Generating Feynman Diagrams and Amplitudes with FeynArts 3

T. Hahn

REVIEW

Generating Feynman Diagrams and Amplitudes with FeynArts 3

T. Hahn

High Energy Physics - Phenomenology · Submitted 20 Dec 2000 · 12 references

Pith's verdict: A solid, honest program paper for a tool people actually use; the one real mismatch is the abstract's SUSY claim against a body that ships no SUSY example.

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arXiv IDhep-ph/0012260 (version 2)

Pith IDTKFKNZIL, Pith's permanent record of this paper and its review

CitationT. Hahn. "Generating Feynman Diagrams and Amplitudes with FeynArts 3." arXiv:hep-ph/0012260 (2000). https://pith.science/paper/TKFKNZIL

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Editor's note

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This is the FeynArts 3 writeup — a program description, not a physics result, and it should be read that way. The tool is a workhorse for one- to three-loop diagram generation, and the paper is a clear, well-organized account of how it works: topologies from starting graphs by recursive leg attachment, field insertion by intersecting allowed-field lists at each propagator end, Feynman rules applied symbolically with the generic amplitude kept separate from the level-substitution rules. The three-level field scheme and the flipping-rule treatment of undirected fermion lines are prior work by Eck, Küblbeck and Denner, and the paper says so plainly rather than dressing them up as new. What is genuinely new in v3 is the graphics layer: the custom PostScript prologue, the LaTeX output with feynarts.sty, the Java topology editor, and the roughly fivefold reduction in PostScript file size. That is a real, if unglamorous, contribution, and the LaTeX fragment in Section 3.4 shows it working rather than just asserting it does. The paper is also candid about its own boundaries: the topology algorithm is not self-contained and depends on externally supplied starting topologies (Section 3.1), and the naive canonical-order comparison can miss equivalent graphs when symmetric vertex groups exist, for which the power-set permutation of tagged indices is offered as the repair. The stress-test note is right that the repair comes without a completeness argument — the symmetry-factor bookkeeping is one sentence, and dividing s by the number of versions found is only correct under a free-action assumption the text never states. But this is a validation gap in a paper whose code is open source and downloadable, not a demonstrated error, and I would not weight it heavily. The concrete soft spot is the abstract: it lists 'support for supersymmetric models' as a main feature of version 3, while Section 2 says the MSSM model file 'will be available soon' and no SUSY example appears anywhere. That is a promise in the abstract and nothing in the body to back it. Second, the 2214-topologies-in-ten-seconds figure has no hardware, memory or version attached, and there is no cross-check of diagram counts or symmetry factors against QGRAF or GRACE, which the paper itself names as comparable. Both are minor and fixable. Who should read it: anyone about to use FeynArts, and anyone writing their own generator who wants a clean description of the three-level insertion idea. It deserves referees — they can run the code, which is the right test here.

Referee report

Significance

FeynArts is one of the standard front ends of the perturbative QCD and electroweak pipeline, and this write-up documents the design decisions that made version 3 usable at scale. Three elements are genuinely valuable and are stated clearly: the three-level field concept (Section 3.2), which lets the bulk of the algebra be done once at generic level and the particle sums be deferred to a fast numerical stage; the flipping-rule algorithm (Section 3.6, Eq. (2)), which extends automated diagram generation to Majorana fermions and hence to supersymmetric models where the textbook arrow-ordering prescription fails; and the custom PostScript prologue with the feynarts.sty style, which removes external figure files from LaTeX documents. The paper also earns credit for shipping open-source, downloadable code with a comprehensive manual, for quoting concrete performance figures (2214 two-loop 2 -> 2 topologies in about 10 seconds; about a minute for a one-loop 2 -> 2 electroweak amplitude set), and for stating its restrictions plainly in the Program Summary rather than burying them. If the tool behaves as described, the practical value to the community is high and durable.

Major objections (3)

[Section 3.1] The symmetry-factor bookkeeping is compressed into a single sentence: after each leg is added, topologically equivalent versions are gathered and replaced by one representative whose s is divided by the number of versions found. Read literally, dividing 1/|Aut_old| by the number of equivalent versions yields the correct 1/|Aut_new| only if the permutation action used to generate those versions is free on the relevant set, and the text does not state or justify that assumption. The same paragraph concedes that the naive canonical-order comparison can miss equivalent graphs when symmetric vertex groups exist, and offers the power-set permutation of tagged symmetric-vertex indices as the repair, but gives no argument that this permutation generates the full orbit rather than a subset of it. Because s propagates directly into RelativeCF and hence into every amplitude, an incompleteness here would be silent. A short orbit-stabilizer argument, or a pointer to the precise statement in Ref. [9], would close this.
[Section 3.1 and Section 2] The paper contains no independent validation of the diagram set or of the symmetry factors. The only quantitative anchor is the count of 2214 two-loop 2 -> 2 topologies in about 10 seconds, quoted without machine specification, Mathematica version, or comparison to an independent enumeration, and the single worked example (Z -> b bbar, 14 classes-level diagrams) is not compared to a published result or to a comparable generator such as QGRAF [4] or GRACE [5], both of which the paper itself names as equivalent in scope. Since the central claim is that the returned diagram set is exactly the set the model allows, a short validation subsection reporting at least one cross-check of topology counts and one of a known amplitude would materially strengthen the paper. This is a validation gap rather than a demonstrated error, and the open-source distribution makes the check feasible for any reader.
[Abstract and Section 2] The abstract lists 'support for supersymmetric models' among the main features of version 3, but Section 2 states that a model file for the Minimal Supersymmetric Standard Model 'will be available soon', and the Program Summary states under Restrictions on the complexity that model files other than the Standard Model and QCD are not contained in FeynArts and must be set up by the user. What version 3 actually provides is the algorithmic capability (the flipping rule of Section 3.6) plus the absence of a shipped MSSM model file. The abstract phrasing will lead users to expect a file that is not in the distribution. Rewording the abstract to distinguish algorithmic support from shipped model files would resolve this without any change to the technical content.

Minor objections (7)

[Program Summary] The entries 'Memory required to execute with typical data: 8M words' and 'No. of bits in a word: 8' appear inconsistent with each other and with the platforms listed; if 8M words at 8 bits per word is intended, the resulting figure is small for a Mathematica session, and if a 32- or 64-bit word is intended the memory entry should be restated. Please check these two form entries.
[Section 2 and Section 3.1] The timing figures ('about a minute' for a one-loop 2 -> 2 electroweak amplitude set, 'about 10 seconds' for the 2214 two-loop topologies) are useful but are given without processor, clock speed, or Mathematica version. A parenthetical specification would make them reproducible.
[Program Summary, Restrictions on the complexity] The three-loop limit is presented as a restriction of the program, but Section 3.1 makes clear that the loop order is set by which starting topologies are supplied as external input, so the limit is a property of the shipped data rather than of the algorithm. Saying so at the point where the restriction is listed would help users who need higher orders.
[Section 3.3] The treatment of mixing propagators is dispatched in two sentences, with the gamma-Z mixing field as the only example. Since the left/right partner distinction changes which lookup table is consulted at each end, a short explicit statement of how the partner fields are recorded at model-initialization time would make this reproducible for users writing their own model files.
[Section 3.5] PickLevel is introduced in one sentence as the way to obtain conventional amplitudes by applying the Insertions replacement rules, but no example of its use or output is given, in contrast to the care taken with the CreateFeynAmp example. A two-line illustration would complete the section.
[Section 3.1, Ref. [9]] The details of the power-set equivalence test and of the starting-topology construction reside in Ref. [9], a Ph.D. thesis distributed only as a PostScript file from the FeynArts website. Restating the essential definitions in the paper itself would make the algorithm self-contained for readers without web access to the thesis.
[Section 1] A small typographical point: 'forseeable' in the first paragraph of Section 1 should read 'foreseeable', if this spelling survives in the typeset version.

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The paper

The paper claims

FeynArts 3 generates Feynman diagrams at three levels of field detail, inserts model-allowed particles into them, and emits both publication-quality LaTeX or PostScript figures and symbolic amplitudes.

The reading

Particle physicists compute predictions by drawing Feynman diagrams, the little pictures of particles splitting, merging and looping, and then turning each picture into an algebraic expression. For anything beyond the simplest process the number of diagrams explodes, and drawing them by hand is slow and error-prone. FeynArts automates the first half of that job inside Mathematica. The program works in three steps. First it enumerates every distinct graph shape with the requested number of loops and external legs, starting from a small library of loop-only seeds and attaching legs one at a time. Second it fills each shape with actual particles, keeping only combinations whose couplings exist in a model file. Third it applies the Feynman rules from that model file and returns a symbolic amplitude, with the generic kinematic structure kept separate from the model-specific constants so that the expensive algebra is done once. Two design choices matter. Fields are handled at three levels of detail (generic fermion, down-type quark, b quark), which lets a user stop the expansion early and sum over generations later in a faster language. And fermion lines are oriented by a flipping rule rather than by following fermion number, which is what allows Majorana fermions and their fermion-number-violating couplings to be handled at all. The version 3 additions are mostly graphical: a custom PostScript prologue, a matching LaTeX style file, and a Java editor for arranging diagram layouts with a mouse. The paper is documentation for a working tool rather than a physics result.

Extended reading notes

Core claim

FeynArts 3 generates, for a requested number of loops and external legs, the set of distinct Feynman topologies, inserts model-allowed fields into them at three levels of detail, and applies the Feynman rules to produce symbolic amplitudes, with publication-quality PostScript or LaTeX output for the diagrams (abstract:s1, Sections 2 and 3.1 to 3.5). If correct, a user can go from a process specification to a full one-loop 2 to 2 amplitude set in about a minute of compute, with no hand drawing and no hand transcription of vertices.

Load-bearing premise

That the diagram set produced by InsertFields is exactly the set the model allows. The insertion routine works by intersecting lookup tables built at model-initialization time from the user's model file (Section 3.3), and the paper reports no cross-check of diagram counts, symmetry factors, or amplitudes against an independent generator such as QGRAF [4] or GRACE [5], which it names as comparable. Any error in the model file or in the lookup-table construction propagates silently into every downstream amplitude, and the paper's only worked example, Z to b bbar, is not compared to a published result.

Original abstract

This paper describes the Mathematica package FeynArts used for the generation and visualization of Feynman diagrams and amplitudes. The main features of version 3 are: generation of diagrams at three levels, user-definable model files, support for supersymmetric models, and publication-quality Feynman diagrams in PostScript or LaTeX.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,314 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.04 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.08 · compares with prior results 0.04 · mentions code or data availability 0.23.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

This paper describes the Mathematica package FeynArts used for the generation and visualization of Feynman diagrams and amplitudes. The main features of version 3 are: generation of diagrams at three levels, user-definable model files, support for supersymmetric models, and publication-quality Feynman diagrams in PostScript or LaTeX.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	This paper describes the Mathematica package FeynArts used for the generation and visualization of Feynman diagrams and amplitudes.	contribution 0.95	0.53	0.17	asserted 1.00
s1	The main features of version 3 are: generation of diagrams at three levels, user-definable model files, support for supersymmetric models, and publication-quality Feynman diagrams in PostScript or LaTeX.	contribution 0.90	0.56	0.14	asserted 1.00

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from simulation or computation 0.53.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** Flowchart for the generation of Feynman amplitude

**Figure 2.** The algorithm of CreateTopologies, shown for a one-loop starting topology to which two external legs are added. The leg added in each step is drawn with a thick line. The fields, their propagators, and their couplings are defined in a special file, the model file, which the user can supply or modify. The following model files are included in FeynArts: the electroweak Standard Model (SM.mod) [11], the same including QCD (SMQCD.mod), and in the background-field formulation (SMbgf.mod) [12]. These model files all include the full set of oneloop counter terms. A model file for the…

Figures reproduced from arXiv:hep-ph/0012260 by the authors.

References

Works cited (12)

[9]

H. Eck, Ph.D. thesis, University of W¨ urzburg (1995), th e PostScript ﬁle is available from http://www.feynarts.de

View on Pith 1995
[4]

P. Nogueira, J. Comput. Phys. 105 (1993) 279

View on Pith 1993
[5]

F. Yuasa et al., Prog. Theor. Phys. Suppl. 138 (2000) 18; T. Kaneko, Comp. Phys. Commun. 92 (1995) 127

View on Pith 2000
[1]

see e.g. M. Veltman, Diagrammatica, Cambridge Universi ty Press (1994)

View on Pith 1994
[2]

R. Mertig, M. B¨ ohm, and A. Denner, Comp. Phys. Commun. 64 (1991) 345

View on Pith 1991
[3]

T. Hahn and M. P´ erez-Victoria, Comp. Phys. Commun. 118 (1999) 153

View on Pith 1999
[6]

E. Boos, M. Dubinin, V. Ilyin, A. Pukhov, V. Savrin, INP MS U 94-36/358 (hep-ph/9503280); A. Pukhov et al., hep-ph/9908288

View on Pith Pith review arXiv
[7]

T. Stelzer, W.F. Long, Comp. Phys. Commun. 81 (1994) 357

View on Pith 1994
[8]

J. K¨ ublbeck, M. B¨ ohm, and A. Denner,Comp. Phys. Commun. 60 (1990) 165

View on Pith 1990
[10]

A. Denner, H. Eck, O. Hahn, and J. K¨ ublbeck, Nucl. Phys. B387 (1992) 467; A. Denner, H. Eck, O. Hahn, and J. K¨ ublbeck, Phys. Lett. B291 (1992) 278

View on Pith 1992
[11]

A. Denner, Fortschr. Phys. 41 (1993) 307

View on Pith 1993
[12]

A. Denner, S. Dittmaier, and G. Weiglein, Nucl. Phys. B440 (1995) 95. 10

View on Pith 1995

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hep-ph 2011-08 conditional novelty 7.0 of 10

A three-loop QCD calculation shifts the charm-quark contribution to kaon mixing by 36%, giving eta_cc = 1.87(76) and updating the Standard Model prediction for epsilon_K to 1.81(28) x 10^-3.
Higher order corrections to Higgs boson decays in the MSSM with complex parameters
hep-ph 2011-03 conditional novelty 7.0 of 10

Full one-loop vertex corrections to MSSM Higgs cascade and fermion decays are large, and they shift which CPX parameter regions the LEP Higgs searches exclude, leaving an open window near 45 GeV.
Electroweak corrections to dilepton + jet production at hadron colliders
hep-ph 2011-03 accept novelty 7.0 of 10

The first complete next-to-leading-order electroweak calculation for Z-boson plus jet production with leptonic decays at hadron colliders, giving percent-level corrections at low jet momentum and roughly minus 25 perc...
Epsilon_K at Next-to-Next-to-Leading Order: The Charm-Top-Quark Contribution
hep-ph 2010-07 accept novelty 7.0 of 10

Three-loop anomalous dimensions and two-loop matching give eta_ct = 0.496 +/- 0.047 at NNLO, a 7% upward shift that moves the Standard Model prediction for epsilon_K to (1.90 +/- 0.26) x 10^-3.
Electroweak and QCD corrections to Higgs production via vector-boson fusion at the LHC
hep-ph 2007-10 accept novelty 7.0 of 10

Complete NLO QCD and electroweak corrections to Higgs production in vector-boson fusion with two jets show both are 5 to 10 percent and distort distributions by about 10 percent.
Electroweak corrections to charged-current e+e- --> 4 fermion processes - technical details and further results
hep-ph 2005-05 accept novelty 7.0 of 10

The complete electroweak O(alpha) corrections to charged-current e+e- to four-fermion processes are computed, with a one-loop generalization of the complex-mass scheme, and the double-pole approximation is shown to be...
DIS-secting the universe with high-energy neutrinos
hep-ph 2026-11 conditional novelty 6.0 of 10

Electroweak radiative corrections shift muon energy and inelasticity distributions in neutrino deep inelastic scattering by over 10% at high energies, with photon-induced and coherent W-boson channels responsible abov...
QED corrections to $e^+e^-\to\pi^+\pi^-(\gamma)$ with amplitude-level resummation
hep-ph 2026-11 conditional novelty 6.0 of 10

Two independent Monte Carlo generators now provide amplitude-level, all-order soft-photon resummation with complete one-loop corrections for e+e- -> pi+pi-(gamma), including new theory-nuisance-parameter uncertainty bands.
Gauge-parameter cancellation and finite form factors in one-loop quark scattering in the refined Gribov-Zwanziger framework
hep-ph 2026-10 conditional novelty 6.0 of 10

The one-loop distinct-flavor massless quark scattering amplitude in the refined Gribov-Zwanziger framework is gauge-parameter independent and finite in the stated nonzero-mass domain, given by eight form factors with ...
Light top-flavoured dark matter in dark SMEFT: one-loop matching and phenomenology
hep-ph 2026-10 accept novelty 6.0 of 10

In dark SMEFT, one-loop matching of top-flavoured dark matter shows that only tree-level operators can explain the Belle II B+→K+ννbar excess with O(1) couplings at Λ=1 TeV, with B0→K*0+inv giving the strongest constraint.
Heavy Pseudo-Dirac Doublet Dark Matter and Non-Thermal Leptogenesis in Light of the LZ Event
hep-ph 2026-10 conditional novelty 6.0 of 10

Heavy pseudo-Dirac doublet dark matter and non-thermal leptogenesis can be reconciled in a low-reheating inflaton-domination cosmology only with kinematically forbidden dark matter pair emission and fine-tuned seesaw ...
Next-to-leading-order QCD corrections to the radiative decays $\chi_{bJ}\to J/\psi+\gamma$
hep-ph 2026-10 accept novelty 6.0 of 10

The first NLO QCD predictions for χbJ→J/ψ+γ find NLO corrections enhance the χb0 and χb1 decay widths while reducing the χb2 width by 36%.
Probing Leptophilic Scalar Dark Matter with SMEFT and Direct Detection
hep-ph 2026-10 conditional novelty 6.0 of 10

Real scalar dark matter coupled to leptons through a fermion mediator remains viable in a broad parameter window, while the complex scalar version is strongly excluded by its loop-induced charge-radius interaction.
Is the Light Neutralino Dark Matter Still Viable in the MSSM After the LZ-2024 Results?
hep-ph 2026-10 conditional novelty 6.0 of 10

Radiative corrections, conservative hadronic inputs, and a likelihood-based recast of LZ-2024 close the h- and Z-resonant annihilation windows for light Bino-like neutralino dark matter in the MSSM.
Phenomenological study of diquark effects in $\bar{B}_{(s)}^0 \to D_{(s)}^{(*)+} L^-$ decays
hep-ph 2026-10 conditional novelty 6.0 of 10

NLO-matched type-IV diquark contributions can bring class-I B-decay branching fractions into line with data if a left-handed coupling dominates, provided the Standard Model factorization baseline is correct.

See all 302 Pith citations

How later papers used it

919 later papers cite it

Evidence: substantial. 912 of the citing papers share no author with it, and 843 of those carry a confident label from Pith's citation classifier.

Pith read 40 of the 1,015 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

38 later papers by other authors are listed below: 38 used its method or tool. 2 more papers by the same authors are listed: 2 used its method or tool.

Uses its method or tool 40 of 837 papers with this label · 2 by the same authors

Generated the amplitudes using this paper and manipulated the expressions with other tools.

Two-loop infrared singularities in the production of a Higgs boson associated with a top-quark pair (2022) · 1.00 · paraphrased: the licence does not allow quoting
Jointly used this paper with other tools to renormalize the bare Lagrangian.

Precision predictions for scalar leptoquark pair-production at hadron colliders (2020) · 1.00 · paraphrased: the licence does not allow quoting
Used this paper and other tools to obtain the results for matrix beta-functions.

Three-loop SM beta-functions for matrix Yukawa couplings (2014) · 1.00 · paraphrased: the licence does not allow quoting
Calculated the 47 one-loop contributions to the decay rate asymmetry using this paper.

CP Violating Asymmetry in Stop Decay into Bottom and Chargino (2009) · 1.00 · paraphrased: the licence does not allow quoting
Obtained the diagrams and corresponding amplitudes with this paper.

Gluino Decays in the Complex MSSM: A Full One-Loop Analysis (2011) · 1.00 · paraphrased: the licence does not allow quoting
Evaluated the relevant one-loop corrections with the help of this paper and other tools.

Higgs Boson masses and B-Physics Constraints in Non-Minimal Flavor Violating SUSY scenarios (2011) · 1.00 · paraphrased: the licence does not allow quoting
Relied on a joint usage of this paper and other packages to automatically generate a UFO model.

A universal framework for t-channel dark matter models (2020) · 1.00 · paraphrased: the licence does not allow quoting
Obtained the diagrams and corresponding amplitudes with this paper.

Neutralinos from Chargino Decays in the Complex MSSM (2012) · 1.00 · paraphrased: the licence does not allow quoting
Obtained the relevant amplitudes using this paper with a model file generated by another tool.

Electroweak Corrections to Higgs to $\gamma\gamma$ and $W^+W^-$ in the SMEFT (2018) · 1.00 · paraphrased: the licence does not allow quoting
To calculate three-loop QED photon spectral density $ρ(s)$ we followed standard procedure: * generation of Feynman diagrams[For this purpose we used FeynArts package [ref] .] for photon self-energy (see Fig. [ref]) * application of projector to extract photon polarization operator $Π(s)$ and subsequent mapping of scalar integrals to the minimal set of prototype integrals * IBP reduction [ref] of prototype integrals to the set of master integrals and application of bipartite cuts with Cutkosky rules for the latter * substitution of expressions for cut master integrals[The calculation of one and two loop cut master integrals is similar to [ref] .] [ref] and renormalization.

Three-loop photon spectral density in QED (2022) · Spectral density calculation · 1.00
Obtained the Feynman diagrams and corresponding amplitudes contributing to the various decays with this paper.

MSSM Higgs Bosons from Stop and Chargino Decays (2012) · 1.00 · paraphrased: the licence does not allow quoting
Jointly used this paper with other tools to generate a UFO module allowing for NLO QCD calculations.

Cornering sgluons with four-top-quark events (2018) · 1.00 · paraphrased: the licence does not allow quoting
Generated amplitudes with this paper, decomposed them into tensor integrals using another tool, and expanded tensor integrals with another tool.

Direct Detection and LHC constraints on a $t$-Channel Simplified Model of Majorana Dark Matter at One Loop (2019) · 1.00 · paraphrased: the licence does not allow quoting
Used this paper as the first step of a toolchain for computing one-loop diagrams.

QCD one-loop correction to Higgs boson decay into quarkonium-pair (2023) · 1.00 · paraphrased: the licence does not allow quoting
The computations are handled with the help of the computer packages FeynArts/FormCalc [ref] .

One-loop induced contributions to the rare decay of $A_0 \rightarrow h_0h_0\gamma$ in Two Higgs Doublet Models (2025) · Loop-induced decay of $A_0 →h_0h_0γ$ in THDM · 1.00
Evaluated the full one-loop neutrino/sneutrino corrections to the self-energies with the help of this paper and another tool.

Heavy Majorana neutrino effects on MSSM-Mh (2012) · 1.00 · paraphrased: the licence does not allow quoting
Computed the loop diagrams with this paper and other tools, then linked the result into another code.

Vector Dark Matter through a Radiative Higgs Portal (2015) · 1.00 · paraphrased: the licence does not allow quoting
This process is tedious and largely prone to error, thus we rely on [ref] and [ref] , with partial cross-checks from [ref] as well.

Constraints on anomalous dimensions from the positivity of the S-matrix (2023) · Explicit computation in the reduced SMEFT · 1.00
Generated reference values using this paper to output all possible diagrams of the amplitude.

Amplitudes within causal loop-tree duality (2022) · 0.97 · paraphrased: the licence does not allow quoting
Generated the one-loop amplitude with the help of this paper, reduced integrals with another tool, and evaluated scalar integrals numerically with another.

A complete one-loop calculation of electroweak supersymmetric effects in $t$-channel single top production at LHC (2008) · 0.96 · paraphrased: the licence does not allow quoting
Both contributions have been calculated and verified with the publicly available tools [ref] , [ref] , [ref] and [ref] .

Radiative corrections to stop-antistop annihilation into gluons and light quarks (2022) · Computational details of the radiative corrections · 1.00
Calculated the corresponding differential cross section with this paper.

X17: A new force, or evidence for a hard $\gamma +\gamma$ process? (2020) · 0.99 · paraphrased: the licence does not allow quoting
Obtained the diagrams and corresponding amplitudes with this paper, using an MSSM model file.

Production of Electroweak SUSY Particles at ILC and CLIC (2018) · 0.92 · paraphrased: the licence does not allow quoting
Obtained the diagrams and corresponding amplitudes with this paper, using an MSSM model file.

Neutral Higgs Boson Production at e+e- Colliders in the Complex MSSM: A Full One-Loop Analysis (2015) · 1.00 · paraphrased: the licence does not allow quoting
Obtained the diagrams and corresponding amplitudes with this paper, using an MSSM model file.

Charged Higgs Boson Production at e+e- Colliders in the Complex MSSM: A Full One-Loop Analysis (2016) · 1.00 · paraphrased: the licence does not allow quoting
QCD ultraviolet and $R_2$ counter terms up to $ O( _s)$ are computed using NLOCT v1.02~ [ref] and FeynArts 3.11~ [ref] .

Doubly Charged Higgs Boson Production at Hadron Colliders II: A Zee-Babu Case Study (2022) · Monte Carlo tool chain · 1.00
The analytical and numerical results shown in this work were obtained with the help of the public codes FeynArts [ref] , FormCalc and LoopTools [ref] , where the implementation of the 2HDM was made with the public code FeynRules [ref] .

Role of $\lambda_{hH^+H^-}$ in Higgs boson decays $h$ to $bs$ in the 2HDM (2023) · $Γ(h→bs)$ in the 2HDM · 1.00
Evaluated the full one-loop corrections to the self-energies with this paper.

Mh in the MSSM-seesaw scenario with ILC precision (2012) · 1.00 · paraphrased: the licence does not allow quoting
We utilize [ref] to generate all the necessary Feynman diagrams and corresponding analytical amplitudes.

Analysis of double-$J/\psi$ production in $Z$ decay at next-to-leading-order QCD accuracy (2023) · NLO · 1.00
The general methodology relies on a Feynman-diagrammatic calculation of radiative corrections, which employs [ref] , [ref] and [ref] .

Decays of the neutral Higgs bosons into SM fermions and gauge bosons in the $\mathcal{CP}$-violating NMSSM (2018) · Introduction · 1.00
Generated diagrams and corresponding amplitudes for the EW contributions using this paper.

Electroweak corrections to squark--anti-squark pair production at the LHC (2008) · 1.00 · paraphrased: the licence does not allow quoting
Generated the diagrams related to the one-loop amplitude with the help of this paper, reduced integrals with another tool, and evaluated scalar integrals numerically with another.

Electroweak Corrections to t-channel single top production at the LHC (2008) · 1.00 · paraphrased: the licence does not allow quoting
Obtained the diagrams and corresponding amplitudes with this paper, using its MSSM model file.

High-Precision Electroweak SUSY Production Cross Sections at e+e- Colliders (2018) · 1.00 · paraphrased: the licence does not allow quoting
We calculated the complete expressions for the amplitudes for all decay channels ($ff$, $VV$, $SV$ and $SS$) of all scalars ($h, H, A, H^±$) using FeynArts [ref] and FormCalc [ref] , using the 2HDM model files including full 1-loop counter terms and renormalization conditions.

Exploring the low $\tan\beta$ region of two Higgs doublet models at the LHC (2019) · Heavy Higgs Decay Channels · 1.00
Generated the Feynman diagrams and amplitudes with this paper, using Feynman rules from another work.

QCD Corrections to $e^+e^- \rightarrow H^{\pm}W^{\mp}$ in Type-I THDM at Electron Positron Colliders (2020) · 1.00 · paraphrased: the licence does not allow quoting
Generated the two-loop virtual diagrams using this paper and manipulated the resulting amplitudes with other tools.

Efficient computation of two-loop amplitudes for Higgs boson pair production (2020) · 1.00 · paraphrased: the licence does not allow quoting
Utilized this paper to generate Feynman diagrams and corresponding amplitudes for the process through NLO.

Next-to-leading-order electroweak correction to $H\to Z^0\gamma$ (2024) · 1.00 · paraphrased: the licence does not allow quoting
Evaluated the full one-loop neutrino/sneutrino corrections to the self-energies with the help of this paper and another tool.

Higgs Boson Masses in the MSSM with Heavy Majorana Neutrinos (2010) · 1.00 · paraphrased: the licence does not allow quoting

By the same authors

Evaluated these contributions using this paper and other packages.

The Charged Higgs Boson Mass of the MSSM in the Feynman-Diagrammatic Approach (2013) (same authors) · 1.00 · paraphrased: the licence does not allow quoting
Generated the complete set of contributing Feynman diagrams with this paper, using a model file including counterterms.

Momentum-dependent two-loop QCD corrections to the neutral Higgs-boson masses in the MSSM (2014) (same authors) · 1.00 · paraphrased: the licence does not allow quoting

How the literature uses it

847 arXiv papers cite this in 936 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 70 sentences without a confident label

Uses its method or tool 772 papers

The EWPOs in the SM4 were calculated with the method described in [ref] , using FeynArts, FormCalc and LoopTools [ref] to compute the SM4 corrections to the EWPOs.

Status of the fourth fermion generation before ICHEP2012: Higgs data and electroweak precision observables · Method and inputs · 1.00
We generate the amplitudes using [ref] , and manipulate the expressions with [ref] .

Two-loop infrared singularities in the production of a Higgs boson associated with a top-quark pair · Setup · 1.00
The diagrammatic calculation has been performed with the help of [ref] in generating the Feynman diagrams, and [ref] and [ref] for the two-loop trace evaluation and tensor reduction.

Complete two-loop QCD contributions to the lightest Higgs-boson mass in the MSSM with complex parameters · Introduction · 1.00

Compares with it 14 papers

A careful check of our implementation has been done by comparing the computation of the partial decay width of squarks into charginos and neutralinos with FeynArts/FormCalc/LoopTools-based programs [ref] .

Effective squark/chargino/neutralino couplings: MadGraph implementation · Conclusions · 0.83
In Table [ref] we present the results of the LO integral cross sections in the SM at the $√(s)=500 GeV$ ILC obtained by using CompHEP-4.5.1 [ref] and FeynArts3.4/FormCalc5.4 packages separately, and the LO $σ_SM$ results by using FeynArts3.3/FormCalc5.3 package presented in Table 1 of Ref. [ref] .

Triple $Z^0$-boson production in large extra dimensions model at ILC · Numerical results and discussions · 0.89
Furthermore, we have compared all partonic channels to Higgs decays into four fermions against the independent calculation [ref] based on / [ref] .

Recola2: REcursive Computation of One-Loop Amplitudes 2 · Checks · 0.98

Cites it as background 13 papers

Nowadays we are able to perform precision predictions in the SM for a vast number of observables as a result of the automation of one-loop QCD [ref] and electroweak (EW) [ref] corrections.

Recola2: REcursive Computation of One-Loop Amplitudes 2 · Introduction · 0.87
Although fully automatic computer programs are not available yet for higher loop calculations, several program packages have been developed, e.g. Caravel [ref] , pySecDec [ref] and AMFlow [ref] , FeynArts [ref] , Qgraf [ref] , FeynCalc [ref] , Pacakge-X [ref] , FormCalc [ref] , tapir [ref] , ALibrary[<https://magv.github.io/alibrary>], etc, where the computer algebra systems (CAS) such as Mathematica[A commercial software available at <https://www.wolfram.com/mathematica>.] and Form [ref] are widely used.

FeAmGen.jl: A Julia Program for Feynman Amplitude Generation · Introduction · 0.82
With one-loop amplitudes being available since a long time, more recently much effort has been spent on the automation of one-loop corrections, which are more important than ever in view of the recent progress in multi-loop calculations. corrections are nowadays available in various approaches, [ref] , [ref] , [ref] , / [ref] , and in our fully recursive approach [ref] .

NLO electroweak corrections in extended Higgs Sectors with RECOLA2 · Introduction · 0.94

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

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H. Eck, Ph.D. thesis, University of W¨ urzburg (1995), th e PostScript ﬁle is available from http://www.feynarts.de

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