Role of rapidity choice for the impact-parameter dependent Balitsky-Kovchegov equation

TL;DR

This paper compares two formulations of the impact-parameter dependent BK equation based on projectile and target rapidity, analyzing their effects on predicted observables relevant for future electron-ion collider experiments.

Contribution

It provides a comparative numerical solution of the two formulations of the BK equation considering all relevant degrees of freedom, highlighting their impact on observable quantities.

Findings

Differences in the evolution of the dipole amplitude between the two formulations.

Impact on predictions of proton structure functions at EIC.

Insights into the role of rapidity choice in saturation physics.

Abstract

Reaching higher energies of electron-ion collisions with facilities like EIC is expected to provide a probe of a kinematic region where the parton densities should start to exhibit signs of saturation. This phenomenon is theoretically implemented by the Balitsky--Kovchegov (BK) equation, which, within the colour dipole model, describes the evolution of the dipole scattering amplitude with respect to rapidity. There are two possible formulations of the BK equation based on which rapidity, projectile or target, is considered. Besides this variable, there are four more degrees of freedom, two of which have been so far incorporated into the numerical solutions. We present a comparative solution of the two-dimensional BK equation formulated in both projectile and target rapidity together with their impact on quantities to be observed at EIC such as proton structure functions.