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arxiv: 2605.11747 · v1 · submitted 2026-05-12 · ✦ hep-ph · hep-ex

Recognition: no theorem link

SMEFT everywhere: a NLO study of boldsymbol{pp to tbar{t}H} with decaying tops

Giuseppe Bevilacqua , Minos Reinartz , Malgorzata Worek
Authors on Pith no claims yet

Pith reviewed 2026-05-13 05:54 UTC · model grok-4.3

classification ✦ hep-ph hep-ex
keywords SMEFTNLO QCD correctionsttH productiontop quark decaysdifferential distributionsLHC Run IIIdimension-6 operatorsdi-lepton channel
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0 comments X

The pith

SMEFT operators in top decays must be included at NLO to capture the shapes of observables in ttH production at the LHC.

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

The paper computes next-to-leading order QCD corrections to proton-proton collisions producing a top-antitop pair and a Higgs boson in the dilepton channel, including four dimension-6 operators from the Standard Model Effective Field Theory. These operators are applied consistently to both the production stage and the subsequent decays of the top quarks. The study finds that higher-order corrections, the operators, and kinematic selection cuts together modify the shapes of differential distributions for observables measured at the LHC. A reader would care because ttH is a key channel for probing the Higgs-top coupling and searching for new physics, and inconsistent treatment could lead to incorrect interpretations of data from Run III.

Core claim

We present the computation of the next-to-leading order QCD corrections to the pp→t¯tH+X process in the di-lepton channel at the LHC, including relevant dimension-6 operators (O_tφ, O_φG, O_tG, O_tW) from the Standard Model Effective Field Theory. In our studies, higher-order corrections and effective operators are consistently included in the production part of the process as well as in the top-quark decays. We show that kinematic cuts, as well as higher-order effects and SMEFT operators in top-quark decays, are important and should be consistently considered together, because they have a significant impact on the shape of the standard observables measured for the pp→t¯tH+X process at the 0

What carries the argument

Consistent inclusion of the four dimension-6 SMEFT operators (O_tφ, O_φG, O_tG, O_tW) in both production and top-quark decays at NLO QCD.

If this is right

  • Linear, cross, and quadratic contributions from the operators affect cross sections and shapes differently.
  • Renormalization group effects of the operators must be accounted for in predictions.
  • Predictions with stable tops differ from those with reconstructed decays from leptons.
  • At 13.6 TeV these effects impact measurements in LHC Run III data.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Global SMEFT fits to ttH data may need to include decay operators to avoid biased constraints on the operators.
  • Similar consistent treatments could be important for other top-associated processes like ttZ or single top production.
  • Future work adding electroweak corrections might modify the uncertainties reported in this NLO QCD study.

Load-bearing premise

The four listed dimension-6 operators capture the dominant new-physics effects and that neglecting higher-dimensional operators or electroweak corrections does not alter the reported shapes and uncertainties at the level claimed.

What would settle it

A measurement at the LHC showing that the shapes of differential distributions in ttH events remain unchanged when SMEFT operators are included in top decays beyond the stated uncertainties, or that adding other operators changes them substantially.

Figures

Figures reproduced from arXiv: 2605.11747 by Giuseppe Bevilacqua, Malgorzata Worek, Minos Reinartz.

Figure 1
Figure 1. Figure 1: Example of effective operators involved in the SMEFT calculation for the pp → ttH¯ + X process in the di-lepton decay channel. The insertion operators are OtG, OϕG, Otϕ and OtW . the Smeft@NLO webpage 1 . The OG operator is rather special as it is already constrained by LHC multi-jet events [46, 47]. In addition, it does not enter the renormalisation group flow of the other operator coefficients listed abo… view at source ↗
Figure 2
Figure 2. Figure 2: Examples of effective-operator insertions of Otϕ, OϕG, OtG, OtW entering ttH¯ production and top-quark decays for the pp → ttH¯ + X process in the NWA. The leptonic decays of the W gauge bosons considered in our study are omitted here for simplicity. W t b tW g W t g b tW W t g b tG t g b tW W t g b tG W [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Examples of effective-operator insertions of OtG, OtW entering top-quark decays for the pp → ttH¯ +X process in the NWA. The leptonic decays of the W gauge bosons considered in our study are omitted here for simplicity. – 5 – [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Schematic representation of the Helac-Smeft framework and its workflow. Newly devel￾oped modules and updated parts of the Helac-NLO program are highlighted in blue. Particular attention should be paid to the treatment of colour degrees of freedom in QCD. The Helac-Smeft framework uses the so-called colour-flow representation [65]. This concept can be better illustrated using the example of a four-gluon ver… view at source ↗
Figure 5
Figure 5. Figure 5: Example of a one-loop topology relevant for the pp → ttH¯ + X process in SMEFT, not included in the original Helac-1Loop Monte Carlo program. The vertex marked in green is associated with the OtG operator. ϕG t ¯ t g H g t ¯ t g g ϕG H [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Example of one-loop topologies relevant for the pp → ttH¯ +X process in SMEFT, for which the rank of one-loop integrals can exceed the number of propagators. The vertices marked in red are associated with the OϕG operator. insertion can bring extra powers of momentum into the numerator. This is the case for the OϕG opera￾tor. The ggH vertex induced by this operator carries a loop momentum on each gluon leg… view at source ↗
Figure 7
Figure 7. Figure 7: Examples of effective-operator insertions of OϕG for the pp → ttH¯ +X process in the NWA that open up at NLO in QCD. The leptonic decays of the W gauge bosons considered in our study are omitted here for simplicity. uncertainties are significantly reduced, highlighting the importance of adding higher-order corrections. However, also in this case, for some partial contributions, the magnitude of theoretical… view at source ↗
Figure 8
Figure 8. Figure 8: Integrated cross-section predictions at LO (upper plot) and NLO in QCD (lower plot) for pp → ttH¯ + X (Stable) and pp → e +νe µ −ν¯µ b ¯b H + X (NWA) at the LHC with √ s = 13.6 TeV presented in the form of a double ratio defined according to Di ≡ σi/σSM σ NWA i /σNWA SM . Results are given for the linear, cross and quadratic terms. They are provided for the NNPDF3.1 PDF set and evaluated using µR = µF = mt… view at source ↗
Figure 9
Figure 9. Figure 9: Integrated cross-section predictions at LO for pp → ttH¯ + X (Stable) and pp → e +νe µ −ν¯µ b ¯b H + X (NWA) at the LHC with √ s = 13.6 TeV presented in the form of a double ratio defined according to Di ≡ σi/σSM σ NWA i /σNWA SM . In the case of NWA predictions, no kinematic cuts are applied to the top-quark decay products. Results are given for the linear, cross and quadratic terms. They are provided for… view at source ↗
Figure 10
Figure 10. Figure 10: Normalised differential cross-section distributions at NLO in QCD as a function of pT (H) for the pp → e +νe µ −ν¯µ b ¯b H + X process at the LHC with √ s = 13.6 TeV. The upper panels show the linear σi (left) and quadratic σii (right) terms. The lower panels display the differential K-factors together with their uncertainty bands estimated with the help of the 7-point scale variation and the relative sca… view at source ↗
Figure 11
Figure 11. Figure 11: Normalised differential cross-section distributions at NLO in QCD as a function of pT (b1) for the pp → e +νe µ −ν¯µ b ¯b H + X process at the LHC with √ s = 13.6 TeV. The upper panels show the linear σi (left) and quadratic σii (right) terms. The lower panels display the differential K-factors together with their uncertainty bands estimated with the help of the 7-point scale variation and the relative sc… view at source ↗
Figure 12
Figure 12. Figure 12: Normalised differential cross-section distributions at NLO in QCD as a function of pT (ℓ1) for the pp → e +νe µ −ν¯µ b ¯b H + X process at the LHC with √ s = 13.6 TeV. The upper panels show the linear σi (left) and quadratic σii (right) terms. The lower panels display the differential K-factors together with their uncertainty bands estimated with the help of the 7-point scale variation and the relative sc… view at source ↗
Figure 13
Figure 13. Figure 13: Normalised differential cross-section distributions at NLO in QCD as a function of p miss T for the pp → e +νe µ −ν¯µ b ¯b H + X process at the LHC with √ s = 13.6 TeV. The upper panels show the linear σi (left) and quadratic σii (right) terms. The lower panels display the differential K-factors together with their uncertainty bands estimated with the help of the 7-point scale variation and the relative s… view at source ↗
Figure 14
Figure 14. Figure 14: Normalised differential cross-section distributions at NLO in QCD as a function of ∆Rℓ1ℓ2 for the pp → e +νe µ −ν¯µ b ¯b H + X process at the LHC with √ s = 13.6 TeV. The upper panels show the linear σi (left) and quadratic σii (right) terms. The lower panels display the differential K-factors together with their uncertainty bands estimated with the help of the 7-point scale variation and the relative sca… view at source ↗
Figure 15
Figure 15. Figure 15: Normalised differential cross-section distributions at NLO in QCD as a function of ∆ϕℓ1ℓ2 /π for the pp → e +νe µ −ν¯µ b ¯b H + X process at the LHC with √ s = 13.6 TeV. The upper panels show the linear σi (left) and quadratic σii (right) terms. The lower panels display the dif￾ferential K-factors together with their uncertainty bands estimated with the help of the 7-point scale variation and the relative… view at source ↗
Figure 16
Figure 16. Figure 16: Normalised differential cross-section distributions at LO and NLO in QCD as a function of yH for the pp → e +νe µ −ν¯µ b ¯b H + X process at the LHC with √ s = 13.6 TeV. The impact of the jet veto with p veto T = 100 GeV on the contributions induced by the OϕG operator is presented. The results for σϕG (left) and σϕG, ϕG (right) are displayed. The lower panels show the corresponding scale uncertainties fo… view at source ↗
Figure 17
Figure 17. Figure 17: Normalised differential cross-section distributions at LO and NLO in QCD as a function of ∆ϕℓ1ℓ2 /π for the pp → e +νe µ −ν¯µ b ¯b H + X process at the LHC with √ s = 13.6 TeV. The impact of the jet veto with p veto T = 100 GeV on the contributions induced by the OϕG operator is presented. The results for σϕG (left) and σϕG, ϕG (right) are displayed. The lower panels show the corresponding scale uncertain… view at source ↗
Figure 18
Figure 18. Figure 18: Normalised differential cross-section distributions at NLO in QCD as a function of pT (t) for pp → ttH¯ + X (Stable) and pp → e +νe µ −ν¯µ b ¯b H + X (NWA) at the LHC with √ s = 13.6 TeV. Results are provided for the linear and quadratic terms together with the corresponding scale uncertainties. The SM result is also plotted for comparison purposes. The upper panels display the ratio of the two prediction… view at source ↗
Figure 19
Figure 19. Figure 19: Normalised differential cross-section distributions at NLO in QCD as a function of Hreco T for pp → ttH¯ + X (Stable) and pp → e +νe µ −ν¯µ b ¯b H + X (NWA) at the LHC with √ s = 13.6 TeV. Results are provided for the linear and quadratic terms together with the corresponding scale uncertainties. The SM result is also plotted for comparison purposes. The upper panels display the ratio of the two predictio… view at source ↗
Figure 20
Figure 20. Figure 20: Normalised differential cross-section distributions at NLO in QCD as a function of pT (H) for pp → ttH¯ + X (Stable) and pp → e +νe µ −ν¯µ b ¯b H + X (NWA) at the LHC with √ s = 13.6 TeV. Results are provided for the linear and quadratic terms together with the corresponding scale uncertainties. The SM result is also plotted for comparison purposes. The upper panels display the ratio of the two prediction… view at source ↗
Figure 21
Figure 21. Figure 21: Normalised differential cross-section distributions at NLO in QCD as a function of y(H) for pp → ttH¯ + X (Stable) and pp → e +νe µ −ν¯µ b ¯b H + X (NWA) at the LHC with √ s = 13.6 TeV. Results are provided for the linear and quadratic terms together with the corresponding scale uncertainties. The SM result is also plotted for comparison purposes. The upper panels display the ratio of the two predictions.… view at source ↗
Figure 22
Figure 22. Figure 22: An example of operator mixing in SMEFT. The ggH vertex is generated by the OϕG operator, but the overall diagram represents a one-loop vertex correction to the ttH¯ vertex with the structure generated by the Otϕ operator. A UV counterterms from the anomalous dimension matrix In this Appendix we summarize the basic steps for deriving the Feynman rules for UV counterterms arising from the OϕG operator. We r… view at source ↗
read the original abstract

We present the computation of the next-to-leading order QCD corrections to the $pp\to t\bar{t} H+X$ process in the di-lepton channel at the LHC, including relevant dimension-6 operators $({\cal O}_{t\phi}, \, {\cal O}_{\phi G},\, {\cal O}_{tG}, \, {\cal O}_{tW})$ from the Standard Model Effective Field Theory. In our studies, higher-order corrections and effective operators are consistently included in the production part of the process as well as in the top-quark decays. We perform a detailed study of linear, cross, and quadratic contributions and their uncertainties, including renormalisation group effects. Our findings are presented at the integrated and differential cross-section level for the LHC Run III center-of-mass energy of $\sqrt{s}=13.6$ TeV. Finally, we provide predictions for $pp\to t\bar{t} H+X$ with stable top quarks and compare them with the results in which top quarks are reconstructed from their decay products. We show that kinematic cuts, as well as higher-order effects and SMEFT operators in top-quark decays, are important and should be consistently considered together, because they have a significant impact on the shape of the standard observables measured for the $pp\to t\bar{t}H+X$ process at the LHC.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The paper computes next-to-leading-order QCD corrections to pp → t t-bar H + X in the dilepton channel at the LHC, incorporating four dimension-6 SMEFT operators (O_tφ, O_φG, O_tG, O_tW) consistently in both production and top-quark decays. It examines linear, cross, and quadratic contributions with uncertainties and renormalization-group evolution, presenting integrated and differential cross sections at √s = 13.6 TeV. Predictions assuming stable top quarks are compared to those with tops reconstructed from decay products, with the conclusion that kinematic cuts, higher-order effects, and SMEFT operators in decays significantly impact the shapes of standard observables.

Significance. If the numerical results hold, the work establishes that consistent inclusion of SMEFT effects in top decays at NLO is required to avoid distorting differential distributions in ttH production, with direct relevance to LHC precision measurements and new-physics searches. The technical advance lies in the simultaneous treatment of production and decay at NLO together with RG running, and the stable-versus-decaying comparison quantifies reconstruction biases.

major comments (1)
  1. [Introduction and operator-selection discussion] The central claim that the reported shape modifications from linear+quadratic SMEFT contributions are robust under truncation relies on the four operators capturing dominant effects. No explicit comparison to an enlarged basis (e.g., adding O_tB or relevant four-fermion operators) or estimate of dimension-8 insertions is provided in the same differential bins where kinematic cuts are shown to amplify deviations. This omission is load-bearing because the paper itself demonstrates that cuts enhance sensitivity in specific phase-space regions.
minor comments (2)
  1. Figure captions and legends should explicitly label the separate linear, interference, and quadratic SMEFT contributions as well as the SM baseline to improve readability of the differential distributions.
  2. A brief statement on the size of neglected electroweak corrections relative to the quoted QCD uncertainties would clarify the truncation assumptions in the results section.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive feedback. We address the single major comment below and have revised the paper accordingly to strengthen the discussion of operator selection.

read point-by-point responses

  1. Referee: The central claim that the reported shape modifications from linear+quadratic SMEFT contributions are robust under truncation relies on the four operators capturing dominant effects. No explicit comparison to an enlarged basis (e.g., adding O_tB or relevant four-fermion operators) or estimate of dimension-8 insertions is provided in the same differential bins where kinematic cuts are shown to amplify deviations. This omission is load-bearing because the paper itself demonstrates that cuts enhance sensitivity in specific phase-space regions.

    Authors: We agree that an explicit justification for the truncation is important, especially given the demonstrated sensitivity to kinematic cuts. The operators O_tφ, O_φG, O_tG and O_tW were chosen as they directly enter the top-Yukawa, Higgs-gluon, top-gluon and top-W vertices that dominate both production and dilepton decays in ttH. Operators such as O_tB primarily affect electroweak vertices with smaller QCD impact at 13.6 TeV, while four-fermion operators are typically bounded to be small by other LHC and precision data and would require separate matching. Dimension-8 terms are parametrically suppressed by additional 1/Λ² factors. In the revised manuscript we have expanded the introduction with a dedicated paragraph that (i) cites global SMEFT fits supporting the dominance of these four operators for ttH observables, (ii) provides a qualitative estimate of the possible size of neglected contributions based on current Wilson-coefficient bounds, and (iii) explicitly states that a full numerical comparison over an enlarged basis in the identical differential bins lies beyond the present computational scope but is planned for future work. We believe this addition addresses the robustness concern without altering the central numerical results. revision: partial

Circularity Check

0 steps flagged

No significant circularity in direct perturbative SMEFT NLO computation

full rationale

The paper performs a standard next-to-leading-order QCD calculation in the SMEFT for the pp→ttH process, incorporating four dimension-6 operators consistently in production and decays. The reported shapes and impacts are direct outputs of the perturbative expansion, including linear, quadratic, and interference terms, without any parameter fitting or self-referential definitions that would make predictions equivalent to inputs by construction. Comparisons to stable top predictions are explicit reconstructions. No self-citation load-bearing or ansatz smuggling is evident in the derivation chain. This is a self-contained computational study within established frameworks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The calculation rests on the standard SMEFT expansion truncated at dimension 6 and on perturbative QCD at NLO; no explicit free parameters or new entities are introduced in the abstract.

axioms (1)
  • domain assumption Validity of SMEFT at LHC energies with only dimension-6 operators
    Assumes higher-dimensional operators and electroweak corrections can be neglected for the reported observables.

pith-pipeline@v0.9.0 · 5553 in / 1265 out tokens · 41503 ms · 2026-05-13T05:54:16.199543+00:00 · methodology

discussion (0)

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Reference graph

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