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The $f_0(980)-a_0(980)$ mixing effects are generated in the scattering amplitudes of the coupled channels with the physical basis, which exploits the important role of the $K\\bar{K}$ channel in the dynamical nature of these resonances. With the scattering amplitudes obtained, we investigate the $f_0(980)$ and $a_0(980)$ contributions to the $J/\\psi\\to \\gamma\\eta\\pi^0$, $J/\\psi\\to \\gamma\\pi^+\\pi^-$ and $J/\\psi\\to \\gamma\\pi^0\\pi^"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1907.09072","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2019-07-22T01:27:27Z","cross_cats_sorted":[],"title_canon_sha256":"788c62cd165db74662330076d20e337693d328ca3fbbc8ad2570dbd4c330603e","abstract_canon_sha256":"c8816db25ccf1e7439685786e59c1de51bb9f952858e6cd4003b5762c5c4499f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:41:33.205069Z","signature_b64":"/9sBBdtBlucERa1jqPr1A4wteDIBSC8sgJ7ov3vPXh7jGNqc2Ohi+7v8wfbz5Jf6MGyWmV5JKR0LATtef3l5Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4847cdee6e6fefa432de493bcb86304cd645ee1d8334a70dd27c66cf7eb4fbc2","last_reissued_at":"2026-07-05T00:41:33.204730Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:41:33.204730Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Investigation of $J/\\psi \\to \\gamma\\, \\pi^0 \\eta (\\pi^+\\pi^-, \\pi^0\\pi^0)$ radiative decays including final-state interactions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"C. 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