{"paper":{"title":"Implications of a Froissart bound saturation of $\\gamma^*$-$p$ deep inelastic scattering. Part I. Quark distributions at ultra small $x$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Douglas W. McKay, Loyal Durand, Martin M. Block, Phuoc Ha","submitted_at":"2013-02-25T15:23:23Z","abstract_excerpt":"We argue that the deep inelastic structure function $F_2^{\\gamma p}(x, Q^2)$, regarded as a cross section for virtual $\\gamma^*p$ scattering, is hadronic in nature. This implies that its growth is limited by the Froissart bound at high hadronic energies, giving a $\\ln^2 (1/x)$ bound on $F_2^{\\gamma p}$ as Bjorken $x\\rightarrow 0$. The same bound holds for the individual quark distributions. In earlier work, we obtained a very accurate global fit to the combined HERA data on $F_2^{\\gamma p}$ using a fit function which respects the Froissart bound at small $x$, and is equivalent in its $x$ depen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.6119","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}