{"paper":{"title":"$0\\nu\\beta\\beta$ nuclear matrix elements, neutrino potentials and $\\mathrm{SU}(4)$ symmetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nucl-th","authors_text":"Adam Smetana, Fedor \\v{S}imkovic, Petr Vogel","submitted_at":"2018-08-15T09:49:27Z","abstract_excerpt":"Intimate relation between the Gamow-Teller part of the matrix element $M^{0\\nu}_\\mathrm{GT}$ and the $2\\nu\\beta\\beta$ closure matrix element $M^{2\\nu}_\\mathrm{cl}$ is explained and explored. If the corresponding radial dependence $C^{2\\nu}_\\mathrm{cl}(r)$ would be known, $M^{0\\nu}$ corresponding to any mechanism responsible for the $0\\nu\\beta\\beta$ decay can be obtained as a simple integral. However, the $M^{2\\nu}_\\mathrm{cl}$ values sensitively depend on the properties of higher lying $1^+$ states in the intermediate odd-odd nuclei. We show that the $\\beta^-$ and $\\beta^+$ amplitudes of such "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.05016","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"}