One-Loop Calculations in Effective Field Theories with GoSam-3.0

Benjamin Campillo Aveleira; Gudrun Heinrich; Jannis Lang; Jens Braun; Marius H\"ofer; Matthias Kerner; Stephen P. Jones; Vitaly Magerya

REVIEW 2 major objections 4 minor 4 cited by

One-Loop Calculations in Effective Field Theories with GoSam-3.0

T0 review · 2 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read GoSam-3.0 claims largely automated one-loop QCD corrections in SMEFT and HEFT, with nine truncation options and unambiguous four-fermion amplitudes.

desk verdict A credible release note for a genuinely useful tool; the SMEFT truncation ambiguity about multiple NP insertions deserves a referee question. read the letter →

arxiv 2507.23549 v1 pith:KUBF6SEL submitted 2025-07-31 hep-ph

Jens Braun , Benjamin Campillo Aveleira , Gudrun Heinrich , Marius Höfer , Stephen P. Jones , Matthias Kerner , Jannis Lang , Vitaly Magerya This is my paper

classification hep-ph PACS 12.38.Bx12.60.-i

keywords GoSam-3.0one-loopamplitudesNLOQCDSMEFTHEFTfour-fermionoperatorsUFOmodelformattruncationschemes

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper presents GoSam-3.0, an update of an automated one-loop amplitude generator, and claims it can now handle Effective Field Theory calculations in a largely automated way. The new version imports EFT models in the UFO format and computes NLO QCD corrections for SMEFT and HEFT, letting the user choose among nine truncation schemes that decide how dimension-6 and loop-suppressed contributions enter squared matrix elements. It also removes sign ambiguities in amplitudes with four-fermion vertices, supports loop-induced processes, and adds a quadruple-precision rescue system for numerically unstable phase-space points. This matters for precision LHC phenomenology, where beyond-Standard-Model effects are often parameterised by EFTs and predictions need to be checked by more than one automated pipeline.

What carries the argument

The central machinery is the UFO-import pipeline together with two coupling-order tags: NP marks the EFT power counting (for example $1/\Lambda$ factors in SMEFT) and QL marks an intrinsic loop suppression of an operator. Every amplitude is organised as $M^{\ell}_{\mathrm{SM}} + M^{\ell}_{6} + \bar{M}^{\ell}_{6}$, where $\ell$ is the topology order, and the EFTcount variable picks how these pieces are combined into Born and virtual squared matrix elements, including variants for loop-induced processes. At multi-fermion vertices, GoSam-3.0 uses the fermion-line tracing algorithm of reference [56] and splits ambiguous Lorentz structures so each vertex has unique leg connections. Numerical stability is governed by pole, K-factor, and rotation tests, with optional re-evaluation in quadruple precision when a phase-space point is flagged unstable.

What would settle it

Recompute the $H\to b\bar b$ four-fermion example of Section 4.4 at a fixed phase-space point and compare the interference term with the analytic expression of Ref. [70] after the scheme conversion of Ref. [71]; a sign mismatch would falsify the claimed unambiguous handling of multi-fermion vertices.

Watch

Extended reading notes

Core claim

The paper's central claim is that GoSam-3.0 can generate and evaluate one-loop QCD amplitudes for theories imported through the UFO model format, including Standard Model Effective Field Theory (SMEFT) and Higgs Effective Field Theory (HEFT). The new truncation machinery decomposes any amplitude into a Standard Model part, a dimension-6 part, and a loop-suppressed dimension-6 part, and a runtime variable EFTcount selects one of nine schemes for building Born and virtual squared matrix elements at linear or quadratic order in $1/\Lambda^2$. Multi-fermion vertices are handled by resolving fermion leg connections inside each Lorentz structure, so diagram signs are unambiguous, and loop-induced processes get a dedicated set of truncation options. Renormalisation of SM QCD stays automatic when EFT operators do not contribute to SM counterterms; otherwise the user supplies Wilson-coefficient counterterms as UFO counterterm vertices, and the code expands the MS scale factor automatically. The paper also documents substantial build-time and evaluation-time speedups and an extended stability-rescue system using quadruple precision.

Load-bearing premise

The truncation mechanism assumes that every dimension-6 operator in the imported model carries the same power-counting tag and that no higher-dimensional operators are present; models violating this convention must be edited by the user, otherwise the EFTcount results are inconsistent.

Editorial extensions

If this is right

NLO QCD predictions for SMEFT/HEFT processes can be produced from a UFO model without hand-written amplitudes, with linear or quadratic truncation in $1/\Lambda^2$ chosen at runtime.
Loop-induced channels such as $gg\to Hg$ can consistently mix SM one-loop contributions with tree-level diagrams from loop-suppressed EFT operators.
Because the BLHA interface passes Born, real, and virtual matrix elements to Monte Carlo programs, truncation and diagram filters apply to all components of an NLO calculation together.
When EFT operators do not feed into SM renormalisation, NLO QCD renormalisation remains automatic; otherwise user-supplied Wilson-coefficient counterterms are inserted with automatic scale-log expansion.
The reported performance gains shorten both code generation and amplitude evaluation, with the largest evaluation gains in spinor-bracket-dominated processes.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A natural extension would be to allow the NP tag to carry an integer dimension so dimension-8 operators could coexist with dimension-6 ones; the present version explicitly requires all EFT operators to share one dimension.
Comparing EFTcount=1 and EFTcount=2 for the same observable gives a direct numerical measure of dimension-6-squared terms, which could serve as a diagnostic for when linear SMEFT truncation is adequate.
The multi-fermion sign-resolution procedure should generalise to contact interactions with more than four fermions, since it only requires each Lorentz structure's leg connections to be unambiguous after splitting.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

GoSam-3.0 is a real, incremental update to a mature one-loop generator. The headline is that the SMEFT/HEFT truncation features are genuinely new: nine EFTcount modes, loop-suppressed operator counting, and the four-fermion sign handling are useful additions that go beyond GoSam-2.0. The performance work is credible, with clear benchmarks, and the quadruple-precision rescue system is a nice addition. The code is public, and the examples cover the claimed features.

The soft spot I want you to be aware of is a documentation gap about how the truncation options interact with the default diagram generation. Section 3.3.1 says that by default GoSam generates diagrams with multiple insertions of non-SM vertices and tells the user to apply Python filters like d.order('NP')<=1 to avoid inconsistent Λ^-4 double insertions. Section 3.3.3 then defines the EFTcount modes in terms of M6, the single-insertion contribution, without saying whether enabling enable_truncation_orders automatically applies that filter. If it does, the paper should say so; if it doesn't, then a user who follows the EFTcount documentation alone may silently get double-insertion contamination in the linear modes (EFTcount 1,3,11,13). This is a real ambiguity, and a careful referee should ask for it to be resolved. It does not sink the paper, because the user-facing warning exists and the code is open, but it does make "largely automated" a bit softer than the abstract implies.

The other weakness is the lack of numeric validation in the text. The H->bbar with four-fermion operators example says it compares against an analytical expression, but no numbers are given. For a software paper, one would like to see at least a table or plot. Again, this is fixable in revision, and the public code lets readers verify.

Overall, the paper is honest about what it does and does not do (renormalization is not fully automated; the user has to provide Wilson coefficient counterterms). The citation pattern is fine. This is a paper for practitioners who use automated one-loop tools in EFT phenomenology; it will be a solid reference for GoSam-3.0. I would send it to peer review, asking for clarification on the truncation/filter interaction and, ideally, one quantitative cross-check.

Referee Report

2 major / 4 minor

Summary. The paper presents GoSam-3.0, a major update of the public one-loop amplitude generator, adding performance improvements, an extended rescue system, and new features for effective field theory (EFT) calculations. The EFT capabilities cover UFO model import, SMEFT truncation options (EFTcount), loop-induced processes, HEFT support, four-fermion operators with sign handling, and user-provided Wilson-coefficient counterterms. The paper describes the implementation, defines nine truncation options in detail, and lists examples distributed with the code.

Significance. If the claims hold, GoSam-3.0 provides a useful public tool for automated NLO QCD calculations in SMEFT/HEFT, complementing existing frameworks such as MG5_aMC@NLO. The truncation formulas in Section 3.3.3 are clearly defined, and the code is publicly available with a documented build system, examples, and a reference manual, which is a strength. The claimed performance gains relative to GoSam-2 are quantified in Figures 1 and 2. The main weakness is that several central claims, notably the automatic behavior of the truncation options and the numerical validation of four-fermion operator handling, are not fully supported in the manuscript text.

major comments (2)

[3.3.1, 3.3.3] The truncation options in Section 3.3.3 are defined through M^ℓ_6 as the contribution of diagrams with a single insertion of a dimension-6 operator, but the paper does not state whether setting enable_truncation_orders=true automatically excludes diagrams with multiple non-SM insertions. Section 3.3.1 explicitly warns that by default GoSam generates multiple insertions of non-SM vertices and instructs the user to apply Python filters (d.order('NP')<=1) to avoid inconsistencies. The requirements listed in Section 3.3.3 (all SMEFT operators of the same dimension with NP=1) do not mention such filtering, and the equations do not show a mechanism for discarding NP>1 contributions. This creates ambiguity about whether the 'largely automated' truncation feature actually delivers the stated linear/quadratic truncations, or whether the user must separately apply the filters from Section 3.3.1. Please state explicitly whether EFTcount modes automatically discard multiple NP insertions, and if not, require the filters as a documented precondition. This is load-bearing for the central claim.
[4.4] Section 4.4 claims that the example 'Hbb_4F' compares the computed interference with the analytical expression of Ref. [70] (with a scheme-conversion factor from Ref. [71]), but no quantitative result is given in the text. No numerical values, agreement precision, or a reference to a table or plot are provided. For a code-release paper that asserts unambiguous sign handling of four-fermion operators, the validation should be documented in the manuscript (or the authors should state that the comparison is only in the example directory). Without this, the claim is not verifiable from the paper alone.

minor comments (4)

[4.3] There is a typo in Section 4.3: 'adpated' should be 'adapted'.
[Author list] The email address 'vitlaly.magerya@cern.ch' appears to be a typo; it should likely be 'vitaly.magerya@cern.ch'.
[3.2, Eq. (8)] In Eq. (8), P_qd is defined as -log10(δq) but δq is not defined; presumably it should be δ_qd as in Eq. (7). Please correct this.
[3.3.3] The notation M^ℓ with ℓ=0,1 is used for tree and one-loop topologies, but later in Section 3.3.4 for loop-induced processes M^1_SM is used in the 'Born' result. A brief remark clarifying the notation for loop-induced processes would improve readability.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the paper reports software capabilities whose truncation options are explicit definitions and whose validating examples use external analytic benchmarks.

full rationale

GoSam-3.0 is a software/tool paper rather than a derivation paper: the central SMEFT truncation feature is presented as a set of definitions (Section 3.3.3, Eqs. (12)-(29) and Table 1), where each EFTcount option explicitly states which amplitude pieces are combined; no quantity is fitted from data and then renamed a prediction. The advertised capabilities are validated in Section 4 against analytic expressions (e.g., the four-fermion example compares with Ref. [70], and with a scheme-conversion factor from Ref. [71]); these benchmarks are independent of the GoSam implementation even though Ref. [71] has overlapping authors, because the conversion factor is a closed-form external result, not an output of the tool. The only self-citations, Refs. [11] and [12], are the original GoSam papers used to attribute the base code and standard renormalisation infrastructure; they are not invoked to prove the new truncation or sign-handling features. Ref. [68] is cited only as an application of the BLHA interface, and Ref. [56] supplies the external algorithm for fermion-line sign tracing. No fitted parameter is called a prediction, no uniqueness theorem is imported from the authors' prior work, and no ansatz is smuggled in via citation. The potential mismatch between the default multiple-NP-insertion generation warned about in Section 3.3.1 and the EFTcount truncation definitions in Section 3.3.3 is at most a documentation or consistency risk for the 'largely automated' claim, not a circular step, since the truncation formulas themselves are definitional. Accordingly no circularity is found.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

The paper introduces no new physical entities or fitted parameters. It relies on existing tools (QGRAF, FORM, NINJA, ONELOOP, UFO) and imposes conventions on user-supplied EFT models.

assumptions (4)

domain assumption Standard Model and QCD as the background theory.
The one-loop amplitude generation is set in the SMEFT/HEFT framework built on the SM, as assumed throughout Sections 3.3 and 3.4.
domain assumption UFO model format faithfully represents the Lagrangian and vertex information.
All EFT calculations read model files in the UFO format (Section 3.3.1); if the model is incorrect, the output is incorrect.
domain assumption IR pole factorisation holds for BSM amplitudes.
The pole test in the rescue system (Section 3.2) assumes the single-pole coefficient factorises as in the SM, and explicitly states this must hold for BSM models.
ad hoc to paper All SMEFT operators have the same dimension and are tagged with NP=1 for truncation options.
Section 3.3.3 imposes this as a requirement for the truncation features and tells users to adjust models that use NP=2.

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Cite this review

Pith. "Pith review of One-Loop Calculations in Effective Field Theories with GoSam-3.0." pith.science (2026). https://pith.science/paper/KUBF6SEL

@misc{pith2026250723549,
  author       = {Pith},
  title        = {Pith review of: One-Loop Calculations in Effective Field Theories with GoSam-3.0},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KUBF6SEL}},
  note         = {Machine review of arXiv:2507.23549}
}

read the original abstract

We present a major update of the one-loop generator GoSam, containing performance improvements as well as new features, in particular functionalities that facilitate calculations beyond the Standard Model in Effective Field Theory frameworks.

Figures

Figures reproduced from arXiv: 2507.23549 by the authors.

**Figure 1.** Runtime of make test for selected examples included in the GOSAM distribution on an Intel Core i7-10700 8-core processor. The runtime of GOSAM-2 relative to GOSAM-3 is indicated next to each bar. CPU cores on the host machine for reduction and compilation, significantly reducing all compile times on modern multicore systems. For the installation procedure of GOSAM itself, this results in a reduction of the runtime… view at source ↗

**Figure 2.** Runtime of a single evaluation of the squared amplitude for selected exam [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

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