Geometric scaling analysis of deep inelastic scattering data including heavy quarks

An analytic massive total cross section of photon-proton scattering is derived, which has geometric scaling. A geometric scaling is used to perform a global analysis of the deep inelastic scattering data on inclusive structure function F₂ measured in lepton-hadron scattering experiments at small values of Bjorken x. It is shown that the descriptions of the inclusive structure function F₂ and longitudinal structure function F_L are improved with the massive analytic structure function, which may imply the gluon saturation effect dominating the parton evolution process at HERA. The inclusion of the heavy quarks prevent the divergence of the lepton-hadron cross section, which plays a significant role in the description of the photoproduction region. (authors)