Unitarity boundary for deep inelastic structure functions

In this letter we derive the unitarity boundaries in QCD for the deep inelastic structure function in low x kinematic region: the Froissart boundary and a more restricted one, linked with experiment and based on additional assumptions, justified in the leading log approximation of perturbative QCD. The comparison of the unitarity boundaries with the new HERA experimental data gives rise to a challenge for QCD to explain the matching between the deep inelastic scattering and real photoproduction process.