{"paper":{"title":"Double Asymptotic Scaling at HERA","license":"","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"R. D. Ball, S. Forte","submitted_at":"1994-05-18T15:52:52Z","abstract_excerpt":"Perturbative QCD predicts that at sufficiently large $Q^2$ and small $x$ nucleon structure functions should exhibit scaling in the two variables $\\sqrt{\\ln\\smallfrac{1}{x}\\ln\\ln Q^2}$ and $\\sqrt{\\ln\\smallfrac{1}{x}\\big/\\ln\\ln Q^2}$, provided only that the small-$x$ behaviour of the input to the perturbative QCD evolution is sufficiently soft. We derive these asymptotic results by writing the gluonic Altarelli--Parisi equation at small $x$ as a two--dimensional wave equation, which propagates the gluon distribution from its boundaries into the asymptotic region. We then show that the existing e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-ph/9405320","kind":"arxiv","version":3},"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"}