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Using the relativistic B-S equation and Mandelstam formalism, we calculate the corresponding decay form factors. The predictions of the corresponding branching ratios are: $Br(B_c^+\\to X(3940)e^+\\nu_e)$$=1.0\\times10^{-4}$ and $Br(B_c^+\\to X(4160)e^+\\nu_e)=2.4\\times10^{-5}$. That will provide us a new way to observe the $X(3940)$ and $X(4160)$ in the future, as well as to improve the knowledg"},"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":"1605.09091","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2016-05-30T02:48:05Z","cross_cats_sorted":[],"title_canon_sha256":"282435f5b3517a617b82f0d4087f0c079068e3e5bef24ea0e9342c5e996fe594","abstract_canon_sha256":"9f5c181d3c0ddb8769526b689e2734a5b78306c1693a9ee1db2c1086da7dfa22"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:06:24.195351Z","signature_b64":"zpx4ieBhWQnMJoYGVBQQLp371nGN2aC5gJlOh5UTCco6YOM92aGQWcamuACWgeBAzeGgoHQP1GDg47CGlCBfBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fddb1448bab7056a84e8052a86bbac8373367a241608cd669e6ada363c4bd184","last_reissued_at":"2026-05-18T01:06:24.194961Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:06:24.194961Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Production of $X(3940)$ and $X(4160)$ in $B_c$ decays","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Guo-Li Wang, Tian-Hong Wang, Yi Zhang, Yue Jiang, Zhi-Hui Wang","submitted_at":"2016-05-30T02:48:05Z","abstract_excerpt":"Considering $X(3940)$ and $X(4160)$ as $\\eta_c(3S)$ and $\\eta_c(4S)$, we study the productions of $X(3940)$ and $X(4160)$ in exclusive weak decays of $B_c$ meson by the improved Bethe-Salpeter(B-S) Method. Using the relativistic B-S equation and Mandelstam formalism, we calculate the corresponding decay form factors. The predictions of the corresponding branching ratios are: $Br(B_c^+\\to X(3940)e^+\\nu_e)$$=1.0\\times10^{-4}$ and $Br(B_c^+\\to X(4160)e^+\\nu_e)=2.4\\times10^{-5}$. 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