{"paper":{"title":"Asymptotic Behaviour of Pion--Pion Total Cross-Sections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","nucl-th"],"primary_cat":"hep-ph","authors_text":"David Greynat, Eduardo de Rafael, Gr\\'egory Vulvert","submitted_at":"2013-12-10T17:11:56Z","abstract_excerpt":"We derive a sum rule which shows that the Froissart-Martin bound for the asymptotic behaviour of the $\\pi\\pi$ total cross sections at high energies, if modulated by the Lukaszuk-Martin coefficient of the leading $\\log^2 s$ behaviour, cannot be an optimal bound in QCD. We next compute the total cross sections for $\\pi^+ \\pi^-$, $\\pi^{\\pm} \\pi^0$ and $\\pi^0 \\pi^0$ scattering within  the framework of the  constituent chiral quark model (C$\\chi$QM) in the limit of a large number of colours $\\Nc$ and discuss their asymptotic behaviours. The same $\\pi\\pi$ cross sections are also discussed within the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2881","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"}