Physical limits in the color-dipole model bounds

The ratio of the cross-sections for the transverse and longitudinal virtual photon polarizations, $$\sigma ^{\gamma ^{*}\mathrm{p}}_\mathrm{L/T}$$, at high photon–hadron energy scattering is studied. The relationship between the gluon distributions obtained using the color-dipole model and standard gluons obtained from the Dokshitzer–Gribov–Lipatov–Altarelli-Parisi (DGLAP) evolution and the Altarelli–Martinelli equations is investigated. It is shown that the color-dipole bounds are dependent on the gluon distribution behavior. This behavior is considered by expansion and Laplace-transform methods. Numerical calculations at leading order (LO) and next-to-leading order (NLO) approximations and a comparison with the color-dipole model (CDM) bounds indicate the range of validity of this method at small dipole sizes, $$r\sim 1/Q{\ll }1/Q_\mathrm{s}$$