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# JIMWLK evolution and small-x asymptotics of 2n-tuple Wilson line correlators

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### Abstract

JIMWLK equation tells how gauge invariant higher order Wilson line correlators would evolve at high energy. In this article we present a convenient integro-differential form of this equation, for 2n-tuple correlator, where all real and virtual terms are explicit. The real' terms correspond to splitting (say at position z) of this 2n-tuple correlator to various pairs of 2m-tuple and (2n+2-2m)-tuple correlators whereas virtual' terms correspond to splitting into pairs of 2m-tuple and (2n-2m)-tuple correlators. Kernels of virtual terms with m=0 (no splitting) and of real terms with m=1 (splitting with atleast one dipole) have poles and when integrated over z they do generate ultraviolet logarithmic divergences, separately for real and virtual terms. Except these two cases in all other terms the corresponding kernels, separately for real and virtual terms, have rather soften ultraviolet singularity and when integrated over z do not generate ultraviolet logarithmic divergences. We went on to study the solution of the JIMWLK equation for the 2n-tuple Wilson line correlator in the strong scattering regime where all transverse distances are much larger than inverse saturation momentum and shown that it also exhibits geometric scaling like color dipole deep inside saturation region.

### Most cited references9

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### The Color Glass Condensate

(2010)
We provide a broad overview of the theoretical status and phenomenological applications of the Color Glass Condensate effective field theory describing universal properties of saturated gluons in hadron wavefunctions that are extracted from deeply inelastic scattering and hadron-hadron collision experiments at high energies.
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### The Wilson renormalization group for low x physics: towards the high density regime

(1997)
We continue the study of the effective action for low $$x$$ physics based on a Wilson renormalization group approach. We express the full nonlinear renormalization group equation in terms of the average value and the average fluctuation of extra color charge density generated by integrating out gluons with intermediate values of $$x$$. This form clearly exhibits the nature of the phenomena driving the evolution and should serve as the basis of the analysis of saturation effects at high gluon density at small $$x$$.
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### Nonlinear Gluon Evolution in the Color Glass Condensate: I

(2000)
We consider a nonlinear evolution equation recently proposed to describe the small-$$x$$ 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 $$x$$. 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 $$x$$ 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.
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### Author and article information

###### Journal
31 January 2019
###### Article
1901.11531