{"paper":{"title":"Self-similarity and the Froissart bound","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Akbari Jahan, D. K. Choudhury","submitted_at":"2014-01-17T12:54:12Z","abstract_excerpt":"The Froissart bound implies that the total cross section (or, equivalently, the structure function) cannot rise faster than the logarithmic growth of $ \\ln^{2} \\left(\\frac{1}{x} \\right)$. In this work, we show that such a slow growth is not compatible with the notion of self-similarity. As a result, it calls for the modification of the defining transverse-momentum-dependent parton density function (TMD PDF) of a self-similarity based proton structure function $F_{2} \\left(x,Q^{2} \\right)$ at small \\textit{x}. Using plausible assumptions, we obtain the Froissart saturation condition on this TMD"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.4327","kind":"arxiv","version":1},"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"}