{"paper":{"title":"Vacuum Stability Conditions From Copositivity Criteria","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Kristjan Kannike","submitted_at":"2012-05-16T20:00:02Z","abstract_excerpt":"A scalar potential of the form $\\lambda_{ab} \\phi_a^2 \\phi_b^2$ is bounded from below if its matrix of quartic couplings $\\lambda_{ab}$ is copositive -- positive on non-negative vectors. Scalar potentials of this form occur naturally for scalar dark matter stabilised by a $\\mathbb{Z}_2$ symmetry. Copositivity criteria allow to derive analytic necessary and sufficient vacuum stability conditions for the matrix $\\lambda_{ab}$. We review the basic properties of copositive matrices and analytic criteria for copositivity. To illustrate these, we re-derive the vacuum stability conditions for the ine"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.3781","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"}