{"paper":{"title":"The $Q^2$ evolution of Soffer inequality","license":"","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"C. Bourrely, J. Soffer, O.V. Teryaev","submitted_at":"1997-10-02T16:00:35Z","abstract_excerpt":"DGLAP evolution equations may be presented in a form completely analogous to the Boltzmann equation. This provides a natural proof of the positivity of the spin-dependent parton distributions, provided the initial distributions at $Q^2_0$ are also positive. In addition, the evolution to $Q^2 < Q^2_0$ may violate positivity, providing therefore a 'time arrow'. The positivity condition is just $|\\Delta P_{ij} (z)| \\leq P_{ij} (z) $ for $z < 1$ for all types of partons, while the $'+'$prescription and terms containing $\\delta(1-z)$ do not affect positivity. This method allows one to complete imme"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-ph/9710224","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"}