Stronger $C$-odd color charge correlations in the proton at higher energy

TL;DR

This paper investigates the energy dependence of $C$-odd color charge correlations in the proton, showing that the Odderon amplitude increases at smaller $x$, with implications for high-energy scattering and small-$x$ evolution.

Contribution

It provides numerical estimates of the perturbative Odderon amplitude considering a combined wave function model and explores its energy dependence at small $x$.

Findings

Odderon amplitude increases as $x$ decreases from 0.1 to 0.01.

Reversal of energy dependence at lower $x$ suggests onset of universal small-$x$ evolution.

Numerical estimates depend on dipole size, impact parameter, and azimuthal angle.

Abstract

The non-forward eikonal scattering matrix for dipole-proton scattering at high energy obtains an imaginary part due to a $C$-odd three gluon exchange. We present numerical estimates for the perturbative Odderon amplitude as a function of dipole size, impact parameter, their relative azimuthal angle, and light-cone momentum cutoff $x$. The proton is approximated as $\psi_\mathrm{qqq}|qqq\rangle + \psi_\mathrm{qqqg}|qqqg\rangle$, where $\psi_\mathrm{qqq}$ is a non-perturbative three quark model wave function while the gluon emission is computed in light-cone perturbation theory. We find that the Odderon amplitude increases as $x$ decreases from 0.1 to 0.01. At yet lower $x$, the reversal of this energy dependence would reflect the onset of universal small-$x$ renormalization group evolution.