Edmond Iancu

Nonlinear gluon evolution in the color glass condensate. 1.

We consider a nonlinear evolution equation recently proposed to describe the small-

The renormalization group equation for the color glass condensate

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The Quark gluon plasma: Collective dynamics and hard thermal loops

hadronic physics in the regime of very high gluon density. This is a functional Fokker-Planck equation in terms of a classical random color source, which represents the color charge density of the partons with large

Saturation and universality in QCD at small x

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Universal behavior of QCD amplitudes at high energy from general tools of statistical physics

. In the saturation regime of interest, the coefficients of this equation must be known to all orders in the source strength. In this first paper of a series of two, we carefully derive the evolution equation, via a matching between classical and quantum correlations, and set up the framework for the exact background source calculation of its coefficients. We address and clarify many of the subtleties and ambiguities which have plagued past attempts at an explicit construction of this equation. We also introduce the physical interpretation of the saturation regime at small

Soft collective excitations in hot gauge theories

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Energy-momentum tensors for the quark-gluon plasma

as a Color Glass Condensate. In the second paper we shall evaluate the expressions derived here, and compare them to known results in various limits.

Kinetic theory and quantum electrodynamics at high temperature

Abstract We present an explicit and simple form of the renormalization group equation which governs the quantum evolution of the effective theory for the Color Glass Condensate (CGC). This is a functional Fokker–Planck equation for the probability density of the color field which describes the CGC in the covariant gauge. It is equivalent to the Euclidean time evolution equation for a second quantized current–current Hamiltonian in two spatial dimensions. The quantum corrections are included in the leading log approximation, but the equation is fully non-linear with respect to the generally strong background field. In the weak field limit, it reduces to the BFKL equation, while in the general non-linear case it generates the evolution equations for Wilson-line operators previously derived by Balitsky and Kovchegov within perturbative QCD.

Effective theory for real-time dynamics in hot gauge theories

Abstract We present a unified description of the high temperature phase of QCD, the so-called quark–gluon plasma, in a regime where the effective gauge coupling g is sufficiently small to allow for weak coupling calculations. The main focus is the construction of the effective theory for the collective excitations which develop at a typical scale gT, well separated from the typical energy of single particle excitations which is the temperature T. We show that the short wavelength thermal fluctuations, i.e., the plasma particles, provide a source for long wavelength oscillations of average fields which carry the quantum numbers of the plasma constituents, the quarks and the gluons. To leading order in g, the plasma particles obey simple gauge-covariant kinetic equations, whose derivation from the general Dyson–Schwinger equations is outlined. By solving these equations, we effectively integrate out the hard degrees of freedom, and are left with an effective theory for the soft collective excitations. As a by-product, the “hard thermal loops” emerge naturally in a physically transparent framework. We show that the collective excitations can be described in terms of classical fields, and develop for these a Hamiltonian formalism. This can be used to estimate the effect of the soft thermal fluctuations on the correlation functions. The effect of collisions among the hard particles is also studied. In particular we discuss how the collisions affect the lifetimes of quasiparticle excitations in a regime where the mean free path is comparable with the range of the relevant interactions. Collisions play also a decisive role in the construction of the effective theory for ultrasoft excitations, with momenta ∼g2T, a topic which is briefly addressed at the end of this paper.

GAUGE STRUCTURE AND SEMI-CLASSICAL ASPECTS OF HARD THERMAL LOOPS.

Abstract We find approximate solutions to the renormalization group equation which governs the quantum evolution of the effective theory for the Color Glass Condensate. This is a functional Fokker–Planck equation which generates in particular the non-linear evolution equations previously derived by Balitsky and Kovchegov within perturbative QCD. In the limit where the transverse momentum of the external probe is large compared to the saturation momentum, our approximations yield the Gaussian ansatz for the effective action of the McLerran–Venugopalan model. In the opposite limit, of a small external momentum, we find that the effective theory is governed by a scale-invariant universal action which has the correct properties to describe gluon saturation.