Geometric scaling behavior of the scattering amplitude for DIS with nuclei

TL;DR

This paper investigates how initial conditions affect the geometric scaling of the scattering amplitude in deep inelastic scattering with nuclei, comparing the McLerran-Venugopalan initial condition with the BFKL Pomeron calculus.

Contribution

It provides an analytical solution to the nonlinear BK equation with different initial conditions, revealing their impact on geometric scaling behavior in high-energy DIS.

Findings

The solution with McLerran-Venugopalan initial condition lacks deep geometric scaling.

The BFKL Pomeron calculus with specific initial conditions exhibits geometric scaling.

Results suggest experimental tests to distinguish between CGC and BFKL approaches.

Abstract

The main question, that we answer in this paper, is whether the initial condition can influence on the geometric scaling behavior of the amplitude for DIS at high energy. We re-write the non-linear Balitsky-Kovchegov equation in the form which is useful for treating the interaction with nuclei. Using the simplified BFKL kernel, we find the analytical solution to this equation with the initial condition given by the McLerran-Venugopalan formula. This solution does not show the geometric scaling behavior of the amplitude deeply in the saturation region. On the other hand, the BFKL Pomeron calculus with the initial condition at $x_A = 1/mR_A$ given by the solution to Balitsky-Kovchegov equation, leads to the geometric scaling behavior. The McLerran - Venugopalan formula is the natural initial condition for the Color Glass Condensate (CGC) approach. Therefore, our result gives a possibility to check experimentally which approach: CGC or BFKL Pomeron calculus, is more adequate.