# On the solution of linearized (linear in S-matrix) Balitsky-Kovchegov equation

## TL;DR

This paper presents an improved analytical solution to the linearized leading order Balitsky-Kovchegov equation, incorporating a transverse width cutoff and higher-order terms, which accurately connects different known solutions and aligns well with numerical results.

## Contribution

It introduces a novel analytical approach to solving the linearized BK equation with a transverse cutoff, including higher-order corrections, enhancing the connection between different limiting solutions.

## Key findings

- Reproduces McLerran-Venugopalan initial condition
- Recovers Levin-Tuchin solution in the appropriate limit
- Provides better accuracy in connecting these solutions across rapidity sets

## Abstract

We revisited solution of a linearized form of leading order Balitsky-Kovchegov equation (linear in S-matrix for dipole-nucleus scattering). Here we adopted dipole transverse width dependent cutoff in order to regulate the dipole integral. We also have taken care of all the higher order terms (higher order in the cutoff) that have been reasonably neglected before. The solution reproduces both McLerran-Venugopalan type initial condition (Gaussian in scaling variable) and Levin-Tuchin solution (Gaussian in logarithm of scaling variable) in the appropriate limits. It also connects this two opposite limits smoothly with better accuracy for sets of rescaled rapidity when compared to numerical solutions of full leading order Balitsky-Kovchegov equation.