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

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.

arXiv comment10 pages, 1 figure

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Cited by in corpus (3)

• Analytic solution of Balitsky-Kovchegov equation with running coupling constant using homogeneous balance method
• Homotopy solution to non-linear evolution for heavy nuclei
• Investigation of proton structure function $F_2^p$ at HERA in light of an analytical solution to Balitsky-Kovchegov equation