Color dipole cross-section from unifying the color-dipole picture and improved saturation models

Abstract We present an analysis of the color-dipole picture for determination of the gluon density at low- x which is obtained from the Altarelli-Martinelli equation by expansion at distinct points of expansion. The dipole cross-sections with respect to the improved saturation model of Bartels–Golec-Biernat–Kowalski are obtained in a wide range of transverse sizes r and compared with the Golec-Biernat-W <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mover accent="true"> <mml:mrow> <mml:mi mathvariant="normal">u</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>̈</mml:mo> </mml:mrow> </mml:mover> </mml:math> sthoff model. We find that the model gives a good description of the dipole cross-section at large r which confirms saturation and matches the perturbative QCD result at a small r due to the significant role of the running of the gluon distribution.