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 carried out our work in perturbative Quantum Chromodynamics (QCD) (pQCD) dipole picture of deep inelastic scattering (DIS). The BK equation in momentum space with some change of variables and truncation of the Balitsky–Fadin–Kuraev–Lipatov (BFKL) kernel can be reduced to Fisher–Kolmogorov–Petrovsky–Piscounov (FKPP) equation. 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 [Formula: see text] plotted at various rapidities. We also extracted the saturation momentum, [Formula: see text], from the obtained solution and plotted it against different rapidities. The result obtained in this work can be helpful for various phenomenological studies in high-density QCD.

Investigation of proton structure function F2p at HERA in light of an analytical solution to the Balitsky–Kovchegov equation

“…travelling wave nature. We suggested an approximate analytical solution of the BK equation (7) in connection with the FKPP equation (8) using the homotopy perturbation method (HPM) in [26].…”

“…Following [26], the solution of the BK equation (7) in connection with the FKPP equation ( 8) is given by…”

“…This equation has been studied and solved numerically; however, due to its complexity, we have not seen an exact analytical solution to this equation to date. We recently proposed an approximate analytical solution to the BK equation that can be useful for phenomenology in the context of gluon saturation and hence small-x physics [26].…”

“…We do not see any theoretical measurement of gluon density at small-x using BK evolution theory, which motivates the current work. We previously presented an analytical expression for the scattering amplitude N(k, Y), which describes the propagation of the quark-antiquark dipole through the target color field in the color dipole model at various rapidities, Y [26]. In this work, we want to extract the gluon density xg(x, Q 2 ) and analyze the proton structure function F p 2 at small-x by combining experimental data with QCD evolution theory using the analytical solution of the BK equation in momentum space.…”