Precision determination of $\alpha_\text{s}$ from Dijet Cross Sections in the Multi-TeV Range

Jo\~ao Pires

REVIEW 3 major objections 5 minor 12 references

Precision determination of $\alpha_\text{s}$ from Dijet Cross Sections in the Multi-TeV Range

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Dijet fits yield the strong coupling as 0.1178 ± 0.0022.

desk verdict A plausible NNLO dijet αs extraction, but this proceedings text mostly points at the companion paper and the PDF/αs coverage argument is the one weak plank. read the letter →

arxiv 2507.01670 v1 pith:7TZM4BXW submitted 2025-07-02 hep-ph hep-ex

João Pires This is my paper

classification hep-phhep-ex

keywords strongcouplingconstantalpha_sdijetproductionNNLOQCDrenormalizationgrouprunningLHCHERAPDFevolution

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 proceedings contribution reports a determination of the strong coupling constant $\alpha_\text{s}$ from the production of two jets (dijets) in proton collisions. Using next-to-next-to-leading-order (NNLO) QCD predictions and a combined fit to five LHC dijet datasets, the author extracts $\alpha_\text{s}(m_Z)=0.1178 \pm 0.0022$, with the uncertainty split into fit/PDF ($\pm 0.0014$), starting-scale ($\pm 0.0001$), and renormalization/factorization-scale ($\pm 0.0017$) parts. Adding HERA dijet data lets the same fit probe $\alpha_\text{s}$ from about 7 GeV up to 7 TeV, more than three orders of magnitude in energy. The running agrees with the QCD renormalization-group prediction, and the paper reports this as the first $\alpha_\text{s}$ determination reaching 7 TeV. The result matters because $\alpha_\text{s}$ is the least precisely known fundamental coupling, and this is an independent collider determination across a previously untested energy range.

What carries the argument

The machinery is the scale-dependent NNLO dijet cross section, built from DGLAP-evolved parton distributions multiplied by partonic cross sections through the QCD factorization theorem. The author takes the initial PDF shapes from a modern global PDF set at $\mu_0 = 90$ GeV and evolves them at three-loop order with $\alpha_\text{s}(m_Z)$ as a free parameter, so $\alpha_\text{s}$ enters both the PDF evolution and the hard-scattering matrix elements. The renormalization and factorization scales are both set to the dijet invariant mass $\mu_R = \mu_F = m_{jj}$, which is what makes each kinematic bin probe $\alpha_\text{s}$ at a different energy. To make the fit feasible, the NNLO calculation is precomputed on interpolation grids so predictions can be regenerated quickly for arbitrary PDF sets, scales, and $\alpha_\text{s}$ values; the result is then compared with data using covariance matrices for experimental, non-perturbative, NNLO-statistical, and PDF uncertainties.

What would settle it

Refit the same 367 dijet data points with the initial PDF shapes refitted at each $\alpha_\text{s}$ value, for example through a simultaneous global PDF and $\alpha_\text{s}$ fit. If the extracted $\alpha_\text{s}(m_Z)$ moves by more than about $\pm 0.0022$ relative to the fixed-PDF result, the paper's claim that the residual bias is covered by the $\mu_0$ variation is falsified.

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Extended reading notes

Core claim

On its own terms, the paper establishes that inclusive dijet cross sections, computed at full NNLO accuracy and compared with LHC data through fast interpolation grids, can determine the strong coupling at the Z mass with a total uncertainty of $\pm 0.0022$. The central value is $\alpha_\text{s}(m_Z)=0.1178$, obtained from a combined fit of 367 dijet measurements out of 493 after restricting the phase space to $y^* < 2.0$ and $y_b < 1.0$; the fit has $\chi^2/\text{ndof} = 0.92$. Individual datasets give values consistent with the world average but with larger uncertainties, and the combination improves the precision. The same NNLO predictions, extended to HERA dijet measurements, reproduce the renormalization-group running of $\alpha_\text{s}$ from about 7 GeV to 7 TeV, which the paper describes as an unprecedented test of QCD's scale dependence.

Load-bearing premise

The load-bearing assumption is that freezing the initial PDF shapes at 90 GeV and evolving them with $\alpha_\text{s}$ free leaves a residual bias no larger than the $\mu_0$ variation covers; if that estimate is wrong, the true uncertainty on $\alpha_\text{s}$ exceeds the quoted $\pm 0.0022$.

Editorial extensions

If this is right

The extracted value $\alpha_\text{s}(m_Z)=0.1178 \pm 0.0022$ is consistent with the world average, so hadron-collider dijet production can stand as an independent determination of the strong coupling.
The fit reaches dijet invariant masses up to 7 TeV, giving the first $\alpha_\text{s}$ determination at that scale from LHC data.
The comparison with HERA dijet data tests the running of $\alpha_\text{s}$ from about 7 GeV to 7 TeV, confirming the renormalization-group prediction over more than three orders of magnitude.
The phase-space restriction to $y^* < 2.0$ and $y_b < 1.0$ is what makes the fit stable, indicating that forward and boosted dijet regions are less suitable for this extraction under the current PDF uncertainties.

Reading between the lines

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

A simultaneous global fit of PDFs and $\alpha_\text{s}$ would provide a direct check of whether the fixed-PDF assumption biases the central value; the $\mu_0$-variation argument in the paper is indirect.
The same interpolation-grid pipeline could be applied to other jet observables, such as inclusive jet spectra or three-jet production, to provide independent cross-checks of $\alpha_\text{s}$ in overlapping kinematic regions.
Since correlations among the five LHC datasets are not provided and are treated as independent, a future analysis with full inter-dataset correlations could change the quoted uncertainty.

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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

What you should know: this is a proceedings summary, not the full analysis. The headline number, αs(mZ)=0.1178±0.0022, comes from a five-LHC-dataset NNLO dijet fit plus a HERA extension, and the result looks plausible. But the evidence in this text for the central precision claim is thin: the methodology, covariance construction, and validation all live in Ahmadova et al. (arXiv:2412.21165). I'd treat this as an extended abstract for the companion paper, not as an independent result.

What it does well: the combination of ATLAS and CMS datasets at 7, 8, and 13 TeV with NNLOJET and APPLfast is a sensible extension of an established program. The running test from roughly 7 GeV to 7 TeV, using HERA plus LHC dijet data, is a real and useful benchmark. The quoted uncertainties are internally consistent (χ²/ndof=0.92), and the text does not oversell: it explicitly acknowledges the kinematic restriction and the lack of cross-dataset correlations.

The soft spot is the PDF/αs decoupling argument in §2. The text claims that varying αs in the PDF set has an impact comparable to varying the starting scale μ0 and is "effectively covered" by the μ0 uncertainty. But Fig. 1 shows PDF ratios at μ0=90 GeV, not shifts in the fitted αs, and μ0 variation and initial-PDF αs mismatch are different perturbations. No fit-level evidence is supplied. If the true bias is closer to the fit+PDF uncertainty (±0.0014) than to the μ0 component (±0.0001), the central value could be systematically off. That is a real gap, though it might be closed in the companion paper. Two additional, acknowledged weaknesses: the post hoc cut on y* and yb to reduce tensions, and treating cross-dataset correlations as independent. Both are common in precision QCD and not fatal, but they do temper confidence.

Who this is for: someone wanting a quick status update on multi-TeV dijet αs determinations. The full audit trail is in [1]. The proceedings text alone is not enough to verify the precision claim, but the underlying analysis clearly matters and deserves a serious referee. I'd engage with the companion paper rather than this summary, and I'd expect the referee to ask for the fit-level evidence on the PDF/αs decoupling.

Recommendation: send to peer review, yes. The underlying analysis is important enough to warrant refereeing, and the gap I named is exactly what referees should probe.

Referee Report

3 major / 5 minor

Summary. This proceedings paper reports a determination of the strong coupling constant from NNLO QCD fits to inclusive dijet cross-section measurements at the LHC. Using ATLAS and CMS data at 7, 8, and 13 TeV, the author obtains alpha_s(mZ) = 0.1178 ± 0.0022, with quoted uncertainties separated into fit/PDF (±0.0014), mu0 (±0.0001), and scale (±0.0017) components. The analysis fixes the initial PDF shape from PDF4LHC21 at mu0 = 90 GeV, treating alpha_s(mZ) as a free parameter in the DGLAP evolution, and uses NNLOJET with APPLfast interpolation grids. By including HERA dijet data, the paper claims a test of the running of alpha_s from roughly 7 GeV to 7 TeV, with results stated to be in agreement with the renormalization group equation. The full methodology and numerical tables are deferred to a companion paper (ref. [1]).

Significance. If the central result is robust, this is a valuable high-scale determination of alpha_s from dijet production, with kinematic reach up to 7 TeV and a combined HERA+LHC test of the running coupling over three orders of magnitude. The use of NNLO matrix elements, a full covariance treatment of experimental and PDF uncertainties within the fit, and the reported chi2/ndof = 0.92 are genuine strengths. However, the precision claim rests on several assumptions that are stated but not demonstrated in this manuscript, most importantly the decoupling of the PDF-initial-shape dependence on alpha_s and the treatment of cross-dataset correlations. Because the paper is a proceedings summary, several load-bearing checks that would be routine in a full-length analysis are only asserted verbally.

major comments (3)

[§2, 'A potential concern...' and Fig. 1] The claim that residual bias from not refitting the PDFs at each alpha_s value is 'effectively covered' by the mu0 variation is not established. Fig. 1 shows gluon and Sigma PDFs at mu0 = 90 GeV for different alpha_s assumptions; it does not show the resulting shift in the fitted alpha_s, and no numerical result is given. Varying mu0 and using a PDF set fitted at a different alpha_s are different perturbations: the former changes the evolution starting point, while the latter changes the input PDFs themselves. Coverage of one does not logically imply coverage of the other. This is load-bearing because the central value alpha_s(mZ) = 0.1178 and the quoted total uncertainty ±0.0022 depend on this decoupling assumption. I recommend a fit-level test: repeat the fit using PDF sets generated or fitted at alpha_s(mZ) = 0.116, 0.118, and 0.120 (or use the alpha_s variants available in PDF4LHC21) and report the shift in the fitted alpha_s. Without such a test, the reader cannot judge whether the bias is at the level of the ±0.0001 mu0 component or comparable to the ±0.0014 fit+PDF uncertainty.
[§3, 'To minimize sensitivity...'] The kinematic restriction to y* < 2.0 and yb < 1.0 is introduced after noting 'moderate tensions observed in some phase space regions.' This is a post hoc selection that excludes 126 of 493 measurements, and the paper does not quantify how the tensions or the selection affect the extracted alpha_s. The central precision claim requires evidence that the result is stable under this restriction: the fit should be shown with and without the cut, and the tension before the cut should be quantified. If the central value shifts by more than the quoted uncertainty when the cut is removed, or if the tension signals a theory or experimental issue, the quoted total uncertainty would be underestimated.
[§2, 'Covariance matrices'] The statement that 'correlations between uncertainties across different datasets are not provided and thus treated as independent' is a significant limitation for the combined fit. The five LHC datasets share common systematic sources (notably jet energy scale and luminosity) and are taken at the same experiments at different center-of-mass energies. Treating them as independent can bias the combined alpha_s and reduce the quoted uncertainty. The paper should either estimate the possible impact of cross-dataset correlations (for example, by conservatively adding a correlated component or by showing the sensitivity to an assumed correlation model) or clearly state that the quoted precision is conditional on the independence assumption. As written, the 'combination' claim in the abstract is not fully supported.

minor comments (5)

[Fig. 1 caption and §2] Fig. 1 is described as showing PDFs from MSHT20nnlo, while the methodology text states that PDFs are taken from PDF4LHC21. Please clarify which PDF set is used for the decoupling check and whether the check uses the same set as the nominal fit.
[Eq. (1)] The chi^2 definition uses log ratios of measured to theory cross sections, but the orientation of the ratio and the treatment of bins where uncertainties approach zero are not defined. Please state precisely how the log is applied and how the relative covariance matrix is converted to this logarithmic form.
[§3, Fig. 2] The lower panel of Fig. 2 is described as showing alpha_s(mZ) 'alongside the world average,' but the text mostly discusses the running of alpha_s. Please clarify what is plotted in each panel and how the hatched region is derived from the combined fit.
[Abstract and §3] The abstract claims the 'first determination of alpha_s up to 7 TeV.' Please cite the previous highest-scale dijet determinations (e.g., CMS and ATLAS 13 TeV extractions) so the novelty claim is verifiable. As written, the reader cannot assess what 'first' means relative to the existing literature.
[Throughout] There are several typographical issues ('approriate', 'programatic', 'T eV' in the title) and the author name/affiliation line appears garbled in the source. These should be corrected in the final version. Also, 'individidual' appears in §3.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: alpha_s is extracted from external dijet data via an NNLO fit; PDF/alpha_s interplay is a robustness check, not a self-referential input.

full rationale

The derivation chain is: measured dijet cross sections from ATLAS/CMS/HERA feed a chi2 minimization against NNLOJET predictions with alpha_s(mZ) as a free parameter, yielding alpha_s(mZ)=0.1178 +/- 0.0022. The fitted quantity is an external measurement result, not defined in terms of itself. The PDF4LHC21 input does carry an assumed alpha_s, and the paper discusses this explicitly as a 'potential concern'; its Fig. 1 check is an empirical coverage argument. Whether that coverage is convincingly demonstrated is a statistical robustness issue, not a circular reduction: the paper never equates the predicted alpha_s with the alpha_s assumed in the PDF fit, nor does it relabel a fitted parameter as an independent prediction. The companion-paper citation [1] supplies methodological detail, but the central result is supported by the actual fit to data, not by that citation alone. The running test compares alpha_s values extracted from individual mjj ranges against the renormalization group equation; because those per-bin values are not forced by construction to lie on the RGE curve, this is a genuine consistency check rather than a tautology. No equation or definition in the paper makes the claimed output equal to an input, and no known empirical result is merely renamed. Hence no significant circularity.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The central claim rests on αs(mZ) as a fitted parameter and on standard perturbative QCD machinery. No new particles, forces, dimensions, or other invented entities are introduced. The main non-standard assumption is the treatment of PDFs as fixed-shape while varying αs, plus the explicit neglect of inter-dataset correlations.

free parameters (2)

αs(mZ) = 0.1178 ± 0.0022 (combined LHC fit; components ±0.0014 fit+PDF, ±0.0001 µ0, ±0.0017 scale)
Central fitted parameter of the χ2 minimization against dijet cross sections. It is a physical constant measured from data, not an ad hoc input, but it is still a number extracted from the fit.
αs per mjj bin (running curve) = Not tabulated in the talk; shown as the running curve in Fig. 2
Values obtained by fitting individual invariant-mass ranges to test the renormalization group running. Each point is a separate fit to data and therefore counts as an additional fitted value.

assumptions (5)

domain assumption QCD factorization expresses the dijet cross section as a convolution of PDFs and partonic cross sections.
Equation in §2 defines dσ; the whole extraction relies on this factorization and on the perturbative expansion being valid at NNLO.
domain assumption Three-loop DGLAP evolution (Apfel++) correctly propagates αs and PDFs from µ0=90 GeV to the dijet invariant mass.
Invoked in §2 via refs [9,10]; the DGLAP kernels are not re-derived in this paper.
domain assumption PDF4LHC21 PDFs at µ0=90 GeV can be used with fixed shape while αs(mZ) is varied in the evolution.
The paper argues the residual bias from not refitting PDFs is covered by the µ0 variation (Fig. 1). This is load-bearing for the uncertainty budget.
domain assumption Correlations between systematic uncertainties across different LHC and HERA datasets are negligible.
Stated in §2: 'correlations between uncertainties across different datasets are not provided and thus treated as independent.' This directly affects the combined fit uncertainty.
domain assumption NNLOJET predictions and APPLfast interpolation grids are correct at NNLO including subleading colour contributions.
Used for all theory predictions; only references [7] and [11] are given, with no validation in this talk.

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Cite this review

Pith. "Pith review of Precision determination of $\alpha_\text{s}$ from Dijet Cross Sections in the Multi-TeV Range." pith.science (2026). https://pith.science/paper/7TZM4BXW

@misc{pith2026250701670,
  author       = {Pith},
  title        = {Pith review of: Precision determination of $\alpha_\texts$ from Dijet Cross Sections in the Multi-TeV Range},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7TZM4BXW}},
  note         = {Machine review of arXiv:2507.01670}
}

abstract

In this talk we present a determination of the strong coupling constant $\alpha_\text{s}$ and its energy-scale dependence based on a next-to-next-to-leading order (NNLO) QCD analysis of dijet production. Using the invariant mass of the dijet system to probe $\alpha_\text{s}$ at different scales, we extract a value of $\alpha_\text{s}(m_\text{Z})=0.1178 \pm 0.0022$ from LHC dijet data. The combination of various LHC datasets significantly extends the precision and scale reach of the analysis, enabling the first determination of $\alpha_\text{s}$ up to 7 TeV. By incorporating dijet cross sections from HERA, we further probe $\alpha_\text{s}$ at smaller scales, covering a kinematic range of more than three orders of magnitude. Our results are in excellent agreement with QCD predictions based on the renormalization group equation, providing a stringent test of the running of the strong coupling across a wide energy range.

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Reference graph

Works this paper leans on

12 extracted references · 10 canonical work pages

[1]

Precise Determination of the Strong Coupling Constant from Dijet Cross Sections up to the Multi-TeV Range

F. Ahmadova, D. Britzger, X. Chen et. al arXiv:2412.21165

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [1]

Precise Determination of the Strong Coupling Constant from Dijet Cross Sections up to the Multi-TeV Range

F. Ahmadova, D. Britzger, X. Chen et. al arXiv:2412.21165

work page Pith review arXiv

[2] [2]

Andreev et al, (H1), Eur

V. Andreev et al, (H1), Eur. Phys. J. C 75, 65 (2015)

work page 2015

[3] [3]

James and M

F. James and M. Roos, Comput. Phys. Commun. 10, 343 (1975) R. Brun and F. Rademakers, Nucl. Instrum. Meth. A389, 81 (1997)

work page 1975

[4] [4]

(ATLAS), JHEP 2014, 05 (059) (ATLAS), JHEP 2018, 05 (195)

work page 2014

[5] [5]

(CMS) Phys. Rev. D 87, 112002 (2013) (CMS) Eur. Phys. J. C 77, 11,746 (2017) (CMS) Eur. Phys. J. C 865, 1,72 (2025)

work page 2013

[6] [6]

Buckley et al, Eur

A. Buckley et al, Eur. Phys. J. C 75, 132 (2015)

work page 2015

[7] [7]

Huss et al, arXiv:2503.22804

A. Huss et al, arXiv:2503.22804

arXiv

[8] [8]

R. D. Ball et al, (PDF4LHC Working Group) J. Phys. G 49, 080501 (2022)

work page 2022