Cubic color charge correlator in a proton made of three quarks and a gluon

TL;DR

This paper explicitly evaluates the three-point color charge correlation function in a proton, including perturbative corrections, verifying key identities, and providing a numerical estimate of its impact parameter dependence at small x.

Contribution

It provides the first explicit calculation of the cubic color charge correlator in a proton, including both C-even and odd contributions, with perturbative corrections and a numerical impact parameter model.

Findings

Correlator is independent of the renormalization scale.

Includes both C-conjugation even and odd contributions.

Provides a numerical estimate of the impact parameter dependence.

Abstract

The three point correlation function of color charge densities is evaluated explicitly in light cone gauge for a proton on the light cone. This includes both $C$-conjugation even and odd contributions. We account for perturbative corrections to the three-quark light cone wave function due to the emission of an internal gluon which is not required to be soft. We verify the Ward identity as well as the cancellation of UV divergences in the sum of all diagrams so that the correlator is independent of the renormalization scale. It does, however, exhibit the well known soft and collinear singularities. The expressions derived here provide the $C$-odd contribution to the initial conditions for high-energy evolution of the dipole scattering amplitude to small $x$. Finally, we also present a numerical model estimate of the impact parameter dependence of quantum color charge three-point correlations in the proton at moderately small $x$.