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It is demonstrated that, as compared to the naive static-pions approximation, the imaginary parts that originate from the inclusion of dynamical pions reduce substantially the width from the $D\\bar{D}\\pi$ intermediate state. In particular, for a resonance peaked at 0.5 MeV below the $D^0\\bar D^{*0}$ threshold, this contribution to the width is reduced by about a factor of 2, and the effect of the"},"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":"1108.5644","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2011-08-29T16:40:33Z","cross_cats_sorted":["nucl-th"],"title_canon_sha256":"926b3b1e55e182d02321dccdba258e19b0e9a6b0efb361c6c2356d255b52001e","abstract_canon_sha256":"83160adb22b5938018637f450bdf6859bee8603a51a0e98826bce537eb55f833"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:00:45.304538Z","signature_b64":"pdknIkEAUvp1nw88HVCKMxlW/k9mSx5+DW1eRH8MobLX1eV0Dd6oezYveKlJjXkleNTneUbpSW698WDTTHuwBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"71fa1214be82718922ece140e7ab73120c9bb1c698263326e5a4c5666cb915c0","last_reissued_at":"2026-05-18T02:00:45.303842Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:00:45.303842Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Three-body $D\\bar{D}\\pi$ dynamics for the X(3872)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nucl-th"],"primary_cat":"hep-ph","authors_text":"A.A. 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