The energy dependence of the saturation momentum

Mueller, A. H.; Triantafyllopoulos, D.N.

doi:10.1016/s0550-3213(02)00581-3

Cited by 357 publications

(757 citation statements)

References 29 publications

(35 reference statements)

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“…Consequently, prior to any discussion of the value and energy dependence of the dipole scattering amplitude, we need to understand how the nextto-leading order corrections could effect the value of the saturation scale. As we have mentioned, these corrections change the value of the scale considerably [19,17]. This can be seen in Fig.…”

Section: The Saturation Scalementioning

confidence: 53%

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A modified Balitsky–Kovchegov equation

et al. 2005

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We propose a modified version of the Balitsky-Kovchegov (B-K) evolution equation, which includes the main NLO corrections. We use the result that the main NLO corrections to the BFKL kernel are the LO DGLAP corrections. We present a numerical solution of the modified nonlinear equation, and compare with the solution of the unmodified B-K equation. We show that the saturation momentum has a sharp increase in the LHC energy range. Our numerical solution shows that the influence of the pre-asymptotic corrections, related to the full anomous dimensions of the DGLAP equation, are rather large. These corrections moderate the energy behaviour of the amplitude, as well as the value of the saturation scale. All our calculations are made with a fixed value of α s .

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Section: The Saturation Scalementioning

confidence: 53%

“…where Y = ln(1/x) is our energy variable, ω ′′ (γ) = d 2 ω(γ)/(dγ) 2 , the value of γ cr can be found from the equation [1,19]: 8) we have normalized the value of the saturation momentum at Y = Y 0 .…”

Section: The Saturation Scalementioning

confidence: 99%

A modified Balitsky–Kovchegov equation

et al. 2005

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“…(7.2) and (7.4) to show that ψ(ρ, Y ) obeys a diffusion equation. For the non-linear BK equation (7.1), one can argue that the main effect of the non-linear term is to introduce an absorptive boundary condition on the diffusion equation for ψ [27]. Alternatively, one can study the full non-linear equation which emerges within the diffusion approximation:…”

Section: Relation With the Sfkpp Equationmentioning

confidence: 99%

A Langevin equation for high-energy evolution with pomeron loops

2005

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We show that the Balitsky-JIMWLK equations proposed to describe non-linear evolution in QCD at high energy fail to include the effects of fluctuations in the gluon number, and thus to correctly describe both the low density regime and the approach towards saturation. On the other hand, these fluctuations are correctly encoded (in the limit where the number of colors is large) in Mueller's color dipole picture, which however neglects saturation. By combining the dipole picture at low density with the JIMWLK evolution at high density, we construct a generalization of the Balitsky hierarchy which includes the particle number fluctuations, and thus the pomeron loops. After an additional coarse-graining in impact parameter space, this hierarchy is shown to reduce to a Langevin equation in the universality class of the stochastic Fisher-Kolmogorov-Petrovsky-Piscounov (sFKPP) equation. This equation implies that the non-linear effects in the evolution become important already in the high momentum regime where the average density is small, which signals the breakdown of the BFKL approximation.

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“…The equation for the "fan" diagrams in the operator expansion formalism was written by I.Balitsky [9], and in the dipole model framework [11] by Yu.Kovchegov [10]. The resulting Balitsky-Kovchegov (BK) equation is very well numerically studied in both, the saturation region and the region of small non-linearity (see [12,13,14] and [15,16]). One of the important features of the BK equation is the presence of the saturation scale at high energies that increases exponentially with rapidity, and a geometrical scaling of the solution [17,18,19].…”

Section: Introductionmentioning

confidence: 99%

BFKL ansatz for BK equation in conformal basis

Bondarenko

Prygarin

2008

Nuclear Physics A

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The BK equation in the conformal basis is considered and analyzed. It is shown that at high energy a factorization of the coordinate and rapidity dependence should hold. This allows to simplify significantly the from of the equation under discussion. An analytical ansatz for the solution to the BK equation at high energies is proposed and analyzed. This analytical ansatz satisfies the initial condition at low energy and does not depend on both rapidity and the initial condition in the high energy limit. The case of the final rapidity being not too large is discussed and the properties of the transition region between small and large final rapidities have been studied.

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The energy dependence of the saturation momentum

Cited by 357 publications

References 29 publications

A modified Balitsky–Kovchegov equation

A modified Balitsky–Kovchegov equation

A Langevin equation for high-energy evolution with pomeron loops

BFKL ansatz for BK equation in conformal basis

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