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We consider the two-loop corrections to the process $\\gamma \\gamma \\leftrightarrow {^3 P_J^{[1]}}$, that has been known only numerically before, and the processes $gg \\leftrightarrow {^3 P_J^{[1]}}$, $\\gamma g \\leftrightarrow {^3 P_J^{[8]}}$ and $gg \\leftrightarrow {^3 P_J^{[8]}}$, which have not been computed before. We observe that the NRQCD pole structure of the two-loop amplitude in the $gg$ channel is more involved for the spin-triplet $P$-wave case than for the pseudo-scalar $S$-"},"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":"2501.04188","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2025-01-07T23:53:47Z","cross_cats_sorted":["nucl-th"],"title_canon_sha256":"6cfc1def0030a8a80b362c931d9ed8221d01dba93952359f9391a120a4c4fbd0","abstract_canon_sha256":"f611dda68a467a9311233302463e110a674392682ed87cec17ce758e07578e11"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:17:39.703832Z","signature_b64":"6SiexV7BC0Lbc8RAm156wchCdzR4sATqGBhvvSWtubAB6U1DpZVRsU0DipbcLyUu6F2Q13kQws4QSgPvu4/eAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"768c1a28eb52f1321b3aa7ee4162fd3b3d6fc120104299ca452a18eb2acc5211","last_reissued_at":"2026-07-05T11:17:39.703351Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:17:39.703351Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Two-loop form factors for $P$-wave quarkonium production and decay","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nucl-th"],"primary_cat":"hep-ph","authors_text":"Melih A. 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