NNLO fits of top-quark mass using total, single-differential and double-differential $t\bar{t}+X$ cross-section data

J. Mazzitelli; M.V. Garzelli; O. Zenaiev; S. Alekhin; S.-O. Moch

REVIEW 4 major objections 4 minor 11 references

NNLO fits of top-quark mass using total, single-differential and double-differential $t\bar{t}+X$ cross-section data

T0 review · 4 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read Combining LHC cross-section data at NNLO constrains the top-quark pole mass to about 171.5-172.2 GeV, compatible with the 2024 world average.

desk verdict Plausible NNLO top-mass extraction from LHC differential data, but the proceedings leaves the unfolding mass-dependence unquantified and the statistical details to the companion paper. read the letter →

arxiv 2412.14348 v1 pith:T4HVGWVN submitted 2024-12-18 hep-ph

S. Alekhin , M.V. Garzelli , J. Mazzitelli , S.-O. Moch , O. Zenaiev This is my paper · ORCID

classification hep-ph

keywords top-quarkpolemassNNLOQCDttbar+XproductiondifferentialcrosssectionspartondistributionfunctionsLHCtopphysicsextractionunfolding

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 reports next-to-next-to-leading-order (NNLO) QCD fits that extract the top-quark pole mass from LHC measurements of total, single-differential, and double-differential $t\bar{t}+X$ cross sections. The fits use unfolded parton-level data from ATLAS and CMS, compared with NNLO theory predictions, and are repeated with four modern PDF sets. Across sets the best-fit values cluster between 171.5 and 172.2 GeV, with data uncertainties of about 0.2-0.3 GeV and PDF and scale uncertainties of similar size. The results are compatible with the 2024 world-average value of $172.4 \pm 0.7$ GeV, while semileptonic and dileptonic datasets show a tension that stays within about two standard deviations. The paper's point is that differential top-pair data at NNLO already provide a competitive and theoretically well-defined determination of the top-quark mass.

What carries the argument

The central machinery is the NNLO QCD computation of $t\bar{t}+X$ production, implemented in the MATRIX code (a fully differential next-to-next-to-leading-order QCD program) and interfaced with PineAPPL (a fast interpolation tool) so that many mass values can be scanned efficiently. The fit compares normalized single- and double-differential cross-section data to these predictions using a $\chi^2$ function whose covariance matrix includes statistical, correlated and uncorrelated systematic, PDF, and scale uncertainties. The top-quark mass enters through the pole-mass dependence of the partonic cross sections, and the extracted value is read off from a parabolic interpolation through the $\chi^2$ values at $m_t^{\rm pole} = 170, 172.5, 175$ GeV.

What would settle it

Recompute the unfolding of the ATLAS and CMS datasets using Monte Carlo generators with the top mass set to 170 GeV and then to 175 GeV, and refit; if the extracted pole mass moves by more than the quoted ~0.3 GeV uncertainty, the mass-independent unfolding assumption is false.

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Extended reading notes

Core claim

The central claim is that comparing NNLO QCD predictions to normalized single- and double-differential $t\bar{t}$ cross sections from ATLAS and CMS determines the on-shell top-quark mass with precision comparable to direct measurements. For the most global fit combining Run 1 and Run 2 differential data plus total inclusive cross sections, the paper obtains $m_t^{\rm pole} = 171.54 \pm 0.24$ GeV (ABMP16), $171.59 \pm 0.22$ GeV (CT18), $171.79 \pm 0.22$ GeV (MSHT20), and $172.15 \pm 0.23$ GeV (NNPDF40), with additional PDF and scale uncertainties listed separately. The fit uses the $\chi^2$ distribution around three mass points (170, 172.5, 175 GeV) and a parabolic interpolation, with seven-point renormalization and factorization scale variations. The authors find that Run 2 differential datasets, especially the CMS 13 TeV semileptonic analysis, dominate the constraint, while total cross-section data contribute little. Semileptonic data pull the mass slightly upward relative to dileptonic data, but the shift stays within about two standard deviations.

Load-bearing premise

The unfolded parton-level data are treated as a fixed external input whose unfolding is assumed to be independent of the top-quark mass, so a residual mass dependence in the unfolding corrections could feed the assumed mass back into the fit and bias the extracted pole mass.

Editorial extensions

If this is right

If the fits are correct, current Run 1 plus Run 2 differential data already determine the top-quark pole mass to about 0.2-0.3 GeV precision, competitive with the world average.
The compatibility among four independent PDF sets indicates that, at the present precision, the choice of PDF set is not the dominant spread in the extracted mass.
The two-sigma shift between semileptonic and dileptonic channels implies that these datasets cannot yet be combined without accounting for their different systematic correlations.
Total inclusive cross-section data contribute little to the constraint, so future determinations should prioritize differential measurements.
Because data uncertainties already match the NNLO scale uncertainties, further progress in precision will require theory corrections beyond NNLO.

Reading between the lines

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

A direct test of the unfolding premise would be to recalculate the unfolded distributions with Monte Carlo generators generated at several top masses; this check is not reported, so the size of any mass-dependence bias remains unquantified.
Because normalized differential cross sections suppress unknown correlated systematics, fits to absolute double-differential distributions with full covariance information could either sharpen or dissolve the semileptonic/dileptonic tension.
The same NNLO plus fast-interpolation pipeline could be applied to other processes, such as single-top production, where the mass dependence enters differently and would provide an independent check on the extracted pole mass.
As data uncertainties continue to shrink, the fit will become dominated by NNLO scale dependence, making soft-gluon resummation for the double-differential distributions the decisive next theoretical upgrade.

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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

Colleague, here's my honest read. The paper is a short proceedings from ICHEP 2024, reporting an updated NNLO extraction of the top-quark pole mass from LHC ttbar+X cross-section data. The genuinely new element is the combined Run 1 + Run 2 fit across four PDF sets, plus the inclusion of the full Run 2 CMS semileptonic dataset. That is a legitimate extension of the authors' earlier Ref [5], not a new method, but the numerical results are new.

What it does well: the fitted masses are mutually compatible across ABMP16, CT18, MSHT20, and NNPDF40, and they fall close to the PDG value. The uncertainty breakdown into data, PDF, and scale components is clear, and the paper honestly notes the ~2-sigma tension between semileptonic and dileptonic datasets, saying it shrinks when PDFs are fitted simultaneously. Using normalized differential distributions to mitigate correlations of systematic uncertainties is sensible.

The soft spots are mostly of the 'proceedings' variety. The text quotes central values and uncertainties but does not give covariance matrices or goodness-of-fit numbers; that detail presumably lives in the companion paper. More substantive, the abstract says the data come from ATLAS/CMS unfolding to parton level, and the paper does not discuss whether the unfolding procedure imprints the Monte Carlo assumed top mass (typically 172.5 GeV) onto the published distributions. Since the best-fit values cluster near that value, an unquantified bias of a few tenths of a GeV is plausible and would sit alongside the quoted data uncertainty of 0.2-0.3 GeV. The stress-test note calls for a closure test with pseudo-data at different input masses; I think that is a fair request, though it may be beyond what a proceedings can contain. Also, the chi2 minimum is determined by parabolic interpolation through only three points (170, 172.5, 175 GeV). The authors state the minima are parabolic, so this is not a red flag, but it is coarse.

Overall: this is a plausible, incremental result. It does not break new methodological ground, but it is a useful cross-check of the top mass with current PDFs and Run 2 data. The central claim is not undermined by anything I see here; the main worry is the unquantified unfolding mass dependence.

If this arrived as a full paper, I would send it to peer review, with the request that the authors either demonstrate the unfolding is mass-independent or quantify that systematic. As a proceedings, it is acceptable, but I would not cite it as a standalone analysis without the companion paper.

Referee Report

4 major / 4 minor

Summary. This proceedings paper reports NNLO fits of the top-quark pole mass using total, single-differential, and double-differential t-tbar cross-section data from ATLAS and CMS at Run 1 and Run 2. The theoretical predictions are computed with the MATRIX code at NNLO and interfaced to PineAPPL, and fits are performed with four PDF+alpha_s sets: ABMP16, CT18, MSHT20, and NNPDF40. The best-fit pole masses cluster between 171.5 and 172.2 GeV, with data uncertainties around 0.2-0.3 GeV and PDF and scale uncertainties of similar size, and are compatible with the PDG 2024 value. The paper also reports a mild tension between semileptonic and dileptonic datasets. The text is short and explicitly refers to Ref. [5] for methodological details.

Significance. If the results hold, this is a valuable independent NNLO extraction of the top-quark pole mass with competitive precision, and the use of multiple modern PDF sets provides a useful cross-check. The paper also highlights which Run 2 differential datasets carry the most constraining power and quantifies the current data-versus-theory uncertainty budget. A strength is that the calculation is based on established NNLO QCD predictions and fast interpolation methods, and the claimed compatibility with the PDG value gives a nontrivial consistency check. However, the proceedings format omits several pieces of information needed to verify the central numerical claims, and one unquantified systematic—the mass dependence of the experimental unfolding—could affect the extracted mass at the level of the quoted uncertainties.

major comments (4)

[Abstract and main text] The unfolded parton-level double-differential data are treated as mass-independent external inputs, but the abstract states that they are obtained 'from unfolding of their experimental data to the parton level.' If the unfolding corrections, migration matrices, or acceptance/efficiency corrections depend on the top-quark mass assumed in the Monte Carlo generators, a residual mass dependence is imprinted on the published distributions and can bias the extracted m_t^pole. The reported best-fit values (171.5-172.2 GeV) lie close to the commonly assumed generator mass of 172.5 GeV, and the quoted data uncertainty of 0.2-0.3 GeV is comparable to the size of a plausible bias. The manuscript does not mention or test this effect. The authors should either provide a closure test in which pseudo-data generated at, e.g., m_t=170 and 175 GeV are unfolded with the nominal response and shown to reproduce the input masses, or quantify the mass dependence of the unfolding corrections and propagate it into the fit.
[Main text, paragraph on chi2 fits] The text states that 'the chi2's close to their minima show a parabolic shape' and that the best-fit mass is obtained by fitting a parabola through only three points, m_t = 170, 172.5, and 175 GeV. With only three points, parabolicity cannot be validated, and the quoted uncertainty from the parabolic interpolation is not assessed. The authors should show chi2 values at additional mass points (or a residual analysis) to justify the parabolic approximation, and should quantify the interpolation error relative to the quoted 0.2-0.3 GeV uncertainty.
[Main text, uncertainty summary and Fig. 2] The manuscript reports best-fit values and uncertainty decompositions (data, PDF, scale) but does not provide any goodness-of-fit information, such as chi2/ndof values, or the covariance matrices used in the global combination. Consequently, the claims that different PDF sets are 'compatible within uncertainties' and that semileptonic and dileptonic datasets are 'compatible within 2 sigma' cannot be checked from the presented material. At minimum, the authors should report the chi2 minimum per fit, the number of data points, and a quantitative definition of the tension (e.g., covariance-aware pulls between dataset groups).
[Main text, scale uncertainty procedure] The scale uncertainties are said to be evaluated by building a separate chi2 for each of the seven-point scale variations around HT/4 and 'accounting for the spread in the fitted m_t values.' The reported asymmetric total uncertainties in the right panel of Fig. 2 (e.g., NNPDF40: +0.19/-0.49 GeV) are not explained in terms of how the spread is combined with the data and PDF uncertainties. The authors should state whether the scale uncertainty is an envelope, a quadrature sum, or a profile, and how asymmetric errors are constructed.

minor comments (4)

[Main text] There is a typo: 'both runs simulteneously' should be 'both runs simultaneously.'
[Main text] The phrase 'the most stringent constraints are played by the dataset' should be reworded to 'the most stringent constraints are provided by the dataset.'
[Fig. 2] The experimental references appear only inside the figure captions; listing the datasets with their references, kinematic ranges, and luminosities in a small table would make the input to the global fit easier to follow.
[Main text] The sentence 'In the near future, data uncertainty reduction will push for theoretical computations beyond NNLO' is vague; consider specifying which NNLL or aN3LO corrections are expected to be most relevant for the double-differential observables used here.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: m_t^pole is extracted from independent NNLO predictions and external data, with no fitted parameter renamed as a prediction.

full rationale

The paper's derivation chain is a standard parameter extraction: external parton-level cross-section data from ATLAS and CMS are compared with NNLO theoretical predictions computed with the MATRIX code interfaced to PineAPPL, and a chi^2 fit is performed with m_t^pole as the free parameter sampled at 170, 172.5, and 175 GeV. The extracted mass is not an input to the predictions that would define the result by construction; the NNLO cross sections are independent calculations. The PDF sets used are external constraints, and the authors' own simultaneous PDF+m_t fit (Ref. [8]) is cited only as a cross-check that reduces tensions, not as the basis for the main quoted values. The only plausible concern, namely that the experimental unfolding may inherit a mass assumption from Monte Carlo generators, is a possible systematic effect in the input data rather than a logically circular step, and the paper does not provide any equation or construction showing that the fit result is equal to the assumed unfolding mass. The results are also benchmarked against the PDG 2024 value, providing an external check. Self-citations for methodological details (Ref. [5]) are normal and do not carry the load of the derivation. Therefore no significant circularity is found.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

No new particles, forces, or entities are introduced; the paper is a measurement of a Standard Model parameter using existing theory and data. The free parameters are limited to the fitted top mass and the central scale choice. The main unstated burden is the assumption that the experimental unfolding does not reintroduce the top-quark mass used in Monte Carlo generators.

free parameters (2)

top-quark pole mass m_t^pole = 171.5 to 172.2 GeV depending on PDF set
The central fitted parameter of the chi-square minimization; the whole paper is an extraction of this number.
central renormalization/factorization scale HT/4 = HT/4, with seven-point variation by factors 0.5 and 2
The central scale is chosen by hand and the quoted scale uncertainty depends on this choice and on the 7-point variation pattern.

assumptions (4)

domain assumption NNLO QCD factorization provides accurate predictions for top-pair production in the considered kinematic ranges.
The analysis uses fixed-order NNLO predictions from MATRIX and does not include NNLL resummation or aN3LO corrections, which the paper itself flags as future work.
domain assumption The 7-point variation of renormalization and factorization scales around HT/4 estimates the missing higher-order uncertainty.
The scale uncertainty on m_t^pole is derived from the spread of the fit minimum over these scale combinations; this is a standard but heuristic prescription.
domain assumption Normalized differential cross sections from ATLAS and CMS can be compared to parton-level NNLO predictions without significant non-perturbative corrections.
The paper uses normalized parton-level differential data and states that normalization reduces the effect of unknown correlations, but it does not validate the absence of residual hadronization or underlying-event effects.
domain assumption The unfolded data are independent of the assumed top-quark mass used in the experimental unfolding procedure.
The abstract and text describe data unfolded to parton level, but the mass dependence of the unfolding corrections is not discussed or tested.

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Cite this review

Pith. "Pith review of NNLO fits of top-quark mass using total, single-differential and double-differential $t\bar{t}+X$ cross-section data." pith.science (2026). https://pith.science/paper/T4HVGWVN

@misc{pith2026241214348,
  author       = {Pith},
  title        = {Pith review of: NNLO fits of top-quark mass using total, single-differential and double-differential $t\bart+X$ cross-section data},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/T4HVGWVN}},
  note         = {Machine review of arXiv:2412.14348}
}

abstract

We describe the fits of the top-quark mass value at NNLO using as input the double-differential distributions in rapidity and invariant mass of $t\bar{t}$ pairs obtained by the ATLAS and CMS collaborations from unfolding of their experimental data to the parton level, compared to NNLO theory predictions. We consider different state-of-the-art PDF sets, finding results of the fits compatible among each other within uncertainties. On the other hand, we observe some tension among the fits to different datasets.

Figures

Figures reproduced from arXiv: 2412.14348 by the authors.

**Figure 1.** 𝜒 2 for different 𝑚 pole 𝑡 values, as well as the best-fit parabolic interpolation to the 𝜒 2 values for 𝑚 pole 𝑡 = 170, 172.5, 175 GeV, for different (PDFs+𝛼𝑠 (𝑀𝑍)) sets (left panel). 𝜒 2 for different (𝜇𝑟 , 𝜇 𝑓 ) combinations in the case of the ABMP16 set (right panel). 164 166 168 170 172 174 m pole t [GeV] PDG2024 m pole t = 172.4 ± 0.7 GeV NNPDF40 MSHT20 CT18 ABMP16 ATLAS+CMS Run1 differential NNPDF40 MSHT20 CT… view at source ↗

**Figure 2.** 𝑚 pole 𝑡 values extracted using datasets on normalized (multi-)differential cross sections obtained at the LHC in Run I (left panel) and Run 2 (central panel), as well as datasets from a global analysis of Run 1 + Run 2 differential and total inclusive cross sections (right panel), compared to the PDG 2024 𝑚 pole 𝑡 value. Our best-fit 𝑚 pole 𝑡 values are reported together with uncertainties for each considered PDF +… view at source ↗

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Reference graph

Works this paper leans on

11 extracted references · 9 linked inside Pith

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Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.

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