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Higher-point correlations from the JIMWLK evolution

E. Iancu, D. N. Triantafyllopoulos

TL;DR

Higher-point Wilson-line correlations in high-energy QCD are governed by the Balitsky-JIMWLK hierarchy and are challenging to solve analytically beyond the dipole. The authors introduce a large-$N_c$ approximation that retains only the virtual terms, yielding global relations that express n-point Wilson-line correlators in terms of the dipole S-matrix and interpolate between the BFKL and saturation regimes. They apply the scheme to the quadrupole and sextupole, obtaining closed-form formulas and identifying symmetric configurations with simple factorization properties; these results are consistent with MV framework initial conditions and with numerical JIMWLK solutions. The approach provides analytic control over higher-point correlations, unifies initial conditions and evolution, and offers a path to systematic extensions to arbitrary n-point functions with implications for multiparticle correlations in high-energy hadronic collisions.

Abstract

We develop a new approximation scheme aiming at extracting higher-point correlation functions from the JIMWLK evolution, in the limit where the number of colors is large. Namely, we show that by exploiting the structure of the 'virtual' terms in the Balitsky-JIMWLK equations, one can derive functional relations expressing arbitrary n-point functions of the Wilson lines in terms of the 2-point function (the scattering amplitude for a color dipole). These approximations are correct not only in the regime of strong scattering, where the evolution is indeed controlled by the 'virtual' terms, but also in the regime of weak scattering, where they reduce to the corresponding BFKL solutions. This last feature follows from the fact that the JIMWLK Hamiltonian is a linear combination of the pieces responsible for the 'real' and 'virtual' terms, respectively. We apply this scheme to two examples: the 'color quadrupole' (the 4-point function of the Wilson lines which enters the cross-section for the production of a pair of jets at forward rapidities) and the 'color sextupole' (the 6-point function). For particular configurations of the quadrupole, our general formula reduces to relatively simple expressions that have been previously proposed on the basis of the McLerran-Venugopalan model and which were recently shown to agree quite well with exact, numerical, solutions to the JIMWLK equation.

Higher-point correlations from the JIMWLK evolution

TL;DR

Higher-point Wilson-line correlations in high-energy QCD are governed by the Balitsky-JIMWLK hierarchy and are challenging to solve analytically beyond the dipole. The authors introduce a large- approximation that retains only the virtual terms, yielding global relations that express n-point Wilson-line correlators in terms of the dipole S-matrix and interpolate between the BFKL and saturation regimes. They apply the scheme to the quadrupole and sextupole, obtaining closed-form formulas and identifying symmetric configurations with simple factorization properties; these results are consistent with MV framework initial conditions and with numerical JIMWLK solutions. The approach provides analytic control over higher-point correlations, unifies initial conditions and evolution, and offers a path to systematic extensions to arbitrary n-point functions with implications for multiparticle correlations in high-energy hadronic collisions.

Abstract

We develop a new approximation scheme aiming at extracting higher-point correlation functions from the JIMWLK evolution, in the limit where the number of colors is large. Namely, we show that by exploiting the structure of the 'virtual' terms in the Balitsky-JIMWLK equations, one can derive functional relations expressing arbitrary n-point functions of the Wilson lines in terms of the 2-point function (the scattering amplitude for a color dipole). These approximations are correct not only in the regime of strong scattering, where the evolution is indeed controlled by the 'virtual' terms, but also in the regime of weak scattering, where they reduce to the corresponding BFKL solutions. This last feature follows from the fact that the JIMWLK Hamiltonian is a linear combination of the pieces responsible for the 'real' and 'virtual' terms, respectively. We apply this scheme to two examples: the 'color quadrupole' (the 4-point function of the Wilson lines which enters the cross-section for the production of a pair of jets at forward rapidities) and the 'color sextupole' (the 6-point function). For particular configurations of the quadrupole, our general formula reduces to relatively simple expressions that have been previously proposed on the basis of the McLerran-Venugopalan model and which were recently shown to agree quite well with exact, numerical, solutions to the JIMWLK equation.

Paper Structure

This paper contains 6 sections, 55 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Evolution equations
  3. From virtual terms to global approximations
  4. A global approximation for the quadrupole
  5. The evolution equation for the quadrupole
  6. The sextupole

Figures (1)

  • Figure 1: Special quadrupole configurations that we shall use to illustrate our general results. The dots represent the positions of the fermions in the transverse plane. (A bar on a transverse coordinate refers to an antiquark.) The lines have no physical meaning, they are meant only to delimitate the shape of the figures, in conformity with the names that we use to refer to them.