Evolution of the color dipole cross section

Abstract Using Laplace transform techniques, we describe the evolution of the color dipole cross section at the leading-order and next-to-leading-order approximations from the Bartels–Golec-Biernat–Kowalski model in a kinematic region of low values of the Bjorken variable x and a wide range of transverse dipole size r . This evolution method shows that the saturation scale and geometric scaling are retained. We derived analytical results for the integrated and unintegrated color dipole gluon distribution functions and compared them with the CJ15 parameterization group and the unintegrated color dipole gluon distribution models, respectively. The Sudakov form factor in the evolution of the unintegrated color dipole gluon distribution is incorporated, and the results are considered at small and large values of $$k_{t}^{2}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>k</mml:mi> <mml:mrow> <mml:mi>t</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msubsup> </mml:math> .