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JIMWLK equation tells how gauge invariant higher order Wilson linecorrelators would evolve at high energy. In this article we present aconvenient integro-differential form of this equation, for 2n-tuple correlator,where all real and virtual terms are explicit. The `real' terms correspond tosplitting (say at position z) of this 2n-tuple correlator to various pairs of2m-tuple and (2n+2-2m)-tuple correlators whereas `virtual' terms correspond tosplitting into pairs of 2m-tuple and (2n-2m)-tuple correlators. Kernels ofvirtual terms with m=0 (no splitting) and of real terms with m=1 (splittingwith atleast one dipole) have poles and when integrated over z they do generateultraviolet logarithmic divergences, separately for real and virtual terms.Except these two cases in all other terms the corresponding kernels, separatelyfor real and virtual terms, have rather soften ultraviolet singularity and whenintegrated over z do not generate ultraviolet logarithmic divergences. We wenton to study the solution of the JIMWLK equation for the 2n-tuple Wilson linecorrelator in the strong scattering regime where all transverse distances aremuch larger than inverse saturation momentum and shown that it also exhibitsgeometric scaling like color dipole deep inside saturation region.

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