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Forward dijets in high-energy collisions: evolution of QCD n-point functions beyond the dipole approximation

Adrian Dumitru, Jamal Jalilian-Marian

TL;DR

Problem: knowledge of QCD n-point Wilson line functions at high energy is limited, and the common dipole/BK-based factorization misses important dynamics for higher-point operators. Approach: derive explicit JIMWLK evolution equations for the 4- and 6-point fundamental Wilson-line operators and compare with Gaussian+BK factorization. Key findings: Gaussian pre-evolution neglects many leading-Nc contributions, especially for the 6-point function; full JIMWLK evolution generates additional color structures and lower-point functions that cannot be reduced to BK. Implications: improved theoretical control of forward dijet angular correlations in pA (and forward proton-proton at the LHC) and potential quantitative differences between JIMWLK and BK approaches. Significance: establishes the necessity of solving the full high-point evolution, potentially via lattice-inspired methods, to accurately predict small-x QCD observables.

Abstract

Present knowledge of QCD n-point functions of Wilson lines at high energies is rather limited. In practical applications, it is therefore customary to factorize higher n-point functions into products of two-point functions (dipoles) which satisfy the BK evolution equation. We employ the JIMWLK formalism to derive explicit evolution equations for the 4- and 6-point functions of fundamental Wilson lines and show that if the Gaussian approximation is carried out before the rapidity evolution step is taken, then many leading order N_c contributions are missed. Our evolution equations could specifically be used to improve calculations of forward dijet angular correlations, recently measured by the STAR collaboration in deuteron-gold collisions at the RHIC collider. Forward dijets in proton-proton collisions at the LHC probe QCD evolution at even smaller light-cone momentum fractions. Such correlations may provide insight into genuine differences between the JIMWLK and BK approaches.

Forward dijets in high-energy collisions: evolution of QCD n-point functions beyond the dipole approximation

TL;DR

Problem: knowledge of QCD n-point Wilson line functions at high energy is limited, and the common dipole/BK-based factorization misses important dynamics for higher-point operators. Approach: derive explicit JIMWLK evolution equations for the 4- and 6-point fundamental Wilson-line operators and compare with Gaussian+BK factorization. Key findings: Gaussian pre-evolution neglects many leading-Nc contributions, especially for the 6-point function; full JIMWLK evolution generates additional color structures and lower-point functions that cannot be reduced to BK. Implications: improved theoretical control of forward dijet angular correlations in pA (and forward proton-proton at the LHC) and potential quantitative differences between JIMWLK and BK approaches. Significance: establishes the necessity of solving the full high-point evolution, potentially via lattice-inspired methods, to accurately predict small-x QCD observables.

Abstract

Present knowledge of QCD n-point functions of Wilson lines at high energies is rather limited. In practical applications, it is therefore customary to factorize higher n-point functions into products of two-point functions (dipoles) which satisfy the BK evolution equation. We employ the JIMWLK formalism to derive explicit evolution equations for the 4- and 6-point functions of fundamental Wilson lines and show that if the Gaussian approximation is carried out before the rapidity evolution step is taken, then many leading order N_c contributions are missed. Our evolution equations could specifically be used to improve calculations of forward dijet angular correlations, recently measured by the STAR collaboration in deuteron-gold collisions at the RHIC collider. Forward dijets in proton-proton collisions at the LHC probe QCD evolution at even smaller light-cone momentum fractions. Such correlations may provide insight into genuine differences between the JIMWLK and BK approaches.

Paper Structure

This paper contains 3 sections, 21 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Evolution equations for higher point functions
  3. Forward $q+g$ production in pA collisions

Figures (1)

  • Figure 1: Left: BK-evolution of a set of dipoles: in an evolution step, emission of a gluon can only split the parent dipole. Right: JIMWLK evolution of the $n$-point function allows for additional contributions.