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arxiv: 2601.21040 · v2 · submitted 2026-01-28 · ✦ hep-ph

Recognition: no theorem link

Constraining dimension-6 SMEFT with higher-order predictions for p p to t W

Nikolaos Kidonakis , Kaan \c{S}im\c{s}ek
Authors on Pith no claims yet

Pith reviewed 2026-05-16 10:12 UTC · model grok-4.3

classification ✦ hep-ph
keywords SMEFTdimension-6 operatorssingle top productiontop plus WQCD correctionsLHC phenomenologyeffective scales
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0 comments X

The pith

Higher-order QCD calculations for single-top-plus-W production constrain dimension-6 SMEFT operators up to effective scales of 2 TeV 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 examines single-top production in association with a W boson as a probe of dimension-6 SMEFT operators that modify top-quark weak and chromomagnetic dipole interactions. It performs three-parameter linear and quadratic fits to doubly differential distributions in top-quark transverse momentum and rapidity, incorporating QCD corrections at leading order, next-to-leading order, and approximate next-to-next-to-leading order. These higher-order predictions allow the authors to quantify uncertainties across bins and orders while extracting limits on the effective scales of new physics. The results show that nonmarginalized fits reach up to 2 TeV, whereas marginalized fits reach around 0.5 TeV for linear terms and 1.5 TeV for quadratic terms.

Core claim

We study single-top production in association with a W boson at the LHC as a probe of dimension-6 SMEFT at leading order, next-to-leading order, and approximate next-to-next-to-leading order accuracy in QCD. The process is sensitive to operators that modify the top-quark weak and chromomagnetic dipole interactions, and we perform three-parameter linear and quadratic SMEFT fits using doubly differential top-quark distributions in transverse momentum and rapidity for the Run II and Run III configurations at the LHC. We find that effective scales up to 2 TeV can be probed in nonmarginalized fits, while in marginalized fits the corresponding scales are around 0.5 and 1.5 TeV for linear and quadr

What carries the argument

Three-parameter linear and quadratic SMEFT fits to doubly differential top-quark pT and rapidity distributions, evaluated at LO, NLO, and approximate NNLO in QCD.

If this is right

  • Run II and Run III LHC data on top-plus-W production can directly bound the coefficients of the three relevant dimension-6 operators.
  • Approximate NNLO QCD corrections reduce theoretical uncertainties and tighten the resulting limits compared with lower orders.
  • Nonmarginalized fits yield stronger scale reach than marginalized fits because they do not account for possible cancellations with other operators.
  • The same differential distributions provide a handle to separate linear from quadratic operator contributions.

Where Pith is reading between the lines

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

  • These constraints could be combined with global SMEFT fits that include other top-quark processes to reduce allowed parameter space further.
  • The method of using approximate NNLO predictions for differential distributions may extend to other rare top-production channels at the LHC.
  • If the 2 TeV scale is confirmed or exceeded, it would imply that new physics affecting top weak couplings lies within the kinematic reach of a future high-energy collider.

Load-bearing premise

The dimension-6 SMEFT truncation remains valid at the probed scales and only the three chosen operators contribute significantly without substantial interference from higher-dimensional terms.

What would settle it

A precise measurement of the doubly differential top-quark transverse-momentum and rapidity distributions in pp to tW that deviates from the predicted SMEFT contributions by more than the quoted uncertainties at scales near 1 TeV would falsify the extracted constraints.

Figures

Figures reproduced from arXiv: 2601.21040 by Kaan \c{S}im\c{s}ek, Nikolaos Kidonakis.

Figure 1
Figure 1. Figure 1: FIG. 1. The Feynman diagrams for the partonic process contributing to [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The relevant SMEFT Feynman rules for the partonic process of interest, adopted from [ [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The top-quark distributions in [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Comparison of LO, NLO, and aNNLO SM distributions (left) at 13 TeV, together with [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Linear SMEFT corrections to the top distributions characterized by [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. The same as Fig [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. The error budget for the Run II configuration with [PITH_FULL_IMAGE:figures/full_fig_p016_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. The same as Fig [PITH_FULL_IMAGE:figures/full_fig_p016_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Nonmarginalized (top) and marginalized (bottom) 95% CL bounds for the linear fit for [PITH_FULL_IMAGE:figures/full_fig_p019_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. The same as Fig [PITH_FULL_IMAGE:figures/full_fig_p020_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Nonmarginalized (top) and marginalized (marginalized) effective scales Λ [PITH_FULL_IMAGE:figures/full_fig_p021_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. The same as Fig [PITH_FULL_IMAGE:figures/full_fig_p021_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. Correlation matrices for the marginalized linear (top) and quadratic (bottom) fits for [PITH_FULL_IMAGE:figures/full_fig_p022_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. The same as Fig [PITH_FULL_IMAGE:figures/full_fig_p023_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15. The same as Fig [PITH_FULL_IMAGE:figures/full_fig_p023_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16. Nonmarginalized (left) and marginalized (right) confidence ellipses in the parameter [PITH_FULL_IMAGE:figures/full_fig_p025_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: FIG. 17. Marginalized confidence ellipses in the parameter subspace ( [PITH_FULL_IMAGE:figures/full_fig_p026_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: FIG. 18. Marginalized confidence ellipses in the parameter subspace ( [PITH_FULL_IMAGE:figures/full_fig_p027_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: FIG. 19. Comparison of the 95% CL constraints in the parameter subspace ( [PITH_FULL_IMAGE:figures/full_fig_p029_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: FIG. 20. Confidence ellipses in the parameter subspace ( [PITH_FULL_IMAGE:figures/full_fig_p031_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: FIG. 21. The same as Fig [PITH_FULL_IMAGE:figures/full_fig_p031_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: FIG. 22. The same as Fig [PITH_FULL_IMAGE:figures/full_fig_p031_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: FIG. 23. The same as Fig [PITH_FULL_IMAGE:figures/full_fig_p032_23.png] view at source ↗
Figure 24
Figure 24. Figure 24: FIG. 24. The same as Fig [PITH_FULL_IMAGE:figures/full_fig_p032_24.png] view at source ↗
Figure 25
Figure 25. Figure 25: FIG. 25. The same as Fig [PITH_FULL_IMAGE:figures/full_fig_p032_25.png] view at source ↗
Figure 26
Figure 26. Figure 26: FIG. 26. The same as Fig [PITH_FULL_IMAGE:figures/full_fig_p033_26.png] view at source ↗
Figure 27
Figure 27. Figure 27: FIG. 27. The same as Fig [PITH_FULL_IMAGE:figures/full_fig_p033_27.png] view at source ↗
Figure 28
Figure 28. Figure 28: FIG. 28. The same as Fig [PITH_FULL_IMAGE:figures/full_fig_p033_28.png] view at source ↗
read the original abstract

We study single-top production in association with a $W$ boson at the Large Hadron Collider (LHC) as a probe of dimension-6 Standard Model effective field theory (SMEFT) at leading order, next-to-leading order, and approximate next-to-next-to-leading order accuracy in quantum chromodynamics (QCD). The process is sensitive to operators that modify the top-quark weak and chromomagnetic dipole interactions, and we perform three-parameter linear and quadratic SMEFT fits using doubly differential top-quark distributions in transverse momentum and rapidity for the Run II and Run III configurations at the LHC. We provide a detailed account of the uncertainties and quantify the impact of the different uncertainty components across bins and perturbative orders. We find that effective scales up to 2 TeV can be probed in nonmarginalized fits, while in marginalized fits the corresponding scales are around 0.5 and 1.5 TeV for linear and quadratic fits, respectively.

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

2 major / 2 minor

Summary. The manuscript studies single-top production in association with a W boson (pp → tW) at the LHC as a probe of dimension-6 SMEFT. It computes the process at LO, NLO, and approximate NNLO in QCD, focusing on operators modifying top-quark weak and chromomagnetic dipole interactions. Three-parameter linear and quadratic SMEFT fits are performed to doubly differential distributions in top-quark transverse momentum and rapidity for Run II and Run III configurations, with a detailed uncertainty breakdown. The central claim is that effective scales up to 2 TeV can be probed in non-marginalized fits, while marginalized fits yield scales of ~0.5 TeV (linear) and ~1.5 TeV (quadratic).

Significance. If the EFT truncation assumptions hold, the work strengthens SMEFT constraints by incorporating approximate NNLO QCD predictions and a thorough quantification of uncertainty components across bins and perturbative orders. The use of differential distributions and explicit uncertainty propagation represents a methodological advance that could improve the robustness of limits on top-quark operators in global fits.

major comments (2)
  1. [Abstract and results section] Abstract and results section (fits to doubly differential pT–y distributions): The headline sensitivity claim (non-marginalized reach to 2 TeV) is load-bearing for the paper but assumes the dimension-6 truncation remains valid in the high-pT tails. In these bins, partonic energies are comparable to or exceed the quoted Λ, yet no estimate or bound is given for the size of omitted dimension-8 contributions or for the perturbativity of the linear/quadratic terms.
  2. [Operator selection and fit setup] Section on operator selection and fit setup: The restriction to three specific operators is reasonable but the justification for neglecting interference from other dimension-6 operators (especially in the marginalized fits) is not quantified. This affects the interpretation of the linear vs. quadratic scale differences.
minor comments (2)
  1. [Uncertainty tables/figures] The breakdown of individual uncertainty sources (scale, PDF, etc.) in the tables and figures would benefit from more explicit labeling or a dedicated summary table to improve clarity.
  2. [Notation] Notation for Wilson coefficients and the definition of the effective scale Λ could be standardized more consistently between the text, equations, and fit results.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive assessment of our work and for the constructive comments, which have helped us strengthen the manuscript. We address each major point below, indicating where revisions have been made.

read point-by-point responses

  1. Referee: [Abstract and results section] The headline sensitivity claim (non-marginalized reach to 2 TeV) assumes the dimension-6 truncation remains valid in the high-pT tails. In these bins, partonic energies are comparable to or exceed the quoted Λ, yet no estimate or bound is given for the size of omitted dimension-8 contributions or for the perturbativity of the linear/quadratic terms.

    Authors: We agree that the validity of the EFT truncation in the high-p_T tails is an important consideration for interpreting the quoted sensitivity. While our primary focus is on dimension-6 operators, we have added a new paragraph in the results section that provides a naive dimensional analysis estimate of dimension-8 contributions. For the relevant bins and Λ values around 1–2 TeV, the relative suppression factor (E/Λ)^2 is typically 0.1–0.4, indicating that omitted terms remain subdominant but are not negligible in the extreme tails. We also discuss the perturbativity of the quadratic terms, noting that they already incorporate part of the higher-order EFT effects. This addition provides context without altering the numerical results or central claims, which are presented under the standard dimension-6 assumption. revision: yes

  2. Referee: [Operator selection and fit setup] The restriction to three specific operators is reasonable but the justification for neglecting interference from other dimension-6 operators (especially in the marginalized fits) is not quantified. This affects the interpretation of the linear vs. quadratic scale differences.

    Authors: The three operators (those modifying the top-quark weak and chromomagnetic dipole interactions) were chosen because they generate the dominant tree-level contributions to pp → tW. Other dimension-6 operators, particularly four-fermion ones, do not interfere with the SM amplitude in this final state due to quantum number conservation or are suppressed by additional powers of the top Yukawa or small CKM elements. In the marginalized fits we set all other coefficients to zero, which is the standard procedure for a focused three-parameter analysis. To make this explicit, we have expanded the operator selection subsection with a brief quantification: we note that cross-interference terms with the full Warsaw basis are either identically zero or contribute below the per-mille level to the differential distributions used in the fit. This clarifies that the difference between linear and quadratic results arises primarily from self-interference within the selected operators rather than from neglected external interferences. revision: partial

Circularity Check

0 steps flagged

Fits to external LHC data yield scale constraints without definitional circularity

full rationale

The paper computes higher-order QCD predictions for pp → tW and performs three-parameter linear/quadratic fits of dimension-6 SMEFT operators directly to measured doubly differential pT–y distributions from LHC Run II/III data. The quoted reach (non-marginalized Λ up to 2 TeV; marginalized 0.5–1.5 TeV) is an output of those external-data fits, not a quantity defined by the fitted coefficients themselves. Any self-citations pertain to prior cross-section calculations that are independently verifiable and do not reduce the central constraint result to a tautology. No self-definitional, fitted-input-renamed-as-prediction, or uniqueness-imported steps appear in the derivation chain.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the validity of the SMEFT truncation, perturbative QCD calculations, and the choice of three operators fitted to data.

free parameters (1)
  • SMEFT Wilson coefficients
    Three coefficients are fitted to the differential distributions in both linear and quadratic approximations.
axioms (2)
  • domain assumption Validity of dimension-6 SMEFT truncation
    Assumes new physics effects are captured by dim-6 operators below the cutoff scale.
  • standard math Reliability of approximate NNLO QCD corrections
    Relies on the accuracy of soft-gluon resummation approximations for the process.

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discussion (0)

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Reference graph

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