Color charge correlations in the proton at NLO: beyond geometry based intuition

TL;DR

This paper numerically evaluates two-point color charge correlations in the proton at NLO, revealing complex behavior influenced by impact parameter, transverse momentum, and angle, and providing initial conditions for evolution models.

Contribution

It introduces a NLO calculation of color charge correlators in the proton that accounts for non-trivial dependencies beyond geometric intuition.

Findings

Color charge correlator shows complex behavior at large momentum transfer.

Correlation depends on impact parameter, transverse momentum, and relative angle.

Provides initial conditions for Balitsky-Kovchegov evolution.

Abstract

Color charge correlators provide fundamental information about the proton structure. In this Letter, we evaluate numerically two-point color charge correlations in a proton on the light cone including the next-to-leading order corrections due to emission or exchange of a perturbative gluon. The non-perturbative valence quark structure of the proton is modelled in a way consistent with high-$x$ proton structure data. Our results show that the correlator exhibits startlingly non-trivial behavior at large momentum transfer or central impact parameters, and that the color charge correlation depends not only on the impact parameter but also on the relative transverse momentum of the two gluon probes and their relative angle. Furthermore, from the two-point color charge correlator, we compute the dipole scattering amplitude. Its azimuthal dependence differs significantly from a impact parameter dependent McLerran-Venugopalan model based on geometry. Our results also provide initial conditions for Balitsky-Kovchegov evolution of the dipole scattering amplitude. These initial conditions depend not only on the impact parameter and dipole size vectors, but also on their relative angle and on the light-cone momentum fraction $x$ in the target.