Paper Citation Record · LEDGER

General finite two-loop amplitude integrand for photoproduction in quark annihilation

As of 19 August 2026, this Paper Citation Record lists 54 of 54 outbound references and 1 inbound Pith citation observation for arXiv:2509.07805.

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pith.paper-citation-record.v1
2509.07805 v1

Coverage vector

measured 54 of 54 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-08-04T21:50:31.074775Z

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One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+00:00

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Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-08T17:42:01.641712Z

measured 0 of 1 external citation measurements

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Source: arxiv_reference, observed 2026-05-11T17:21:07.703901Z

Reference resolution

54 of 54 outbound references displayed

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External citation measurements

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Outbound references

Observation 0f0b5026-ccbc-4e4e-87c7-f6ba3c033981 · outbound

This paper cites Sen,Asymptotic Behavior of the Wide Angle On-Shell Quark Scattering Amplitudes in Nonabelian Gauge Theories,Phys.

General finite two-loop amplitude integrand for photoproduction in quark annihilation Sen,Asymptotic Behavior of the Wide Angle On-Shell Quark Scattering Amplitudes in Nonabelian Gauge Theories,Phys

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-04T21:50:27.971274Z

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Observation 35a7b053-9035-45fc-be31-78e60c38349a · outbound

This paper cites The Singular Behaviour of QCD Amplitudes at Two-loop Order.

General finite two-loop amplitude integrand for photoproduction in quark annihilation The Singular Behaviour of QCD Amplitudes at Two-loop Order

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-04T21:50:28.051278Z

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Observation 3565c848-b636-4647-95bd-8ac0dccf6230 · outbound

This paper cites Multi-loop Amplitudes and Resummation.

General finite two-loop amplitude integrand for photoproduction in quark annihilation Multi-loop Amplitudes and Resummation

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-04T21:50:28.111805Z

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Observation e609727c-2bff-4304-97c5-5c2fc8dea0e7 · outbound

This paper cites Universal structure of subleading infrared poles in gauge theory amplitudes.

General finite two-loop amplitude integrand for photoproduction in quark annihilation Universal structure of subleading infrared poles in gauge theory amplitudes

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-04T21:50:28.201753Z

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Observation 6ae20913-48a4-4210-b2f2-c61bf61881bf · outbound

This paper cites Collins,Foundations of perturbative QCD, vol.

General finite two-loop amplitude integrand for photoproduction in quark annihilation Collins,Foundations of perturbative QCD, vol

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-04T21:50:28.280368Z

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Observation ca2b4f11-9153-489c-a414-45dcc52ac197 · outbound

This paper cites Hard-Soft-Collinear Factorization to All Orders.

General finite two-loop amplitude integrand for photoproduction in quark annihilation Hard-Soft-Collinear Factorization to All Orders

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-04T21:50:28.335867Z

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Observation 0668d01a-eeec-4fc2-b196-cafecfd33021 · outbound

This paper cites Ultraviolet divergences and factorization for coordinate-space amplitudes.

General finite two-loop amplitude integrand for photoproduction in quark annihilation Ultraviolet divergences and factorization for coordinate-space amplitudes

Reference 7

Resolution: verified exact; local_arxiv, observed 2026-08-04T21:50:31.609299Z

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Observation 2b4be38c-bbfd-4d5c-9367-5d78900cb55b · outbound

This paper cites A Forest Formula to Subtract Infrared Singularities in Amplitudes for Wide-angle Scattering.

General finite two-loop amplitude integrand for photoproduction in quark annihilation A Forest Formula to Subtract Infrared Singularities in Amplitudes for Wide-angle Scattering

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-04T21:50:28.486850Z

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Observation 255300a7-434e-47fa-9f0e-6c53c8718e88 · outbound

This paper cites Locally finite two-loop QCD amplitudes from IR universality for electroweak production.

General finite two-loop amplitude integrand for photoproduction in quark annihilation Locally finite two-loop QCD amplitudes from IR universality for electroweak production

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-04T21:50:28.550892Z

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Observation 3cf0cbdb-e95d-440b-a959-a3d250b87cf8 · outbound

This paper cites Locally finite two-loop amplitudes for electroweak production through gluon fusion.

General finite two-loop amplitude integrand for photoproduction in quark annihilation Locally finite two-loop amplitudes for electroweak production through gluon fusion

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-04T21:50:28.636249Z

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Observation 14cbb151-e0fe-4493-b2c8-84f5f2c1a95e · outbound

This paper cites Haindl,Local form factor subtraction for three-loop QCD corrections to electroweak production in quark-antiquark annihilation,JHEP06(2025) 257 [2502.00572].

General finite two-loop amplitude integrand for photoproduction in quark annihilation Haindl,Local form factor subtraction for three-loop QCD corrections to electroweak production in quark-antiquark annihilation,JHEP06(2025) 257 [2502.00572]

Reference 11

Resolution: verified exact; arxiv_id, observed 2026-08-04T21:50:31.566686Z

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Observation 81a33e60-319c-4ee4-8c32-b1984d016a2a · outbound

This paper cites Locally finite two-loop amplitudes for off-shell multi-photon production in electron-positron annihilation.

General finite two-loop amplitude integrand for photoproduction in quark annihilation Locally finite two-loop amplitudes for off-shell multi-photon production in electron-positron annihilation

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-04T21:50:28.753237Z

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Unavailable: canonical work link unavailable.

Observation 18fdeca2-2a4a-4a63-af1c-f58ce45d95be · outbound

This paper cites Sterman,Mass Divergences in Annihilation Processes.

General finite two-loop amplitude integrand for photoproduction in quark annihilation Sterman,Mass Divergences in Annihilation Processes

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:50:31.698307Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation fa87e4e4-f3eb-4928-b2d0-01f35870be2e · outbound

This paper cites Sterman,Mass Divergences in Annihilation Processes.

General finite two-loop amplitude integrand for photoproduction in quark annihilation Sterman,Mass Divergences in Annihilation Processes

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:50:31.688736Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation b9038997-049e-4ba3-a5c5-c02b30304dc1 · outbound

This paper cites Kermanschah and M.

General finite two-loop amplitude integrand for photoproduction in quark annihilation Kermanschah and M

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-04T21:50:28.934767Z

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Observation b037046f-bf2d-4ce9-9db5-208dd6032931 · outbound

This paper cites Numerical Loop-Tree Duality: contour deformation and subtraction.

General finite two-loop amplitude integrand for photoproduction in quark annihilation Numerical Loop-Tree Duality: contour deformation and subtraction

Reference 16

Resolution: verified exact; local_arxiv, observed 2026-08-04T21:50:31.532372Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation a3d1a410-93eb-4632-b178-0e9d48fc1c04 · outbound

This paper cites Bodwin,Factorization of the Drell-Yan Cross-Section in Perturbation Theory,Phys.

General finite two-loop amplitude integrand for photoproduction in quark annihilation Bodwin,Factorization of the Drell-Yan Cross-Section in Perturbation Theory,Phys

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:50:31.679024Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 75f0886a-344d-435f-8230-fc13af4c415c · outbound

This paper cites Collins, D.E.

General finite two-loop amplitude integrand for photoproduction in quark annihilation Collins, D.E

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:50:31.668756Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 033f88a3-12f9-4bb7-961b-5cbd58d32179 · outbound

This paper cites Sterman,An Introduction to quantum field theory, Cambridge University Press (8, 1993).

General finite two-loop amplitude integrand for photoproduction in quark annihilation Sterman,An Introduction to quantum field theory, Cambridge University Press (8, 1993)

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:50:31.658581Z

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Observation 99b3ddb9-9ad3-405d-b2ae-064c948cbefd · outbound

This paper cites Partons, Factorization and Resummation, TASI95.

General finite two-loop amplitude integrand for photoproduction in quark annihilation Partons, Factorization and Resummation, TASI95

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-04T21:50:29.274905Z

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Observation f6fb3836-c956-43fd-9bb4-a4f1f04670fa · outbound

This paper cites Local infrared safety in time-ordered perturbation theory.

General finite two-loop amplitude integrand for photoproduction in quark annihilation Local infrared safety in time-ordered perturbation theory

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-04T21:50:29.350261Z

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Observation a9efaeea-ea8d-4728-b38c-851fb93b00b9 · outbound

This paper cites From loops to trees by-passing Feynman's theorem.

General finite two-loop amplitude integrand for photoproduction in quark annihilation From loops to trees by-passing Feynman's theorem

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-04T21:50:29.455595Z

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Observation 518d9256-bc94-47fd-a5e7-fc97e7f738cf · outbound

This paper cites Causality, unitarity thresholds, anomalous thresholds and infrared singularities from the loop-tree duality at higher orders.

General finite two-loop amplitude integrand for photoproduction in quark annihilation Causality, unitarity thresholds, anomalous thresholds and infrared singularities from the loop-tree duality at higher orders

Reference 23

Resolution: verified exact; local_arxiv, observed 2026-08-04T21:50:31.490931Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 8c29cc0e-9ae7-4135-b3f2-379c73b4a2f8 · outbound

This paper cites Open loop amplitudes and causality to all orders and powers from the loop-tree duality.

General finite two-loop amplitude integrand for photoproduction in quark annihilation Open loop amplitudes and causality to all orders and powers from the loop-tree duality

Reference 24

Resolution: verified exact; local_arxiv, observed 2026-08-04T21:50:31.477623Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation b2b7719d-1977-41b4-8b04-654727c1a97e · outbound

This paper cites Mathematical properties of nested residues and their application to multi-loop scattering amplitudes.

General finite two-loop amplitude integrand for photoproduction in quark annihilation Mathematical properties of nested residues and their application to multi-loop scattering amplitudes

Reference 25

Resolution: metadata mismatch; local_arxiv, observed 2026-08-04T21:50:31.463600Z

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Observation de7294ec-0c02-4887-b974-7ccb4632f0ba · outbound

This paper cites Causality and loop-tree duality at higher loops.

General finite two-loop amplitude integrand for photoproduction in quark annihilation Causality and loop-tree duality at higher loops

Reference 26

Resolution: verified exact; local_arxiv, observed 2026-08-04T21:50:31.450274Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation b64919f3-49d1-4736-a731-dc4b38989cb9 · outbound

This paper cites Loop Tree Duality for multi-loop numerical integration.

General finite two-loop amplitude integrand for photoproduction in quark annihilation Loop Tree Duality for multi-loop numerical integration

Reference 27

Resolution: verified exact; local_arxiv, observed 2026-08-04T21:50:31.436117Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 3c5ab204-b9d6-4ee3-a08e-079169ecc1d4 · outbound

This paper cites Causal representation of multi-loop Feynman integrands within the loop-tree duality.

General finite two-loop amplitude integrand for photoproduction in quark annihilation Causal representation of multi-loop Feynman integrands within the loop-tree duality

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-04T21:50:30.075636Z

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Observation 149f6551-486f-41e8-80d2-2f37b9421364 · outbound

This paper cites Universal opening of four-loop scattering amplitudes to trees.

General finite two-loop amplitude integrand for photoproduction in quark annihilation Universal opening of four-loop scattering amplitudes to trees

Reference 29

Resolution: metadata mismatch; local_arxiv, observed 2026-08-04T21:50:31.412084Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 1bf9ec82-f505-484e-8841-ba24081f7250 · outbound

This paper cites Manifestly Causal Loop-Tree Duality.

General finite two-loop amplitude integrand for photoproduction in quark annihilation Manifestly Causal Loop-Tree Duality

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-04T21:50:30.337929Z

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Observation 98a7b377-2e34-477f-9807-1f4b7e102a40 · outbound

This paper cites Capatti, V.

General finite two-loop amplitude integrand for photoproduction in quark annihilation Capatti, V

Reference 31

Resolution: verified exact; doi, observed 2026-08-04T21:50:31.106158Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 4402dbe0-3650-4d6b-83a2-15c6bd3c451d · outbound

This paper cites Geometrical approach to causality in multi-loop amplitudes.

General finite two-loop amplitude integrand for photoproduction in quark annihilation Geometrical approach to causality in multi-loop amplitudes

Reference 32

Resolution: verified exact; local_arxiv, observed 2026-08-04T21:50:31.389656Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation a10ceab5-f59c-4be1-ae3b-70f596f8f478 · outbound

This paper cites Loop-tree duality from vertices and edges.

General finite two-loop amplitude integrand for photoproduction in quark annihilation Loop-tree duality from vertices and edges

Reference 33

Resolution: verified exact; local_arxiv, observed 2026-08-04T21:50:31.374685Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation ec00bc38-67b2-4909-8c48-20f814f94ae0 · outbound

This paper cites Lotty -- The loop-tree duality automation.

General finite two-loop amplitude integrand for photoproduction in quark annihilation Lotty -- The loop-tree duality automation

Reference 34

Resolution: verified exact; local_arxiv, observed 2026-08-04T21:50:31.362512Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation fc2df81c-5960-420c-a6cd-ad9a87b62ac5 · outbound

This paper cites Physical Representations for Scattering Amplitudes and the Wavefunction of the Universe.

General finite two-loop amplitude integrand for photoproduction in quark annihilation Physical Representations for Scattering Amplitudes and the Wavefunction of the Universe

Reference 35

Resolution: verified exact; local_arxiv, observed 2026-08-04T21:50:31.349670Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation ce40262f-32ce-4627-a197-0c88fdf8c2e4 · outbound

This paper cites Amplitudes within causal loop-tree duality.

General finite two-loop amplitude integrand for photoproduction in quark annihilation Amplitudes within causal loop-tree duality

Reference 36

Resolution: verified exact; local_arxiv, observed 2026-08-04T21:50:31.335591Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation b573bc4e-bec1-46b4-8f9b-eca8058b2c9d · outbound

This paper cites From five-loop scattering amplitudes to open trees with the Loop-Tree Duality.

General finite two-loop amplitude integrand for photoproduction in quark annihilation From five-loop scattering amplitudes to open trees with the Loop-Tree Duality

Reference 37

Resolution: metadata mismatch; local_arxiv, observed 2026-08-04T21:50:31.322608Z

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Observation f2fc0fcb-177d-46c1-a22a-e3675f098aa9 · outbound

This paper cites Exposing the threshold structure of loop integrals.

General finite two-loop amplitude integrand for photoproduction in quark annihilation Exposing the threshold structure of loop integrals

Reference 38

Resolution: verified exact; local_arxiv, observed 2026-08-04T21:50:31.309525Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 33efe54d-5b8e-41f0-a99e-bae72bd99ee1 · outbound

This paper cites Derivation of the Cross-Free Family representation for the box diagram.

General finite two-loop amplitude integrand for photoproduction in quark annihilation Derivation of the Cross-Free Family representation for the box diagram

Reference 39

Resolution: verified exact; local_arxiv, observed 2026-08-04T21:50:31.295498Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation e589c635-c84e-4532-8482-52ef8f6b5191 · outbound

This paper cites Numerical integration of the double- and triple-box integrals using threshold subtraction.

General finite two-loop amplitude integrand for photoproduction in quark annihilation Numerical integration of the double- and triple-box integrals using threshold subtraction

Reference 40

Resolution: verified exact; local_arxiv, observed 2026-08-04T21:50:31.282011Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation f9bc7805-0004-4039-bf5f-fddd4075332c · outbound

This paper cites Techniques for QCD calculations by numerical integration.

General finite two-loop amplitude integrand for photoproduction in quark annihilation Techniques for QCD calculations by numerical integration

Reference 41

Resolution: verified exact; local_arxiv, observed 2026-08-04T21:50:31.269218Z

Source-reported events for the cited work

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Observation 40f7324f-7645-44fc-86e2-416a7942b689 · outbound

This paper cites Numerical integration of one-loop Feynman diagrams for N-photon amplitudes.

General finite two-loop amplitude integrand for photoproduction in quark annihilation Numerical integration of one-loop Feynman diagrams for N-photon amplitudes

Reference 42

Resolution: verified exact; local_arxiv, observed 2026-08-04T21:50:31.256274Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation aa0d47a6-924d-4eba-b090-91b17ef62a3a · outbound

This paper cites Direct numerical integration of one-loop Feynman diagrams for N-photon amplitudes.

General finite two-loop amplitude integrand for photoproduction in quark annihilation Direct numerical integration of one-loop Feynman diagrams for N-photon amplitudes

Reference 43

Resolution: verified exact; local_arxiv, observed 2026-08-04T21:50:31.242869Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 6f8e7bc6-f6cf-4492-a513-4afbef45f91e · outbound

This paper cites Numerical NLO QCD calculations.

General finite two-loop amplitude integrand for photoproduction in quark annihilation Numerical NLO QCD calculations

Reference 44

Resolution: unresolved; no resolver link, observed 2026-08-04T21:50:31.040955Z

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Observation f12d70e5-8d45-4643-8649-338d90d6f2eb · outbound

This paper cites A simple formula for the infrared singular part of the integrand of one-loop QCD amplitudes.

General finite two-loop amplitude integrand for photoproduction in quark annihilation A simple formula for the infrared singular part of the integrand of one-loop QCD amplitudes

Reference 45

Resolution: verified exact; local_arxiv, observed 2026-08-04T21:50:31.220359Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation ef34261a-7832-4fb2-b449-8903e3a77f79 · outbound

This paper cites Efficiency improvements for the numerical computation of NLO corrections.

General finite two-loop amplitude integrand for photoproduction in quark annihilation Efficiency improvements for the numerical computation of NLO corrections

Reference 46

Resolution: verified exact; local_arxiv, observed 2026-08-04T21:50:31.206218Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 45c82735-4700-4f1e-8f3c-f2652c1b5557 · outbound

This paper cites NLO results for five, six and seven jets in electron-positron annihilation.

General finite two-loop amplitude integrand for photoproduction in quark annihilation NLO results for five, six and seven jets in electron-positron annihilation

Reference 47

Resolution: unresolved; no resolver link, observed 2026-08-04T21:50:31.051281Z

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Observation ebaf7ed2-8575-4851-a0d6-6ec01ee1d64a · outbound

This paper cites Direct numerical integration for multi-loop integrals.

General finite two-loop amplitude integrand for photoproduction in quark annihilation Direct numerical integration for multi-loop integrals

Reference 48

Resolution: verified exact; local_arxiv, observed 2026-08-04T21:50:31.183062Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 9d85ed18-512b-45bc-8b5a-3b5ec5cf3166 · outbound

This paper cites To $d$, or not to $d$: Recent developments and comparisons of regularization schemes.

General finite two-loop amplitude integrand for photoproduction in quark annihilation To $d$, or not to $d$: Recent developments and comparisons of regularization schemes

Reference 49

Resolution: unresolved; no resolver link, observed 2026-08-04T21:50:31.058020Z

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Observation cfa8bc81-b350-4dc0-beda-6c0f78990126 · outbound

This paper cites Numerical integration of subtraction terms.

General finite two-loop amplitude integrand for photoproduction in quark annihilation Numerical integration of subtraction terms

Reference 50

Resolution: verified exact; local_arxiv, observed 2026-08-04T21:50:31.159465Z

Source-reported events for the cited work

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Observation 179ef349-e4c6-4d64-863d-92b439c41fe1 · outbound

This paper cites Local Unitarity: a representation of differential cross-sections that is locally free of infrared singularities at any order.

General finite two-loop amplitude integrand for photoproduction in quark annihilation Local Unitarity: a representation of differential cross-sections that is locally free of infrared singularities at any order

Reference 51

Resolution: unresolved; no resolver link, observed 2026-08-04T21:50:31.064969Z

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Observation 4157f11c-cca2-4f43-ba00-7d509608391e · outbound

This paper cites May the four be with you: Novel IR-subtraction methods to tackle NNLO calculations.

General finite two-loop amplitude integrand for photoproduction in quark annihilation May the four be with you: Novel IR-subtraction methods to tackle NNLO calculations

Reference 52

Resolution: unresolved; no resolver link, observed 2026-08-04T21:50:31.068221Z

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Observation 36e78ba2-3cf5-4a72-91c5-b1cd68400934 · outbound

This paper cites Numerical integration of loop integrals through local cancellation of threshold singularities.

General finite two-loop amplitude integrand for photoproduction in quark annihilation Numerical integration of loop integrals through local cancellation of threshold singularities

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This paper cites Towards multiloop local renormalization within Causal Loop-Tree Duality.

General finite two-loop amplitude integrand for photoproduction in quark annihilation Towards multiloop local renormalization within Causal Loop-Tree Duality

Reference 54

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Pseudo-Evanescent Feynman Integrals from Local Subtraction cites this paper.

Pseudo-Evanescent Feynman Integrals from Local Subtraction General finite two-loop amplitude integrand for photoproduction in quark annihilation

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