Small-x Behavior of Parton Distributions from the Observed Froissart Energy Dependence of the Deep-Inelastic-Scattering Cross Sections

We fit the reduced cross section for deep-inelastic electron scattering data to a three parameter ln2s fit, A+βln2(s/s0), where s=(Q2/x)(1-x)+m2, and Q2 is the virtuality of the exchanged photon. Over a wide range in Q2 (0.11≤Q2≤1200 GeV2) all of the fits satisfy the logarithmic energy dependence of the Froissart bound. We can use these results to extrapolate to very large energies and hence to very small values of Bjorken x--well beyond the range accessible experimentally. As Q2→∞, the structure function F2p(x,Q2) exhibits Bjorken scaling, within experimental errors. We obtain new constraints on the behavior of quark and antiquark distribution functions at small x