss in this framework quark and gluon production in high energy collisions.
We explain the main ideas of the color glass condensate in high energy collisions. Different approaches to the problem are outlined with emphasis on the resummation approach. We present evidence that the color glass condensate can be described by an effective conformal field theory or even by a string theory.
We systematically compute the Gaussian average of Wilson lines inherent in the Color Glass Condensate, which provides useful formulae for evaluation of the scattering amplitude in the collision of a light projectile and a heavy target.
We make quantitative predictions for the rapidity and centrality dependencies of hadron multiplicities in $AA$, $pA$ and $pp$ collisions at the LHC energies basing on the ideas of parton saturation in the Color Glass Condensate.
A model for the Color Glass Condensate as opposed to jet quenching is proposed for the explanation of the presently available RHIC data. Good fits to these data are presented. A clear way to distinguish between the two possible explanations is also given.
Axial charge production at the early stage of heavy-ion collisions is investigated within the framework of real-time lattice simulations at leading order in QCD coupling. Starting from color glass condensate initial conditions, the time evolution of quantum quark fields under classical color gauge fields is computed on a lattice in longitudinally expanding geometry. We consider simple color charge distributions in Lorentz contracted nuclei that realize flux tube-like configurations of color fields carrying nonzero topological charge after a collision. By employing the Wilson fermion extended t…
The Color Glass Condensate is a theory of the dynamical properties of partons in the Regge limit of QCD: x_{\rm Bj}\to 0$, $Q^2 >> Λ_{\rm QCD}^2={\rm fixed} and the center of mass energy squared s\to \infty. We provide a brief introduction to the theoretical ideas underlying the Color Glass Condensate and discuss the application of these ideas to high energy scattering in QCD.
We give an elementary discussion of parton saturation and its description by the effective theory of the Color Glass Condensate. We report on progress in calculating multi-gluon correlators. The latter are necessary for many phenomenological applications, upon some of which we briefly touch.
The Color Glass Condensate is a state of high density gluonic matter which controls the high energy limit of hadronic matter. These lectures begin with a discussion of general problems of high energy strong interactions. The infinite momentum frame description of a single hadron at very small x is developed, and this picture is applied to the description of ultrarelativistic nuclear collisions. Recent developments in the renormalization group description of the Color Glass Condensate are reviewed.
This contribution discusses the phenomenon of parton saturation, the color glass picture of hadronic wavefuntions, and their relevance in the early stages of nucleus-nucleus collisions. Evidence for the color glass condensate in the presently available RHIC data is critically reviewed.
I review the problem of parton saturation and its implications through three in principal different approaches, but somewhat related: saturation in a geometrical approach, QCD saturation through the Color Glass Condensate and shadowing in a Pomeron approach.
We discuss general properties of the Color Glass Condensate. We show that predictions for particle production in p(d)A and AA collisions derived from these properties are in agreement with data collected at RHIC.
The early-time evolution of the system generated in ultra-relativistic heavy ion collisions is dominated by the presence of strong color fields known as Glasma fields. These can be described following the classical approach embodied in the Color Glass Condensate effective theory, which approximates QCD in the high gluon density regime. In this framework we perform an analytical first-principles calculation of the two-point correlator of the divergence of the Chern-Simons current at proper time $τ\!=\!0^+$, which characterizes the early fluctuations of axial charge density in the plane transver…
We report recent progress on understanding the thermalization of the quark-gluon plasma during the early stage in a heavy ion collision. The initially high overpopulation in the far-from-equilibrium gluonic matter ("Glasma") is shown to play a crucial role. The strongly interacting nature (and thus fast evolution) naturally arises as an {\em emergent property} of this pre-equilibrium matter where the intrinsic coupling is weak but the highly occupied gluon states coherently amplify the scattering. A possible transient Bose-Einstein Condensate is argued to form dynamically on a rather general g…
We confront the colour glass condensate motivated dipole model parameterization of Iancu, Itakura and Munier with the available HERA data on the diffractive structure function F2D3 and with existing dipole model parameterizations. Reasonably good agreement is found with only two adjustable parameters. We caution against interpreting the success of the model as compelling evidence for low-x perturbative saturation dynamics.
The high energy limit of QCD is controlled by very high energy density gluonic matter, the Color Glass Condensate. In the first instants of the collisions of two sheets of Colored Glass Condensate, a Glasma is formed with longitudinal flux tubes of color electric and magnetic fields. These flux tubes decay and might form a turbulent liquid that eventually thermalizes into a Quark Gluon Plasma
We discuss forward-backward correlations in the mutliplicity of produced particles in heavy ion collisions. We find the Color Glass Condensate generates distinctive predictions for the long range component of this correlation. In particular, we predict the growth of the long range correlation with the centrality of the collision. We argue that the correlation for mesons is stronger than that for baryons.
The high energy limit of QCD is controlled by the small-$x$ part of a hadron wavefunction. I argue that this part is universal to all hadrons and is composed of a new form of matter: a Colored Glass Condensate. This matter is weakly interacting at very small $x$, but is non-perturbative because of the highly occupied boson states which compose the condensate. Such a matter might be studied in high energy lepton-hadron or hadron-hadron interactions.
The proton structure function F_2(x,Q^2) for x < 0.01 and 0.045< Q^2 < 45 GeV^2, measured in the deep inelastic scattering at HERA, can be well described within the framework of the Color Glass Condensate.
We present an analytical calculation of the covariance of the energy-momentum tensor associated to the gluon field produced in ultra-relativistic heavy ion collisions at early times, the Glasma. This object involves the two-point and single-point correlators of the energy-momentum tensor ($\langle T^{μν}(x_{\perp})T^{σρ}(y_{\perp})\rangle$ and $\langle T^{μν}(x_{\perp})\rangle$, respectively) at proper time $τ\!=\!0^+$. Our approach is based on the Color Glass Condensate effective theory, which allows us to map the fluctuations of the valence color sources in the colliding nuclei to those of t…
The purpose of these lectures is to provide an introduction to the physics issues which are being studied in the RHIC heavy ion program. These center around the production of new states of matter. The Quark Gluon Plasma is thermal matter which once existed in the big bang which may be made at RHIC. The Color Glass Condensate is a universal form of matter which controls the high energy limit of strong interactions. Both such forms of matter might be produced and probed at RHIC.
In these lectures, we develop the theory of the Colour Glass Condensate. This is the matter made of gluons in the high density environment characteristic of deep inelastic scattering or hadron-hadron collisions at very high energy. The lectures are self contained and comprehensive. They start with a phenomenological introduction, develop the theory of classical gluon fields appropriate for the Colour Glass, and end with a derivation and discussion of the renormalization group equations which determine this effective theory.
Multi-particle production in QCD is dominated by higher twist contributions. The operator product expansion is not very effective here because the number of relevant operators grow rapidly with increasing twist. The Color Glass Condensate (CGC) provides a framework in QCD to systematically discuss "classical" (multiple scattering) and "quantum" evolution (shadowing) effects in multi-particle production. The apparently insuperable problem of nucleus-nucleus scattering in QCD simplifies greatly in the CGC. A few examples are discussed with emphasis on open problems.
We discuss proton-nucleus collisions in the framework of the color glass condensate. By assuming that the proton can be described as a low density color source, we solve exactly the Yang-Mills equations corresponding to this type of collision, and then use this solution in order to calculate inclusive gluon production or quark-antiquark production. Our result shows that k_T-factorization, while valid for gluon production, is violated for quark pair production in proton-nucleus collisions.
Following the Good-and-Walker picture, hard diffraction in the high-energy/small-x limit of QCD can be described in terms of eigenstates of the scattering matrix off a Color Glass Condensate. From the CGC non-linear evolution equations, it is then possible to derive the behavior of diffractive cross-sections at small $x.$ I discuss recent results, in particular the consequences of the inclusion of Pomeron loops in the evolution.
The Color Glass Condensate is a universal state of matter which can manifest itself in hadronic processes involving small-x partons, like DIS and pp, pA and AA collisions at high energy. Observables are given in terms of multi-gluon correlators, whose ensemble evolves according to a RG equation, the JIMWLK equation. We focus on recent progress towards its solution which lead to quasi-exact, analytic expressions for the multi-gluon correlators at high energy.
We discuss heavy quark production in High Parton Density QCD in quasi-classical approximation and including low-$x$ quantum evolution. We also consider an alternative approach based on the effect of pair production in external fields.
We examine the violation of the kT factorization approximation for quark production in high energy proton-nucleus collisions. We comment on its implications for the open charm and quarkonium production in collider experiments.
We apply the effective theory of color glass condensate to the analysis of gluon states in dense quark matter, in which the saturation region of gluons is also present. We find that in the region two point function of gluons shows algebraic long range order. The order is completely the same as the one gluons show in the dense quark matter, which form quantum Hall states. The order leads to the vanishing of massless gluon pole. We also find that the saturation region of gluons extends from small $x$ to even large $x\lesssim 1$ in much dense quark matter. We point out a universality that the col…
