“Bottom-up” thermalization in heavy ion collisions

Baier, Rudolf; Mueller, A. H.; Schiff, D.; Son, D.C.

doi:10.1016/s0370-2693(01)00191-5

Cited by 618 publications

(1,069 citation statements)

References 26 publications

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“…There are strong hints that a deeper understanding of thermalization requires an analysis incorporating energy loss effects [61,62,63]. These may include the scattering contributions of the bottom-up scenario [64,65], or equivalently the energy loss induced by collective effects [66,67,68]. In the CGC framework, these effects can be shown to appear at next-to-leading order in the coupling.…”

Section: Discussionmentioning

confidence: 99%

Particle production in field theories coupled to strong external sources, I: Formalism and main results

2006

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We develop a formalism for particle production in a field theory coupled to a strong time-dependent external source. An example of such a theory is the Color Glass Condensate. We derive a formula, in terms of cut vacuum-vacuum Feynman graphs, for the probability of producing a given number of particles. This formula is valid to all orders in the coupling constant. The distribution of multiplicities is non-Poissonian, even in the classical approximation. We investigate an alternative method of calculating the mean multiplicity. At leading order, the average multiplicity can be expressed in terms of retarded solutions of classical equations of motion. We demonstrate that the average multiplicity at next-to-leading order can be formulated as an initial value problem by solving equations of motion for small fluctuation fields with retarded boundary conditions. The variance of the distribution can be calculated in a similar fashion. Our formalism therefore provides a framework to compute from first principles particle production in proton-nucleus and nucleus-nucleus collisions beyond leading order in the coupling constant and to all orders in the source density. We also provide a transparent interpretation (in conventional field theory language) of the well known Abramovsky-Gribov-Kancheli (AGK) cancellations. Explicit connections are made between the framework for multi-particle production developed here and the framework of Reggeon field theory.

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Section: Discussionmentioning

confidence: 99%

Particle production in field theories coupled to strong external sources, I: Formalism and main results

2006

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“…4 Here we define the 'induced U(1) current' for the U(1) gauge field in the Lagrangian: J µ = δL/δA µ . Its z-component is given by…”

Section: Induced Current and The Azimuthal Magnetic Fieldmentioning

confidence: 99%

“…Preceding studies on this subject [2] include the scenario based on the plasma instability (in particular, the Weibel instability) caused by coupling between hard particles and soft fields [3], the 'bottom-up' scenario based on the perturbative scatterings of hard particles [4], and so on. In addition to them, we have recently proposed a novel scenario based on the Nielsen-Olesen (N-O) instability [5] which is characteristic of the configuration of a uniform magnetic field in non-Abelian gauge theories [6,7].…”

Section: Introductionmentioning

confidence: 99%

Instabilities in non-expanding glasma

2009

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A homogeneous color magnetic field is known to be unstable for the fluctuations perpendicular to the field in the color space (the Nielsen-Olesen instability). We argue that these unstable modes, exponentially growing, generate an azimuthal magnetic field with the original field being in the z-direction, which causes the Nielsen-Olesen instability for another type of fluctuations. The growth rate of the latter unstable mode increases with the momentum p z and can become larger than the former's growth rate which decreases with increasing p z . These features may explain the interplay between the primary and secondary instabilities observed in the real-time simulation of a non-expanding glasma, i.e., stochastically generated anisotropic Yang-Mills fields without expansion.

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“…The minimum scattering angle is given by the relation m 2 D = p 2 χ 2 min , where m D is the Debye mass, an expression of which can be obtained in terms of the distribution function in the linear response approximation [15], and where p is the typical momentum of particles in the medium. We shall see below that for early times, because of the expansion, the particles in the central region have essentially zero longitudinal momentum 6 . In this situation, the exchanged gluon is essentially transverse and the relevant screening mass is the transverse mass [8] …”

Section: A Screeningmentioning

confidence: 94%

Kinetic equilibration in heavy ion collisions: The role of elastic processes

Serreau¹,

Schiff²

2001

J. High Energy Phys.

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We study the kinetic equilibration of gluons produced in the very early stages of a high energy heavy ion collision in a "self-consistent" relaxation time approximation. We compare two scenarios describing the initial state of the gluon system, namely the saturation and the minijet scenarios, both at RHIC and LHC energies. We argue that, in order to characterize kinetic equilibration, it is relevant to test the isotropy of various observables. As a consequence, we find in particular that in both scenarios elastic processes are not sufficient for the system to reach kinetic equilibrium at RHIC energies. More generally, we show that, contrary to what is often assumed in the literature, elastic collisions alone are not sufficient to rapidly achieve kinetic equilibration. Because of longitudinal expansion at early times, the actual equilibration time is at least of the order of a few fermis.PACS numbers: 25.75.-q, 12.38.Mh

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“Bottom-up” thermalization in heavy ion collisions

Abstract: We describe how thermalization occurs in heavy ion collisions in the framework of perturbative QCD. When the saturation scale Q s is large compared to Λ QCD , thermalization takes place during a time of order α −13/5 Q −1 s and the maximal temperature achieved is α 2/5 Q s .

Cited by 618 publications

References 26 publications

Particle production in field theories coupled to strong external sources, I: Formalism and main results

Particle production in field theories coupled to strong external sources, I: Formalism and main results

Instabilities in non-expanding glasma

Kinetic equilibration in heavy ion collisions: The role of elastic processes

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