Initial singularity of the little bang

Fukushima, Kenji; Gelis, François; McLerran, Larry

doi:10.1016/j.nuclphysa.2007.01.086

Cited by 103 publications

(129 citation statements)

References 58 publications

(41 reference statements)

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“…In accordance with Ref. [54], the longitudinal magnetic field is set to zero initially through A η | τ =τ 0 = 0, but the non-Abelian Gauss law leads to nonvanishing longitudinal chromoelectric fields even though j τ ≡ 0 initially. With A η = 0 initially, the Gauss law constraint in the 1+1-dimensional setting gives…”

Section: Color-glass-condensate-inspired Initial Conditionsmentioning

confidence: 61%

“…5 we show results obtained by using initial seed fields which reflect the spectral properties obtained by Fukushima, Gelis, and McLerran (FGM) within the Color-Glass-Condensate (CGC) framework [54]. We use again a random superposition of modes, but now involving already initially both chromoelectric and chromomagnetic transverse fields with a spectrum 7…”

Section: Color-glass-condensate-inspired Initial Conditionsmentioning

confidence: 97%

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Instabilities of an anisotropically expanding non-Abelian plasma:1D+3Vdiscretized hard-loop simulations

2008

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Non-Abelian plasma instabilities play a crucial role in the nonequilibrium dynamics of a weakly coupled quark-gluon plasma and they importantly modify the standard perturbative bottom-up thermalization scenario in heavy-ion collisions. Using the auxiliary-field formulation of the hard-loop effective theory, we study numerically the real time evolution of instabilities in an anisotropic collisionless Yang-Mills plasma expanding longitudinally in free streaming. In this first real-time lattice simulation we consider the most unstable modes, long-wavelength coherent color fields that are constant in transverse directions and which therefore are effectively 1+1-dimensional in spacetime, except for the auxiliary fields which also depend on discretized momentum rapidity and transverse velocity components. We reproduce the semi-analytical results obtained previously for the Abelian regime and we determine the nonlinear effects which occur when the instabilities have grown such that non-Abelian interactions become important.

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Section: Color-glass-condensate-inspired Initial Conditionsmentioning

confidence: 61%

Section: Color-glass-condensate-inspired Initial Conditionsmentioning

confidence: 97%

Instabilities of an anisotropically expanding non-Abelian plasma:1D+3Vdiscretized hard-loop simulations

2008

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“…[4]. It is interesting to apply our formula (16) to the Au-Au collision at RHIC in the physical unit. We make use of the parameter choice as commonly used in the numerical simulation, i.e., g 2 /4π = 1/π and g 2 µ = 2 GeV [4,5,6,10].…”

mentioning

confidence: 99%

“…As formulated in Ref. [16], δE η should be constrained by the Gauss law and we drop δA η because it is accompanied by τ 2 from the metric. In what follows we regard η-dependent fluctuations, δA i and δE i , as the "soft" fields and η-independent CGC fields as the "hard" background which brings about instability.…”

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confidence: 99%

Erratum: Initial fields and instabilities in the classical model of relativistic heavy-ion collisions [Phys. Rev. C76, 021902 (2007)]

Fukushima¹

2008

Phys. Rev. C

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Color Glass Condensate (CGC) provides a classical description of dense gluon matter at high energies. Using the McLerran-Venugopalan (MV) model we calculate the initial energy density ε(τ ) in the early stage of the relativistic nucleus-nucleus collision. Our analytical formula reproduces the quantitative results from lattice discretized simulations and leads to an estimate ε(τ = 0.1 fm) = 40 ∼ 50 GeV · fm −3 in the Au-Au collision at RHIC energy. We then formulate instability with respect to soft fluctuations that violate boost invariance inherent in hard CGC backgrounds. We find unstable modes arising, which is attributed to ensemble average over the initial CGC fields.In the relativistic heavy-ion collision Color Glass Condensate (CGC) describes the initial state of energetic gluon matter with the transverse momentum p t up to the saturation scale Q s which universally characterizes the hadron or nucleus wavefunction in the smallx regime [1,2,3,4,5,6,7,8,9,10]. Given the scale Q s at a certain value of Bjorken's x, the gluon distribution probed by processes with Q 2 ≪ Q 2 s is so dense that coherent fields should be more relevant than the individual particle picture during τ Q −1s . Physically Q 2 s corresponds to the transverse density of partons and is estimated by the Golec-Biernat and Wüsthoff fit,, where A is the atomic number. We can expect Q s around 1 ∼ 2 GeV for the Relativistic Heavy Ion Collider (RHIC) and 2 ∼ 3 GeV for the Large Hadron Collider (LHC) in case of A = 197 (Au-Au collision) assuming relevant p t is ∼ 1 GeV. This transient but still coherent gluon matter, which is often referred to as "Glasma" [7], should melt toward a quark-gluon plasma.The physical property of Glasma has been mainly analyzed by numerical simulations in the lattice discretized formulation [4,5,6,7,8,9]. In this paper we aim to approach Glasma in an analytical way along a similar line to the near-field expansion proposed by Fries-KapustaLi [10]. The analytical method is desirable for a deeper insight into the Glasma, which presumably exists up to τ Q −1 s ∼ 0.1 fm in the Au-Au (central) collision at RHIC energy, √ s = 200 GeV/nucleon, or even longer depending on the interpretation of the Glasma. In particular, the problem of early thermalization still has interesting unanswered questions [11]. We will specifically address the following; is there any unstable mode growing around the initial CGC fields right after the collision? If any, it could speed up thermalization (or isotropization) even in the classical regime (τ Q −1 s ), besides non-Abelian plasma instabilities [12,13,14,15] which take place at later times. The pioneering numerical simulation [9] suggests the existence of "Glasma instability", though the literal time scale of instability seems to be greater than Q −1 s by three order of magnitude, probably because of the choice of tiny instability seeds. The delay in the instability onset has also been pointed out in the Hard Expanding Loop (HEL) approach to non-Abelian plasma instabilities [15].We shall start w...

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“…If one adds small fluctuations which are random in rapidity, they in fact exponentially grow. [53]- [58] The characteristic time scale corresponds to exponential growth in the square root of time with a time scale t ∼ 1/Q sat . During this time, the fields are still large and coherent.…”

Section: Phenomenological Consequences Of the Color Glass Condensatementioning

confidence: 99%

Gluon Saturation and the Formation Stage of Heavy Ion Collisions

McLerran¹

2010

Relativistic Heavy Ion Physics

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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 color magnetic fields. These flux tubes decay and might form a turbulent liquid that eventually thermalizes into a Quark Gluon Plasma.

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Initial singularity of the little bang

Cited by 103 publications

References 58 publications

Instabilities of an anisotropically expanding non-Abelian plasma:1D+3Vdiscretized hard-loop simulations

Instabilities of an anisotropically expanding non-Abelian plasma:1D+3Vdiscretized hard-loop simulations

Erratum: Initial fields and instabilities in the classical model of relativistic heavy-ion collisions [Phys. Rev. C76, 021902 (2007)]

Gluon Saturation and the Formation Stage of Heavy Ion Collisions

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