An analytical solution of Balitsky-Kovchegov equation using homotopy perturbation method

TL;DR

This paper presents an approximate analytical solution to the Balitsky-Kovchegov equation in high-density QCD using the homotopy perturbation method, revealing a traveling wave behavior in scattering amplitudes relevant for deep inelastic scattering.

Contribution

It introduces a novel application of the homotopy perturbation method to solve the BK equation analytically, linking it to the FKPP equation and geometric scaling phenomena.

Findings

Solution indicates traveling wave nature of scattering amplitude

Supports geometric scaling in high-energy QCD

Potential for phenomenological applications in DIS

Abstract

An approximate analytical solution of the Balitsky-Kovchegov (BK) equation using the homotopy perturbation method (HPM) is suggested in this work. We have carried out our work in perturbative QCD (pQCD) dipole picture of deep inelastic scattering (DIS). The BK equation in momentum space with some change of variables and truncation of the BFKL (Balitsky-Fadin-Kuraev-Lipatov) kernel can be reduced to the FKPP (Fisher-Kolmogorov-Petrovsky-Piscounov) equation [Munier and Peschanski 2003]. The observed geometric scaling phenomena are similar to the travelling wave solution of the FKPP equation. We solved the BK equation using the HPM. The obtained solution in this work also suggests the travelling wave nature of the measured scattering amplitude N(k, Y) plotted at various rapidities. The result obtained in this work can be helpful for different phenomenological studies in high-density QCD.