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REVIEW 2 major objections 5 minor 94 references

First separate top and anti-top differential spectra at 13 TeV, measured out to 500 GeV, match QCD and tighten a four-quark new-physics bound to ±0.12 TeV⁻².

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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2026-08-03 11:49 UTC pith:RVWFXIOY

load-bearing objection Solid first separate tq/tbarq differential measurement at 13 TeV; EFT constraint is plausible but under-systematised. the 2 major comments →

arxiv 2601.04938 v2 pith:RVWFXIOY submitted 2026-01-08 hep-ex

Measurement of differential t-channel single top (anti)quark production cross-sections at 13 TeV with the ATLAS detector

ATLAS Collaboration This is my paper
classification hep-ex
keywords single top quark productiont-channeldifferential cross sectioneffective field theoryWilson coefficientparton distribution functionsiterative Bayesian unfoldingATLAS Run 2
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper establishes, for the first time at 13 TeV, separate differential measurements of t-channel single top quark (tq) and top antiquark (t̄q) production, using the full 140 fb⁻¹ Run 2 dataset recorded at the ATLAS detector. It claims the parton-level cross sections as functions of transverse momentum pT — measured out to 500 GeV — and absolute rapidity |y| agree with next-to-leading-order and next-to-next-to-leading-order QCD predictions, and that the tq/t̄q ratio is measured as well; most of the discriminating power between predictions is limited by systematic uncertainties. A sympathetic reader would care because these shapes are direct probes of the proton's parton densities (the charge ratio tracks the u/d valence ratio) and of possible four-quark contact interactions that would show up as excesses at high pT. Interpreting the pT spectra in an effective field theory framework, the paper constrains the Wilson coefficient C_Qq^{3,1}/Λ² to the interval −0.12 to +0.12 TeV⁻² at 95% confidence, an improvement over the inclusive cross-section constraint, and argues that this bound is only valid if the operator's large effect on the selection acceptance is properly accounted for.

Core claim

The central result is the first separate differential measurement of tq and t̄q production at 13 TeV. Events with one isolated lepton, large missing transverse momentum, and exactly two jets (one b-tagged) are selected, backgrounds are suppressed by a neural network, and the pT and |y| distributions are unfolded to parton level with iterative Bayesian unfolding, using migration matrices and efficiencies from the nominal four-flavour-scheme Powheg+Pythia8 signal simulation, including a shadow bin to 2000 GeV. The absolute and normalised cross sections and their ratio agree with NLO predictions from several generator/shower combinations and with NNLO fixed-order calculations. For the EFT inter

What carries the argument

The carrying mechanism is the unfolding chain that converts detector-level spectra into parton-level cross sections: an iterative Bayesian unfolding implemented with the RooUnfold package, inverting the relation N_data = M·ε·σ·L + background without direct matrix inversion, where M_jk (the migration matrix) gives the probability that an event produced in parton-level bin k is reconstructed in bin j and ε_k is the selection efficiency; both are computed from the nominal Powheg+Pythia8 four-flavour-scheme signal sample. The EFT interpretation reuses this same machinery: the expected fractional change of each bin under a new-physics operator is parameterised as Δσ̃(C) = 1 + a1·C + a2·C² with Λ

Load-bearing premise

The load-bearing premise is that the simulated signal sample — which provides the bin-to-bin migration and selection-efficiency corrections used for both the data and the new-physics templates — describes the true kinematics of high-pT events closely enough, with agreement validated only by sub-2% closure tests, so that if the real signal kinematics differ from the simulation the measured spectra and the ±0.12 TeV⁻² interval would shift.

What would settle it

Recompute the unfolded pT spectra and the EFT fit using Wilson-coefficient-dependent unfolding — e.g., unfolding each of the five EFT samples with its own migration matrix and efficiency, or adding an acceptance nuisance parameter that varies with C/Λ² — and compare the resulting 95% CL interval with −0.12 < C < 0.12 TeV⁻²; a shift larger than the quoted uncertainty shows the nominal, coefficient-independent corrections are the limiting step. As a second check, generate high-pT pseudo-data with an alternative parton shower and unfold with the nominal corrections to test the sub-2% closure abov

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • The separate tq and t̄q pT spectra now extend to 500 GeV, roughly doubling the kinematic reach of previous 13 TeV differential measurements, and the normalised |y| shapes reach 3–6% precision (versus 7–15% at 8 TeV).
  • Because the tq/t̄q ratio cancels most systematic uncertainties, the measured ratio as a function of pT and |y| is a more discriminating test of PDF sets than the individual spectra — the data visibly disfavour the ABMP16 prediction for the |y| ratio while the other predictions agree.
  • If the EFT interpretation's acceptance treatment is correct, the interval −0.12 < C_Qq^{3,1}/Λ² < 0.12 TeV⁻² improves the bound from the inclusive single-top cross-section measurement, with the high-pT bins (175–500 GeV) carrying most of the sensitivity and the quadratic term in the parameterisation growing rapidly in those bins.
  • The agreement of NNLO predictions with the measured pT shapes, where LO fails as expected, provides a benchmark for using single-top events to constrain proton PDFs, specifically the u/d ratio and, in future, the b-quark density.

Where Pith is reading between the lines

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

  • My inference: the paper's EFT method — unfolding every Wilson-coefficient sample with the nominal migration matrix and efficiency — is a workable compromise only if the operator's shape distortion is modest at the fitted values; a straightforward stress test is to repeat the fit with a coefficient-dependent response matrix, or to profile over the acceptance uncertainty, and check whether the ±0.12
  • My inference: since the tq/t̄q ratio is nearly free of detector and rate systematics (most cancel in the ratio), a global PDF fit that includes these five-bin normalised |y| shapes would sharpen the u/d determination at intermediate x — an extension the paper flags as a motivation but does not itself carry out.
  • My inference: the measured pT extension to 500 GeV is exactly the region where four-quark operators grow fastest, so combining this single-top spectrum with the top-pair pT spectrum in a joint SMEFT fit could separate C_Qq^{3,1} from the operators O_phiQ³ and O_tW, which the paper deliberately sets to zero — a next step made possible by the published per-bin parameterisations.
  • My inference: the shadow-bin technique (an upper edge at 2000 GeV whose content is not measured but absorbs migration) is a reusable prescription for other inclusive measurements reaching the edge of their kinematic range; it keeps the highest measured bin unbiased at the cost of not reporting cross sections above 500 GeV.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 5 minor

Summary. The paper reports ATLAS measurements of differential t-channel single top quark and top antiquark production at 13 TeV using the full Run 2 data set (140 fb^-1). Absolute and normalized cross sections are measured as functions of pT and |y| for tq and tbarq separately, together with their ratio. The unfolding uses iterative Bayesian unfolding with corrections from the nominal Powheg+Pythia8 4FS signal sample. The results are compared with NLO MC generators, different PDF sets, and NNLO MCFM predictions. The paper also presents an EFT interpretation constraining the Wilson coefficient C_Qq^{3,1}/Lambda^2, claiming a 95% CL interval of [-0.12, 0.12] TeV^-2 and noting that this is the first separate differential measurement of tq and tbarq at 13 TeV, with pT coverage extended to 500 GeV.

Significance. If the measurement is correct, it provides a valuable precision result: the first separate differential tq/tbarq cross sections at 13 TeV, an extended pT range, a new charge-ratio measurement, and a competitive EFT constraint. The paper is careful in its unfolding validation (non-closure below 2%), provides detailed systematic uncertainty tables, and gives chi^2 probabilities for many theory predictions. The EFT interpretation is the least secure part: the response function is derived from a single MadGraph 5FS model with no systematic assigned for generator, scale, or PDF choices in the EFT template, despite the large acceptance effect and the large signal-modelling uncertainties in high-pT bins. This gap should be addressed before the EFT constraint is considered final.

major comments (2)
  1. [§9.1, Eq. (1)] The EFT response parameters a1 and a2 are determined from MadGraph5_aMC@NLO 5FS samples unfolded with the nominal Powheg 4FS migration matrix and efficiency, and the least-squares fit includes only MC statistical uncertainties. No systematic uncertainty is assigned for the generator choice (5FS vs 4FS), for renormalization/factorization scale or PDF variations in the EFT generation, or for the assumption that the C-dependent acceptance (Figure 14) is correctly modeled. The high-pT bins carry 12–24% signal-modelling uncertainties (Tables 6–11) that are not propagated into the EFT template. Because the acceptance effect is large, this could shift the quoted 95% CL interval [-0.12, 0.12] TeV^-2 by a substantial fraction of its width. Please add a systematic uncertainty on the EFT response (or validate it with an alternative generator/4FS EFT sample) and quantify the impact on the interval.
  2. [§7, §9.1] The non-closure test in Section 7 alters signal shapes according to the difference between expected and observed distributions, not according to the large EFT-induced distortions. Since the EFT samples are unfolded with the nominal C=0 migration matrix and efficiency, a dedicated closure test for EFT-like templates (e.g., unfolding the C!=0 MadGraph samples with the nominal response and comparing with truth) is needed to rule out a bias in the extracted a1, a2 parameterization. The current validation is insufficient to support the claim that the EFT acceptance effect is correctly accounted for.
minor comments (5)
  1. [§9.1] The sentence 'The correlation of the total uncertainty in the measurement result between bins is not considered for the least-squares fit' is confusing, since the a1, a2 fit is to EFT MC predictions, not to data. Please clarify that the data covariance is used only in the final EFTfitter step, not in the response-function fit.
  2. [Tables 4, 5] Several chi^2 probabilities are reported as exactly 1.0 (e.g., ratio pT rows). Consider giving more significant digits or adding a note explaining that large systematic correlations lead to high p-values.
  3. [Tables 20, 21 captions] Typo: 'fuction' should be 'function' in both captions.
  4. [Figure 15 caption] The dashed line description is ambiguous: 'the measurement result over the theoretical prediction calculated with MCFM at NNLO' should specify exactly which ratio is plotted (e.g., unfolded data divided by MCFM NNLO per bin).
  5. [Section 3] Typo: 'pertubation' should be 'perturbation'; please check for similar typos throughout the text.

Circularity Check

0 steps flagged

No significant circularity: data enter only as observables; EFT response is fitted to MC, not to data; self-citation is methodological.

full rationale

The differential measurement is obtained from data counts via the unfolding equation in Section 6, N_data_j = sum_k M_jk * eps_k * L * DeltaX_k * d(sigma)_k/dX + B_j, with M and eps derived from the nominal Powheg 4FS sample. The data enter as observed yields, not as the MC prediction, and the closure test against perturbed signal shapes is below 2% (Section 7), so agreement with Powheg or MCFM is not forced by construction. The EFT interpretation fits a1 and a2 in Eq. (1) to EFT MC samples only, using the measured unfolded spectra once in EFTfitter; no parameter fitted to the data is later renamed a prediction. The acceptance effect is explicitly modeled (Figure 14) and is therefore an assumption, not a tautology. The heavy reliance on Ref. [9] for event selection, the neural network, and the uncertainty scheme is methodological reuse by the same collaboration; the differential cross-sections and the EFT interval are new results not entailed by the inclusive measurement of [9]. The skeptic's concern about missing 4FS/5FS, scale, or generator systematics in the EFT response is a legitimate robustness limitation, but it is not circular reasoning: the response is an independent MC-derived template that could disagree with the data, and the paper does not define its prediction as the data.

Axiom & Free-Parameter Ledger

4 free parameters · 5 axioms · 0 invented entities

No new particles, mediators, forces, dimensions, or conserved quantities are introduced. The SMEFT four-quark operator O_Qq^{3,1} is taken from the existing Warsaw-basis literature. The main analysis-specific fitted numbers are background normalisations, EFT response coefficients, the unfolding iteration count, and selection thresholds.

free parameters (4)
  • Background normalization scale factors (per process, per lepton charge) = Post-fit yields in Table 3 (e.g., tq 29740±590, tbarq 15550±300)
    Extracted from a binned profile maximum-likelihood fit to data; they set the background rates subtracted before unfolding and therefore enter the measured cross-sections.
  • EFT response coefficients a1, a2 (per pT bin for tq and tbarq) = Table 22, e.g. a1=-2.452, a2=1.694 in the 275–500 GeV tq bin
    Least-squares fits to MC predictions at five values of C_Qq/Λ^2; they interpolate the cross-section response used in the EFT interpretation.
  • Unfolding iteration count = 4
    Chosen by minimising statistical correlation between bins; affects the unfolded central values, though bias is validated below 2%.
  • Event-selection thresholds = Lepton pT>28 GeV, jet pT>30 GeV, NN output Dnn>0.93, m(lb)<160 GeV
    Optimised in this or the predecessor inclusive analysis; they define the acceptance that the unfolding corrects.
axioms (5)
  • standard math D'Agostini iterative Bayesian unfolding with four iterations converges to the true distribution.
    Used in Sections 6–7; assumes the migration matrix is a valid response model and that four iterations balance bias versus variance. Non-closure is validated below 2%.
  • domain assumption The nominal Powheg+Pythia8 4FS sample correctly describes the parton-level signal kinematics after unfolding.
    Migration matrices and efficiencies are computed from this sample (Section 7); bias is validated against altered shapes but not against all beyond-SM possibilities.
  • domain assumption SMEFT truncation at dimension six with only O_Qq^{3,1} active; O_phiQ^3 and O_tW are set to zero.
    Section 9.1; the resulting constraint is conditional on this operator basis and on the other coefficients vanishing.
  • domain assumption Backgrounds from ttbar, Wt, s-channel, W/Z+jets, diboson, and multijet are correctly modelled or normalised by the profile fit.
    Section 5; no dedicated control regions for prompt-lepton backgrounds, so residual mismodelling would enter the unfolded signal.
  • domain assumption ATLAS detector simulation and calibration (JES, JER, b-tagging, lepton efficiencies) provide unbiased corrections.
    Used throughout; uncertainties are propagated as nuisance parameters but the central corrections rely on simulation.

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read the original abstract

The production of single top quarks and top antiquarks via the $t$-channel exchange of a virtual $W$ boson is measured in proton-proton collisions at a centre-of-mass energy of 13 TeV at the Large Hadron Collider. The full Run 2 data sample recorded with the ATLAS detector in the years 2015-2018 is used, corresponding to an integrated luminosity of 140 fb$^{-1}$. The absolute and normalised production cross-sections are measured differentially as a function of the transverse momentum and absolute rapidity of the top quark and top antiquark. In addition, the ratio of top quark to top antiquark production cross-sections is measured. The measured distributions are compared with next-to-leading-order quantum chromodynamics predictions obtained with different combinations of matrix-element generators, parton-shower programs and proton parton distribution functions, as well as to next-to-next-to-leading-order calculations. Overall, good agreement is observed between the measurements and the theoretical predictions. For most measured distributions, the sensitivity to differences between the predictions is limited by the systematic uncertainties in the measurement. The measured differential distributions are also interpreted in an effective field theory approach to constrain the Wilson-Coefficient $C_{Qq}^{3,1}$ associated with a four-quark operator. The interpretation accounts for the effect of the selection efficiency, which is altered significantly by non-zero contributions from $C_{Qq}^{3,1}$.

Figures

Figures reproduced from arXiv: 2601.04938 by ATLAS Collaboration.

Figure 1
Figure 1. Figure 1: Example Feynman diagrams of (a) single top quark and (b) single top antiquark production via the 𝑡-channel exchange of a virtual 𝑊 boson at LO in perturbation theory with the leptonic decay channel of the top (anti)quark. In this paper, the ATLAS measurements of differential 𝑡𝑞 and 𝑡𝑞¯ production cross-sections are presented using the full Run 2 data sample, recorded with the ATLAS detector between 2015 an… view at source ↗
Figure 2
Figure 2. Figure 2: Post-fit agreement between data and the expected distributions in events containing a (a) positively charged lepton and (b) negatively charged lepton. The experimental, background-related and MC statistical uncertainties are incorporated in the uncertainty bands. The region 𝐷𝑛𝑛 > 0.93 is excluded from the fit. Per-process scale factors are obtained from the post-fit over pre-fit event yield ratio and the r… view at source ↗
Figure 3
Figure 3. Figure 3: Comparison of the measured data to the expected distributions estimated from MC simulation in the (a),(c) ℓ + SR and (b),(d) ℓ − SR (i.e. the requirement 𝐷𝑛𝑛 > 0.93 is imposed). The distributions are shown for variables (a) 𝑝T(ℓ + 𝜈𝑏), (b) 𝑝T(ℓ − 𝜈𝑏), (c) |y(ℓ + 𝜈𝑏)| and (d) |y(ℓ − 𝜈𝑏)|, utilising the binning optimised for the unfolding as described in Section 7. The uncertainty bands incorporate the MC st… view at source ↗
Figure 4
Figure 4. Figure 4: Summary of the uncertainties in the absolute differential 𝑡𝑞 or 𝑡𝑞¯ production cross-sections measured as a function of (a) 𝑝T(𝑡), (b) 𝑝T(𝑡¯), (c) |y(𝑡)| and (d) |y(𝑡¯)| and on the ratio of the differential 𝑡𝑞 and 𝑡𝑞¯ production cross-sections measured as a function of (e) 𝑝T(𝑡 or 𝑡¯) and (f) |𝑦(𝑡 or 𝑡¯)|. Similar sources of uncertainties are grouped using their quadratic sum. The shaded band indicates the… view at source ↗
Figure 5
Figure 5. Figure 5: Summary of the uncertainties in the normalised differential 𝑡𝑞 or 𝑡𝑞¯ production cross-sections measured as a function of (a) 𝑝T(𝑡), (b) 𝑝T(𝑡¯), (c) |y(𝑡)| and (d) |y(𝑡¯)|. Similar sources of uncertainties are grouped using their quadratic sum. The shaded band indicates the total uncertainty, defined as the quadratic sum of all sources of uncertainties. measured cross-sections. Their contributions differ b… view at source ↗
Figure 6
Figure 6. Figure 6: Absolute unfolded differential (a) (c) 𝑡𝑞 cross-sections and (b) (d) 𝑡𝑞¯ cross-sections as a function of (a) (b) 𝑝T(𝑡) or 𝑝T(𝑡¯) and (c) (d) |y(𝑡)| or |y(𝑡¯)|. The shaded band indicates the total measurement uncertainty. The cross-sections are compared with the theoretical predictions from FO calculations done with MCFM at LO, NLO and NNLO. The uncertainty in the theoretical predictions comprises the uncer… view at source ↗
Figure 7
Figure 7. Figure 7: Absolute unfolded differential (a) (c) 𝑡𝑞 cross-sections and (b) (d) 𝑡𝑞¯ cross-sections as a function of (a) (b) 𝑝T(𝑡) or 𝑝T(𝑡¯) and (c) (d) |y(𝑡)| or |y(𝑡¯)|. The shaded band indicates the total measurement uncertainty. The cross-sections are compared with the predictions from Powheg +Pythia 8 with different PDF sets. The uncertainty in the theoretical predictions comprises the MC statistical uncertainty … view at source ↗
Figure 8
Figure 8. Figure 8: Absolute unfolded differential (a) (c) 𝑡𝑞 cross-sections and (b) (d) 𝑡𝑞¯ cross-sections as a function of (a) (b) 𝑝T(𝑡) or 𝑝T(𝑡¯) and (c) (d) |y(𝑡)| or |y(𝑡¯)|. The shaded band indicates the total measurement uncertainty. The cross-sections are compared with the predictions from different MC event generators and parton shower programs. All predictions are generated with the NNPDF3.0 PDF set. The uncertainty… view at source ↗
Figure 9
Figure 9. Figure 9: Normalised unfolded differential (a) (c) 𝑡𝑞 cross-sections and (b) (d) 𝑡𝑞¯ cross-sections as a function of (a) (b) 𝑝T(𝑡) or 𝑝T(𝑡¯) and (c) (d) |y(𝑡)| or |y(𝑡¯)|. The shaded band indicates the total measurement uncertainty. The cross-sections are compared with the theoretical predictions from FO calculations done with MCFM at LO, NLO and NNLO. The uncertainty in the theoretical predictions from FO calculati… view at source ↗
Figure 10
Figure 10. Figure 10: Normalised unfolded differential (a) (c) 𝑡𝑞 cross-sections and (b) (d) 𝑡𝑞¯ cross-sections as a function of (a) (b) 𝑝T(𝑡) or 𝑝T(𝑡¯) and (c) (d) |y(𝑡)| or |y(𝑡¯)|. The shaded band indicates the total measurement uncertainty. The cross-sections are compared with the predictions from Powheg +Pythia 8 with different PDF sets. The uncertainty in the theoretical predictions comprises the MC statistical uncertain… view at source ↗
Figure 11
Figure 11. Figure 11: Normalised unfolded differential (a) (c) 𝑡𝑞 cross-sections and (b) (d) 𝑡𝑞¯ cross-sections as a function of (a) (b) 𝑝T(𝑡) or 𝑝T(𝑡¯) and (c) (d) |y(𝑡)| or |y(𝑡¯)|. The shaded band indicates the total measurement uncertainty. The cross-sections are compared with the predictions from different MC event generators and parton shower programs. All predictions are generated with the NNPDF3.0 PDF set. The uncertai… view at source ↗
Figure 12
Figure 12. Figure 12: Ratio of the unfolded differential cross-sections as a function of (a) (c) (e) 𝑝T(𝑡 or 𝑡¯) and (b) (d) (f) |y(𝑡 or 𝑡¯)|. The shaded band indicates the total measurement uncertainty. The cross-sections are compared with theoretical predictions obtained from (a) (b) FO calculations done with MCFM at LO, NLO and NNLO, (c) (d) Powheg +Pythia 8 with different PDF sets and (e) (f) different MC event generators … view at source ↗
Figure 13
Figure 13. Figure 13: Representative LO Feynman diagram of a four-quark contact interaction leading to the production of a single top quark. For large absolute values of 𝐶 3,1 𝑄𝑞/Λ 2 , the number of single top quarks and top antiquarks produced with a high transverse momentum is expected to increase. Therefore, the high-𝑝T region of the spectra provides a high sensitivity to 𝐶 3,1 𝑄𝑞/Λ 2 . Since the radiation of additional jet… view at source ↗
Figure 14
Figure 14. Figure 14: Selection efficiencies for the (a) 𝑝T(𝑡) and (b) 𝑝T(𝑡¯) spectra calculated for 𝑡𝑞 and 𝑡𝑞¯ production events generated with different values of 𝐶 3,1 𝑄𝑞/Λ 2 , with Λ set to 1 TeV. The parameters 𝑎1 and 𝑎2 in Eq. (1) are determined via least-squares fits performed for each bin of the unfolded distributions. The uncertainties in the measured result, the SM prediction and the statistical uncertainty due to th… view at source ↗
Figure 15
Figure 15. Figure 15: Comparison of the parameterisation for the expected relative change of the differential 𝑡𝑞 production cross-section as a function of 𝐶 3,1 𝑄𝑞/Λ 2 , with Λ set to 1 TeV, obtained from parton level predictions and by unfolding the detector level predictions with the nominal unfolding corrections. The uncertainties in the predictions are MC statistical uncertainties only. The dashed line indicates the measur… view at source ↗
Figure 16
Figure 16. Figure 16: Migration matrices for the (a),(b) 𝑝T(ℓ + 𝜈𝑏) and (c),(d) |y(ℓ + 𝜈𝑏)| distributions in the (a),(c) ℓ + SR and (b),(d) ℓ − SR. The variables on parton-level are shown on the 𝑦-axis and the reconstructed variables are shown on the 𝑥-axis. The rows are normalised to unity. Systematic and statistical uncertainties The statistical and systematic uncertainties in the measured results are evaluated according to … view at source ↗

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