The BFKL equation from the Wilson renormalization group

Jalilian‐Marian, Jamal; Kovner, Alex; Leonidov, A.; Weigert, Heribert

doi:10.1016/s0550-3213(97)00440-9

Cited by 910 publications

(1,004 citation statements)

References 18 publications

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“…All the diagrams contributing to φ c,1 (x) include a closed loop, to which may be attached an arbitrary number of tree diagrams. All but one of these tree diagrams are terminated by sources j; this last one has an external leg at the 14 The prefactor i is due to the fact that the inverse of + m 2 is iG according to our conventions for the propagators. The first simplification one can perform is to use eq.…”

Section: Evaluation Of Eq (68)mentioning

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: Evaluation Of Eq (68)mentioning

confidence: 99%

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

2006

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“…Indeed, reaching much softer scale, there are large radiative corrections which invalidate the classical approximation. The modifications to the effective classical theory are governed by a functional, nonlinear, evolution equation JIMWLK [26,27] for the statistical weight functional W Λ + [ρ] associated with the random variable ρ a (x).…”

Section: Dilepton Production In the Color Glass Condensatementioning

confidence: 99%

High density QCD through eletromagnetic probes

Betemps

2007

Braz. J. Phys.

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In this work we investigate the high density QCD system through the dilepton production. First, the dilepton production in the color dipole approach is investigated, studing perturbative unitarity corrections to the dipole cross section and its consequence in the transverse momentum distribution of the dileptons at RHIC and LHC energies. Second, the dilepton production in the context of the Color Glass Condensate is investigated. The transverse momentum distribution and the rapidity distribution are investigated to dilepton production at RHIC and LHC energies in this framework.

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“…Kovchegov [5] derived a closed equation for the amplitude using a mean field approximation, and this equation is referred to as the Balitsky-Kovchegov (BK) equation. The same hierarchy of equations also follows from the JIMWLK equation [6][7][8][9] which is the master equation of the Color Glass Condensate (CGC) formalism [10] and describes the non-linear evolution of dense hadronic matter in the presence of saturation effects.…”

Section: Introductionmentioning

confidence: 98%

On the dipole swing and the search for frame independence in the dipole model

Avsar

2007

J. High Energy Phys.

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Small-x evolution in QCD is conveniently described by Mueller's dipole model which, however, does not include saturation effects in a way consistent with boost invariance. In this paper we first show that the recently studied zero and one dimensional toy models exhibiting saturation and explicit boost invariance can be interpreted in terms positive definite k → k + 1 dipole vertices. Such k → k + 1 vertices can in the full model be generated by combining the usual dipole splitting with k − 1 simultaneous dipole swings. We show that, for a system consisting of N dipoles, one needs to combine the dipole splitting with at most N − 1 simultaneous swings in order to generate all colour correlations induced by the multiple dipole interactions.

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The BFKL equation from the Wilson renormalization group

Cited by 910 publications

References 18 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

High density QCD through eletromagnetic probes

On the dipole swing and the search for frame independence in the dipole model

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