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arxiv: 1907.01435 · v1 · pith:VBCWEDZOnew · submitted 2019-07-02 · ✦ hep-ph · hep-ex

α_s(2019): Precision measurements of the QCD coupling

David d'Enterria , Stefan Kluth (eds.) , S. Alekhin , P. A. Baikov , A. Banfi , F. Barreiro , A. Bazavov , S. Bethke
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J. Bl\"umlein D. Boito N. Brambilla D. Britzger S. J. Brodsky S. Camarda K. G. Chetyrkin D. d'Enterria M. Dalla Brida X. Garcia i Tormo M. Golterman R. Horsley J. Huston M. Jamin A. Kardos A. Keshavarzi S. Kluth J. K\"uhn K. Maltman R. Miravitllas S.-O. Moch P. F. Monni D. Nomura T. Onogi R. P\'erez-Ramos S. Peris P. Petreczky J. Pires A. Poldaru K. Rabbertz F. Ringer S. Sint R. Sommer G. Somogyi J. Soto Z. Sz\H{o}r H. Takaura T. Teubner Z. Tr\'ocs\'anyi Z. Tulip\'ant A. Vairo A. Verbytskyi J.H. Weber X. Weichen G. Zanderighi
This is my paper

Pith reviewed 2026-05-25 11:05 UTC · model grok-4.3

classification ✦ hep-ph hep-ex
keywords strong coupling constantalpha_sQCDlattice QCDtau decaysdeep inelastic scatteringevent shapesworld average
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The pith

The strong coupling α_s is extracted from six categories of measurements and combined into a world average at the Z boson mass.

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

This paper collects summaries of all contributions from a 2019 workshop on precision measurements of the QCD coupling α_s. It reviews the theoretical and experimental uncertainties for determinations in lattice QCD, hadronic tau decays, deep-inelastic scattering with parton distributions, event shapes and jets in electron-positron collisions, hadronic decays of W and Z bosons, and hadronic final states in proton-proton collisions. The document discusses novel extraction approaches and the specific method used to combine the results from these categories. A sympathetic reader would care because α_s sets the strength of the strong interaction and enters predictions for many high-energy processes.

Core claim

The document collects written summaries of the workshop contributions and reviews the latest status of theoretical and experimental uncertainties for α_s extractions in the six listed categories. It also covers future perspectives and the combination method applied to arrive at a world-average value of the coupling at the Z mass pole.

What carries the argument

The combination method that produces the world-average value of α_s(M_Z) from the separate extractions in each category.

If this is right

  • Improved precision in any one category directly tightens the uncertainty on the combined world average.
  • Agreement among the six categories supports the internal consistency of QCD calculations used in each extraction.
  • The reviewed uncertainties set quantitative targets for future theoretical work on higher-order corrections and non-perturbative effects.
  • The combination procedure provides a standard reference value that can be updated as new results become available.

Where Pith is reading between the lines

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

  • The world average can serve as a fixed input when testing whether extensions of the Standard Model alter the running of the coupling at higher energies.
  • Persistent tension between one category and the others would motivate re-examination of the theoretical tools specific to that category rather than the overall framework.
  • If future data reduce the lattice-QCD uncertainty below the current level, the average will be dominated by that method and the role of the other five will shift toward cross-checks.

Load-bearing premise

The individual extractions from the six categories can be treated as sufficiently independent for a statistically meaningful combination without large unaccounted correlations or method-specific biases.

What would settle it

A new analysis that demonstrates large unaccounted correlations between the uncertainty estimates of two or more categories, or a high-precision measurement whose central value lies many standard deviations outside the combined average after all stated errors are included.

Figures

Figures reproduced from arXiv: 1907.01435 by A. Banfi, A. Bazavov, A. Kardos, A. Keshavarzi, A. Poldaru, A. Vairo, A. Verbytskyi, David d'Enterria, D. Boito, D. Britzger, D. d'Enterria, D. Nomura, F. Barreiro, F. Ringer, G. Somogyi, G. Zanderighi, H. Takaura, J. Bl\"umlein, J. Huston, J.H. Weber, J. K\"uhn, J. Pires, J. Soto, K. G. Chetyrkin, K. Maltman, K. Rabbertz, M. Dalla Brida, M. Golterman, M. Jamin, N. Brambilla, P. A. Baikov, P. F. Monni, P. Petreczky, R. Horsley, R. Miravitllas, R. P\'erez-Ramos, R. Sommer, S. Alekhin, S. Bethke, S. Camarda, S. J. Brodsky, S. Kluth, S.-O. Moch, S. Peris, S. Sint, Stefan Kluth (eds.), T. Onogi, T. Teubner, X. Garcia i Tormo, X. Weichen, Z. Sz\H{o}r, Z. Tr\'ocs\'anyi, Z. Tulip\'ant.

Figure 1
Figure 1. Figure 1: World average values of αs(mZ ) over time. 8 [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: 2016 summary of determinations of αs(mZ ). The light-shaded bands and long-dashed vertical lines indicate the pre-average values; the dark-shaded band and short-dashed line represents the new overall world average of αs(mZ ). 9 [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: summarises the history and values of pre-averages of αs(mZ ) for the different classes of measurements. Note that the change in error determinations predominantly affected the class of [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Summary of measurements of αs as a function of the energy scale Q. 11 [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 1
Figure 1. Figure 1: The plane α (3) MS(µ) for Nf = 3 against the scale µ in lattice units, where a is the lattice spacing and the blue region corresponds to the rough bound a > 0.04 fm. Note that the continuum limit is approached by extrapolations with aµ 1. The points on the left correspond to actual Monte Carlo simulations in category (III). The 2019 FLAG review. The Flavour Lattice Averaging Group (FLAG) formed a working g… view at source ↗
Figure 2
Figure 2. Figure 2: The [PITH_FULL_IMAGE:figures/full_fig_p017_2.png] view at source ↗
Figure 1
Figure 1. Figure 1: The lattice spacing dependence of R4 and R6/R8 for mh = mc. The filled symbols correspond to the lattice results of Ref. [10], while the open symbols correspond to HPQCD results from Refs. [5,7]. The solid line corresponds to polynomial fit, see text. The dashed line corresponds to simple a 2 fit. The errors for the HPQCD-14 result for R6/R8 have been obtained by propagating the errors on R6 and R8. calcul… view at source ↗
Figure 2
Figure 2. Figure 2: The running coupling in three-flavor QCD constant corresponding to Λ [PITH_FULL_IMAGE:figures/full_fig_p022_2.png] view at source ↗
Figure 1
Figure 1. Figure 1: Left: Continuum extrapolation of the lattice data for Σ( [PITH_FULL_IMAGE:figures/full_fig_p026_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Estimates for ΛL0 as a function of the parametric uncertainty α 2 . “Fit A” and “Fit B” correspond to two different fit functions for σ(u), cf. [14] for details. ‡Note that evolving towards higher energies requires to invert the step-scaling function. This poses no practical problems. 27 [PITH_FULL_IMAGE:figures/full_fig_p027_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Statistical (interior error band) and total (exterior error band) uncertainties in the [PITH_FULL_IMAGE:figures/full_fig_p028_3.png] view at source ↗
Figure 1
Figure 1. Figure 1: Left: Continuum extrapolations of the lattice SSF of ¯g [PITH_FULL_IMAGE:figures/full_fig_p032_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Left: Continuum extrapolations of the ratio [PITH_FULL_IMAGE:figures/full_fig_p033_2.png] view at source ↗
Figure 1
Figure 1. Figure 1: Results for r1ΛMS at three-loop accuracy, also showing the outcome of analyses with extended distance ranges. For reference and comparison, the band shows our previous result in Ref. [6]. This figure is taken from [9]. As one can see from the figure, the fits that use distances larger than 0.6r1 give results for r1ΛMS that are compatible with those used in our main analysis. The error bars, which come from… view at source ↗
Figure 2
Figure 2. Figure 2: Comparison of the lattice data for the static energy with perturbative expressions at [PITH_FULL_IMAGE:figures/full_fig_p040_2.png] view at source ↗
Figure 1
Figure 1. Figure 1: Consistency check of the OPE. The blue date are the lattice continuum limit and the [PITH_FULL_IMAGE:figures/full_fig_p045_1.png] view at source ↗
Figure 1
Figure 1. Figure 1: Top: Comparison of the predicted nonperturbative coupling, based on the dilaton [PITH_FULL_IMAGE:figures/full_fig_p048_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The PMC scales at LL and NLL accuracy for the thrust distribution at [PITH_FULL_IMAGE:figures/full_fig_p050_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The thrust differential distributions using the conventional (Conv.) and PMC scale [PITH_FULL_IMAGE:figures/full_fig_p051_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The extracted αs(Q2 ) in the MS scheme from the comparison of PMC predictions with ALEPH data [32] at √ s = mZ. The error bars are from the combination of the experimental and theoretical errors. The three lines are the world average evaluated from αs(mZ) = 0.1181 ± 0.0011 [31]. experimental data at single center-of-mass-energy, √ s = mZ. In this case we have used the most precise data from ALEPH [32]. We … view at source ↗
Figure 1
Figure 1. Figure 1: The value of αs preferred by various DIS data samples employed in the ABMP16 analysis as a function of the year of publication of the data. Three variants of the fit with different treatments of the HT terms are presented: HT set to 0 or to the one obtained in the combined fit (circles and squares, respectively) or fitted to one particular data set (triangles). The αs bands obtained using combination of th… view at source ↗
Figure 1
Figure 1. Figure 1: An important aspect of the small-x DIS data interpretation is to account for the heavy-quark contribution. In particular final-state configurations including the c-quark are responsible for an essential part of the NC inclusive cross section in the region of HERA kinematics. Therefore, an accurate treatment of this term is a necessary ingredient of the related phenomenology [10]. This applies also to the e… view at source ↗
Figure 2
Figure 2. Figure 2: The MS value of the t-quark mass mt(mt) obtained in the variants of present analysis with the value of α (nf =5) s (mZ) fixed in comparison with the 1σ bands for mt(mt) and α (nf =5) s (mZ) obtained in our nominal fit (left-tilted and right-tilted hatch, respectively). Plot from Ref. [1]. The results of a version of the fit performed with the NLO QCD accuracy [6] can be employed for an estimate of the theo… view at source ↗
Figure 1
Figure 1. Figure 1: Values of αs(mZ ) obtained from fits to H1 jet data with similar values of µR (full circles) in comparison to values from other ex￾periments and processes at least in NNLO. The values of αs(µR) (upper panel) are related to αs(mZ ) by the solution of the QCD renormalisa￾tion group equation as it also enters the predic￾tions. The inner error bars indicate the exper￾imental uncertainties and the outer error b… view at source ↗
Figure 1
Figure 1. Figure 1: The MMHT NNLO gluon distribution plotted for several values of [PITH_FULL_IMAGE:figures/full_fig_p071_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The Lagrange Multiplier study of the sensitivity of the data sets included in CT18 to the [PITH_FULL_IMAGE:figures/full_fig_p071_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The value of αs(mZ ) and its uncertainty is shown for several PDF fits, and compared with the central value and uncertainty from the world average. From Ref. [5]. To summarize: global PDF fits have a sensitivity to the value of αs(mZ ), somewhat clouded by the remaining sensitivity to the gluon distribution. The deep-inelastic data from HERA will continue to be the most important data set in modern global … view at source ↗
Figure 1
Figure 1. Figure 1: Fixed-order (left) and resummed (right) predictions for EEC. [PITH_FULL_IMAGE:figures/full_fig_p075_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Selected results of fits to data at NNLO+NNLL and NLO+NNLL accuracy. [PITH_FULL_IMAGE:figures/full_fig_p077_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The soft-drop thrust distribution at LO, NLO and NNLO accuracy with [PITH_FULL_IMAGE:figures/full_fig_p079_3.png] view at source ↗
Figure 1
Figure 1. Figure 1: Selected data and predictions with different Monte Carlo setups for EEC (top) and jet [PITH_FULL_IMAGE:figures/full_fig_p084_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Selected data and fit results in the EEC (top) and jet rates (bottom) analyses. [PITH_FULL_IMAGE:figures/full_fig_p085_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Dependence of fit results in the EEC (top) and jet rates (bottom) analyses on the [PITH_FULL_IMAGE:figures/full_fig_p086_3.png] view at source ↗
Figure 1
Figure 1. Figure 1: Left: R-ratio data from Ref. [3], as a function of s, the hadronic invariant squared mass. Right: A blow-up of the region 2 ≤ s ≤ 6 GeV2 . 88 [PITH_FULL_IMAGE:figures/full_fig_p088_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Comparison of the data for I (w) (s0) with the fits on the interval s min 0 = 3.25 to 4 GeV2 , for w = w0 (upper left panel), w = w2 (upper right panel), w = w3 (lower left panel), and w = w4 (lower right panel). Solid black curves indicate FOPT fits, dashed curves CIPT. The fit window is indicated by the dashed vertical lines. leading to two different values for αs. For a more detailed discussion, we refe… view at source ↗
Figure 3
Figure 3. Figure 3: Comparison of FESR fits extracting αs from hadronic τ -decay data (left panels) vs. e +e − → hadrons(γ) (right panels). Top panels show fits with weight w0, bottom panels show fits with weight w2. Because of the comparison between τ -based moments and e +e −-based moments, we show those obtained from the vector channel in the plots on the left. These values are both consistent, within errors, with the worl… view at source ↗
Figure 1
Figure 1. Figure 1: Theoretical energy evolution of the jet charged-hadron multiplicity (left) and FF peak [PITH_FULL_IMAGE:figures/full_fig_p097_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: “Hump-backed plateau” charged-hadron distributions in jets as a function of [PITH_FULL_IMAGE:figures/full_fig_p097_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Energy evolution of the charged-hadron multiplicity (left) and of the FF peak position [PITH_FULL_IMAGE:figures/full_fig_p098_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Summary of αs determinations using different methods. The top points show N2,3LO extractions currently included in the PDG [1], the bottom ones shown those obtained with other approaches at lower degree of accuracy today [13], including the result of our work. The dashed line and shaded (orange) band indicate the current PDG world-average and its uncertainty. [3] A. Abada et al. [FCC Collaboration], CERN-A… view at source ↗
Figure 1
Figure 1. Figure 1: Relative systematic uncertainty for the inclusive jet cross-section as a function of the [PITH_FULL_IMAGE:figures/full_fig_p100_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Left: Double-differential inclusive jet cross sections as function of jet [PITH_FULL_IMAGE:figures/full_fig_p101_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Ratio of data over theory prediction (closed circles) using the CT10 NLO PDF set, with [PITH_FULL_IMAGE:figures/full_fig_p101_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Left: Double-differential inclusive jet cross sections [PITH_FULL_IMAGE:figures/full_fig_p102_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: CMS data [4] (black data points) and NNLO prediction (in red) normalised to the NLO [PITH_FULL_IMAGE:figures/full_fig_p103_5.png] view at source ↗
Figure 1
Figure 1. Figure 1: The soft drop groomed jet mass distribution at NLL (left) and NNLL (right) compared [PITH_FULL_IMAGE:figures/full_fig_p107_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Scale dependence of αs values obtained from TEEC (left) and ATEEC (right) measure￾ments [5]. From a global fit to the complete data sample the following values for the strong coupling constant at the Z boson mass are obtained: α TEEC s (mZ) = 0.1162 ± 0.0011 (exp) +0.0076 −0.0061 (scale) ± 0.0018 (PDF) ± 0.0003 (NP) α ATEEC s (mZ) = 0.1196 ± 0.0013 (exp) +0.0061 −0.0013 (scale) ± 0.0017 (PDF) ± 0.0004 (NP)… view at source ↗
Figure 3
Figure 3. Figure 3: Left: Azimuthal decorrelations as a function of [PITH_FULL_IMAGE:figures/full_fig_p112_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Left: Dependence of αs on the scale from [9]. Right: Summary of αs(mZ) values obtained at colliders. In blue, those based on NNLO calculations. In green is the PDG average value [11]. Copyright 2018 CERN for the benefit of the ATLAS Collaboration. Reproduction of this article or parts of it is allowed as specified in the CC-BY-4.0 license. References [1] ATLAS Collaboration, JINST 03 (2008) S08003. [2] A. … view at source ↗
Figure 1
Figure 1. Figure 1: Summary of αs(mZ ) determinations from CMS. The data points show the values of αs(mZ ) for the various determinations as listed in [PITH_FULL_IMAGE:figures/full_fig_p116_1.png] view at source ↗
Figure 1
Figure 1. Figure 1: Examples of experimental W± and Z cross sections (lines with grey uncertainty bands) compared to theoretical NNLO predictions (ellipsoids, for each PDF set) as a function of αs(mZ ). calculate the Pearson correlation coefficients for all data points and take it as the correlations of their corresponding uncertainties. For the experimental systematic uncertainties, we did a detailed study based on the CMS m… view at source ↗
Figure 2
Figure 2. Figure 2: Final αs(mZ ) obtained by combining 28 individual extractions based on the W±, Z cross sections listed in [PITH_FULL_IMAGE:figures/full_fig_p122_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Overview of the sensitivity of the final [PITH_FULL_IMAGE:figures/full_fig_p122_3.png] view at source ↗
Figure 1
Figure 1. Figure 1: Sensitivity of the Z-boson transverse-momentum distribution to [PITH_FULL_IMAGE:figures/full_fig_p127_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Results of the fit of αs(mZ ) to the CDF measurement of Z-boson transverse-momentum distribution. Post-fit predictions are compared to the measured distributions. The results of the fit of αs(mZ ) to the CDF measurement of Z-boson transverse-momentum distribu￾tion are shown in [PITH_FULL_IMAGE:figures/full_fig_p128_2.png] view at source ↗
Figure 1
Figure 1. Figure 1: Contour used in the derivation of the FESRs, Eq. (2). [PITH_FULL_IMAGE:figures/full_fig_p131_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Left: V +A fake data, generated as described in the text, as a function of s. Right: True ALEPH data [13] as a function of s. The fake data has been generated for s ≥ 1.55 GeV2 ; below this value the two sets of data are identical. experiment, by letting the data points fluctuate according to a multivariant Gaussian distribution defined with the experimental covariance matrix.¶ An example of the resulting … view at source ↗
Figure 3
Figure 3. Figure 3: Left: V + A spectral function. Right: V + A spectral function, after the parton model contribution has been subtracted. The black dashed curve is the result of perturbation theory. the fact that a group of three data points, with central values very close together at s ' 2.2 GeV2 , are above the perturbative curve while another group of three data points, again very close together at s ' 2 GeV2 , are below… view at source ↗
Figure 4
Figure 4. Figure 4: Left: V spectral function, together with the parton model result (dashed black curve) and the result from the DV parametrization (6) obtained from Eq. (4) (blue curve). Right: The same for the A spectral function. 1.5 2.0 2.5 3.0 -0.010 -0.005 0.000 0.005 0.010 0.015 ssw (GeV2 ) WSR1 (no DV) 1.5 2.0 2.5 3.0 -0.010 -0.005 0.000 0.005 0.010 0.015 ssw (GeV2 ) WSR1 [PITH_FULL_IMAGE:figures/full_fig_p135_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Left: First Weinberg sum rule without DVs. Right: First Weinberg sum rule with DVs [PITH_FULL_IMAGE:figures/full_fig_p135_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Comparison of the agreement between the lefthand and righthand sides of the FESR (4) [PITH_FULL_IMAGE:figures/full_fig_p136_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Electromagnetic FESR tests of the tOPE strategy using the set of weights of Eq. (10). [PITH_FULL_IMAGE:figures/full_fig_p137_7.png] view at source ↗
Figure 1
Figure 1. Figure 1: Extraction of αs from the hadronic/leptonic W decay ratio RW, using the current data (left) and expected at the FCC-ee with experimental uncertainties alone (right) [9]. Note the wildly different x- and y-axes scales. The diagonal blue line in both plots assumes CKM matrix unitarity. At the FCC-ee, the total W width Γtot W can be accurately measured through a threshold e +e − → W+W− scan around √ s = 2mW, … view at source ↗
Figure 2
Figure 2. Figure 2: Extracted αs values from hadronic Z decay data compared to the current world-average (circle). Left: Using the current experimental measurements of Γtot Z (dashed-dotted), RZ (dashed), and σ had Z (dotted lines). Right: Expected at the FCC-ee from Γtot Z and RZ (yellow band) without theoretical uncertainties (dotted curve) and with the current ones divided by a factor of four (solid curve). The blue band i… view at source ↗
read the original abstract

This document collects a written summary of all contributions presented at the workshop "$\alpha_s$(2019): Precision measurements of the strong coupling" held at ECT* (Trento) in Feb. 11--15, 2019. The workshop explored in depth the latest developments on the determination of the QCD coupling $\alpha_s$ from the key categories where high precision measurements are available: (i) lattice QCD, (ii) hadronic $\tau$ decays, (iii) deep-inelastic scattering and parton distribution functions, (iv) event shapes, jet cross sections, and other hadronic final-states in $e^+e^-$ collisions, (v) Z boson and W boson hadronic decays, and (vi) hadronic final states in p-p collisions. The status of the current theoretical and experimental uncertainties associated to each extraction method, and future perspectives were thoroughly reviewed. Novel $\alpha_s$ determination approaches were discussed, as well as the combination method used to obtain a world-average value of the QCD coupling at the Z mass pole.

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

0 major / 1 minor

Summary. This document collects written summaries of contributions from the α_s(2019) workshop at ECT* (Trento), February 11-15, 2019. It reviews precision measurements of the QCD coupling α_s in six categories: (i) lattice QCD, (ii) hadronic τ decays, (iii) deep-inelastic scattering and PDFs, (iv) event shapes, jets in e+e- collisions, (v) Z and W hadronic decays, (vi) hadronic final states in pp collisions. The status of theoretical and experimental uncertainties, novel approaches, and the combination method for the world average at the Z pole are discussed.

Significance. As a workshop summary, the manuscript offers a timely snapshot of the field’s progress on α_s determinations, which is a key input for many precision calculations in particle physics. By compiling reviews from experts across methods and discussing combination procedures, it aids in assessing the current world average and identifying areas for improvement. The document does not introduce new theoretical results but fulfills an important role in disseminating workshop outcomes.

minor comments (1)
  1. [Abstract] Abstract, final paragraph: the description of the combination method is brief and does not indicate how correlations across the six categories are handled; a short clarifying phrase would improve standalone readability without altering the descriptive nature of the summary.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of the manuscript and the recommendation to accept.

Circularity Check

0 steps flagged

Workshop summary contains no derivation chain subject to circularity

full rationale

This manuscript is explicitly a collection of written summaries of contributions presented at the 2019 workshop. It reviews status, uncertainties, and combination methods across six established categories of α_s extractions but advances no original first-principles derivation, prediction, or fitted result whose output is equivalent to its inputs by construction. No equations or claims reduce to self-definition, fitted-input renaming, or load-bearing self-citation chains. The document therefore lies outside the patterns that trigger circularity scoring.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Because the document is a review of prior extractions, its content rests on the axioms, free parameters, and invented entities already present in the six categories of α_s determinations (lattice, τ decays, DIS, jets, Z/W decays, pp). No new free parameters or entities are introduced by the summary itself.

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