Pith Number

pith:GSNK2BXQ

pith:2024:GSNK2BXQQMLKRUZP3LQHTUE7SA

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Feynman Integral Reduction without Integration-By-Parts

Li Lin Yang, Ziwen Wang

Equivalence relations among Feynman integration contours yield universal reduction formulas for any one-loop integral without integration-by-parts.

arxiv:2412.15962 v3 · 2024-12-20 · hep-th · hep-ph

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Claims

C1strongest claim

We apply this idea to one-loop integrals, and derive universal reduction formulas that can be used to efficiently reduce any one-loop integral.

C2weakest assumption

The assumption that the more general integration contours identified via equivalence relations produce mathematically valid and physically correct reductions for arbitrary one-loop integrals, extending beyond the Cheng-Wu theorem without introducing new errors.

C3one line summary

Contour equivalence in Feynman parameterization yields universal reduction formulas for one-loop integrals without integration-by-parts.

References

81 extracted · 81 resolved · 31 Pith anchors

[1] Kotikov,Differential equations method: New technique for massive Feynman diagrams calculation,Phys 1991

[2] Kotikov,Differential equation method: The Calculation of N point Feynman diagrams, Phys 1991

[3] Remiddi,Differential equations for Feynman graph amplitudes,Nuovo Cim 1997

[4] Differential Equations for Two-Loop Four-Point Functions 2000 · arXiv:hep-ph/9912329

[5] Calculation of master integrals by difference equations 2001 · arXiv:hep-ph/0102032

Receipt and verification

First computed	2026-06-03T01:05:43.247396Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

349aad06f08316a8d32fdae079d09f902cb0289203555f6441bde41a68d707f6

Aliases

arxiv: 2412.15962 · arxiv_version: 2412.15962v3 · doi: 10.48550/arxiv.2412.15962 · pith_short_12: GSNK2BXQQMLK · pith_short_16: GSNK2BXQQMLKRUZP · pith_short_8: GSNK2BXQ

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/GSNK2BXQQMLKRUZP3LQHTUE7SA \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 349aad06f08316a8d32fdae079d09f902cb0289203555f6441bde41a68d707f6

Canonical record JSON

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    "abstract_canon_sha256": "d6370317a19dd1350bd1b85e13faa73b0b993be47fe5c8bd0bb0368c8a288bcf",
    "cross_cats_sorted": [
      "hep-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-th",
    "submitted_at": "2024-12-20T14:57:51Z",
    "title_canon_sha256": "53c293a5d32ff560cacf08143ad675da54a3a1cb872a526bd788b7b273e2e592"
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  "source": {
    "id": "2412.15962",
    "kind": "arxiv",
    "version": 3
  }
}