Quantitative study of the transverse correlation of soft gluons in high energy QCD

TL;DR

This study investigates the validity of factorization in high energy QCD, revealing strong transverse correlations of soft gluons that challenge mean field approximations and influence nonlinear evolution at accessible energies.

Contribution

It provides a detailed analytical and numerical analysis of transverse gluon correlations, highlighting their impact on the evolution of dipole scattering amplitudes in high energy QCD.

Findings

Transverse correlations can cause factorization violation by factors of 1.5 to 10.

Correlations are significant even at zero impact parameter.

Running coupling reduces but does not eliminate factorization violation.

Abstract

We examine both analytically and numerically the validity of factorization for the double dipole scattering amplitude T^{(2)} which appears on the right hand side of the BK--JIMWLK equation. We demonstrate that, if one uses a dilute object (e.g., a proton in DIS) as the initial condition, the correlation in the transverse plane induced by the leading order BFKL evolution is generally strong, resulting in a violation of the mean field approximation T^{(2)} \approx TT even at zero impact parameter by a factor ranging from 1.5 to O(10) depending on the relative size of the scatterers and rapidity. This suggests that, within the experimentally accessible energy interval, the transverse correlation can significantly affect the nonlinear evolution of the dipole scattering amplitude. It also suggests that the nonlinear effects may set in earlier, already in the weak scattering regime. In the case of the simulation with a running coupling, the violation of factorization is somewhat milder, but still noticeable.