The shape of the proton at high energies

TL;DR

This paper models the fluctuating gluon distribution in protons at high energies, incorporating confinement effects, and analyzes how the proton's shape evolves with rapidity and impact parameter.

Contribution

It introduces a novel calculation of the impact parameter-dependent gluon distribution using the JIMWLK equation with confinement effects included.

Findings

The evolution remains unitary when confinement effects are included.

The proton's valence quark structure influences its shape even at small x.

The study determines the rapidity evolution of the saturation scale and proton radius.

Abstract

We present first calculations of the fluctuating gluon distribution in a proton as a function of impact parameter and rapidity employing the functional Langevin form of the JIMWLK renormalization group equation. We demonstrate that when including effects of confinement by screening the long range Coulomb field of the color charges, the evolution is unitary. The large-x structure of the proton, characterized by the position of three valence quarks, retains an effect on the proton shape down to very small values of x. We determine the dipole scattering amplitude as a function of impact parameter and dipole size and extract the rapidity evolution of the saturation scale and the proton radius.