{"id":"58365b89-0198-4864-8939-d443cdb2313d","arxiv_id":"2502.01453","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A first, preliminary extraction of the QCD strong coupling from static quark-antiquark energy in (2+1+1)-flavor lattice QCD, consistent with previous determinations but not yet final.","lead":"Physicists matched lattice QCD data for the force between a heavy quark and antiquark to perturbative calculations, obtaining a preliminary value of the strong coupling in a theory with four quark flavors. The result is an early step toward a new high-precision determination of the strong coupling at the Z boson mass.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The stability claim rests on fits at r/a≈3–4 where residual discretization errors are covered only by a hand-assigned 0.1% systematic; the decisive check is whether the available one-loop improved distance changes r1ΛMS by more than that.","rationale":"I read the paper as a preliminary feasibility report, not a final alpha_s determination. The authors are appropriately cautious: they present no quotable number, note the missing continuum extrapolation, and flag the one-loop improvement as unfinished. My concern is not that the analysis is circular or dishonest; it is that the central observable-level claim—stability across fit options and agreement with previous extractions—is supported by a fit window at r/a≈3–4 where the only discretization control is tree-level improvement plus an ad hoc 0.1% error. The text says the one-loop calculation is 'still being finalized' and that the biggest correction occurs at on-axis points, which are excluded, but the size of the remaining off-axis one-loop correction is not quantified. If the true residual cutoff effect is larger than 0.1%, the extracted r1ΛMS could shift by more than the quoted systematic error, and the apparent agreement with TUMQCD/FLAG could be coincidental. The specific check—repeating the extraction with the one-loop improved distance—directly settles whether the hand-assigned systematic is adequate. This is exactly the kind of sensitivity test that should appear in the final publication and would move the claim from preliminary to robust. The reader's weakest assumption already names the tree-level discretization improvement as a possible bias; my focus is narrower and more testable, which is why I mark agreement as partial rather than full.","tokens_in":10129,"tokens_out":7752,"duration_ms":71817,"concrete_test":"Recompute r1ΛMS on the finest ensemble with the same jackknife blocks, fit-range selection, and AIC weighting, but replace the tree-level improved distance with the one-loop improved distance of Ref. [35]. Compare the resulting r1ΛMS for both the Nf=4 and Nf=3+1 fits to the tree-level result; if the shift is larger than the 0.1% systematic assigned to r^2≤8a, the quoted systematic is not conservative and the stability claim is not established. As a cross-check, also extract the per-point difference between tree-level and one-loop r_I for each included off-axis separation and compare it with the 0.1% error budget.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The proceedings' central claim is that all fit options are stable and agree with earlier TUMQCD and FLAG determinations. The data that carry this claim are the short-distance points on the finest ensemble (a=0.03216 fm), with fit ranges rmax≈0.1 fm for Nf=4 and 0.13 fm for Nf=3+1 (Section 3). These windows translate to r/a between roughly 3 and 4, where the only control of discretization errors is the tree-level improved distance r_I (Section 2.2). The authors explicitly do not use the one-loop improvement of Ref. [35]; instead they 'add 0.1% error as an extra systematics to all points r^2 ≤ 8a' and exclude on-axis points. The 0.1% figure is not derived from the one-loop calculation displayed in Fig. 2, and the actual tree-level vs one-loop difference at the included off-axis separations is not reported. If that difference exceeds 0.1% at r^2≈8a, then the assigned systematic underestimates the discretization bias, and the 'stability between all fit options' and 'general agreement' with previous extractions could be an artifact of inflated errors rather than evidence that the two-loop finite-charm plus renormalon-subtracted perturbation theory describes the lattice static energy. This is load-bearing because the new Nf=4/3+1 extraction has no continuum extrapolation in these proceedings, so the short-distance improvement is the only protection against O(a^2/r^2) cutoff effects.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript is a Lattice 2024 proceedings contribution from the TUMQCD collaboration reporting preliminary results for the extraction of Lambda_MS, and hence alpha_s(MZ), from the static energy in (2+1+1)-flavor QCD. The analysis uses MILC ensembles with the finest lattice spacing a=0.03216 fm as the primary data set, comparing the lattice static energy with two perturbative treatments: the force-integration method and the minimal renormalon subtraction (MRS) prescription, both with and without a finite-charm correction. Fits are performed with a two-parameter fit of a shift constant and Lambda_MS, using correlated jackknife errors and AIC model averaging over fit ranges. Results are expressed in r1 units, no continuum extrapolation is attempted, and no quotable numbers are given because the analysis is preliminary. The central claim is that the extracted r1 Lambda_MS is stable among all fit options and agrees with previous TUMQCD 2+1-flavor extractions and the recent FLAG average.","tokens_in":10378,"tokens_out":4263,"duration_ms":41661,"significance":"If the result holds, this would be the first static-energy determination of Lambda_MS in 2+1+1-flavor QCD, providing an important cross-check of the strong coupling from a four-flavor lattice calculation. The paper has several strengths: it uses publicly available MILC ensembles, it employs two independent renormalon-control strategies, it uses a transparent jackknife and AIC fit procedure, and it is appropriately cautious in not quoting final numbers and in stating that the continuum extrapolation and the one-loop improvement are left to a future publication. The main limitation is that all quantitative conclusions in these proceedings rest on a single finest lattice spacing and on a hand-assigned discretization systematic, so the significance is that of a solid progress report rather than a final determination.","major_comments":[{"comment":"The text states that the one-loop improved distance of Ref. [35] is not used and that a 0.1% extra systematic is assigned to all points with r^2 <= 8a, but it does not report the actual magnitude of the tree-level versus one-loop improvement at the off-axis separations included in the fits. This matters because the fits on the finest ensemble use r/a in the range of roughly 3 to 4 (rmax ~ 0.1 and 0.13 fm in Section 3), and the paper performs no continuum extrapolation. The stability claim in Section 3 therefore depends on the 0.1% figure covering the missing one-loop discretization effects. I would ask the authors to quantify the difference between the tree-level and one-loop improved distances at the fitted separations, or to explicitly state that the stability claim is contingent on the finalization of the one-loop calculation.","section":"Section 2.2, Figure 2, and Section 3"},{"comment":"The 'general agreement' with previous TUMQCD and FLAG results is displayed in r1 units, but the scale-setting conventions differ: the (2+1)-flavor extraction used r1 = 0.3106(17) fm from f_pi, while the (2+1+1)-flavor scale used here is r1 = 0.3037(25) fm. The paper itself notes that presenting the comparison in physical units would make the difference more pronounced. As it stands, the agreement in r1 units could be partly an artifact of the different r1 conventions. The authors should either provide the comparison in physical units or temper the agreement claim so that the reader can assess the genuine level of consistency.","section":"Section 3.1 and Figure 4 (left)"},{"comment":"The figure contains a '3-loop' extraction for the Nf=3+1 case, but the text correctly notes that this point is incomplete because the finite-charm corrections are known only at two loops. Since the paper's main stability claim is based on seeing agreement among all fit options, including an incomplete three-loop point weakens the evidence: a two-loop calculation with a partial three-loop term is not a full three-loop result. I recommend separating the two-loop results from the incomplete three-loop point in the stability discussion, and phrasing the convergence statement only in terms of the complete two-loop orders.","section":"Section 3, Figure 4 (left)"}],"minor_comments":[{"comment":"The manuscript contains many missing spaces and OCR-type artifacts (e.g., 'Thestrongcoupling', '𝛼s( 𝑀𝑍)', 'Nf = 3+ 1'), which make the text difficult to read; a careful proofreading pass is needed.","section":"Throughout"},{"comment":"The last displayed line with the product over N_st terms and the ellipsis is ambiguous about how many states are included in the truncation; please clarify the notation, for example by explicitly defining the range of n and the meaning of the ellipsis.","section":"Equation (3)"},{"comment":"The legend and axis labels mix 'Bare', 'Euclidean', 'Tree-level', and '1-loop'; it would be helpful to state explicitly which curves are the bare data, which are the improved-distance curves, and which points are excluded from fits.","section":"Figure 2"},{"comment":"The residual-panel labels '1 2 3 4 5 9 16 rI/a' are cryptic; please spell out these labels (e.g., as rI/a values for the paths contributing at each separation) so that the residual structure can be interpreted without the reader having to reconstruct the path topologies.","section":"Figure 3"},{"comment":"The sentence describing fits over 'all possible ranges' should specify the minimum number of data points and the granularity in rmin and rmax, since the AIC weighting depends on the set of candidate ranges.","section":"Section 3"},{"comment":"References [35] and [40] are marked as in preparation; this is acceptable for proceedings, but the text should make it explicit that the numerical comparison of tree-level versus one-loop improvement is not yet peer-reviewed and will be provided in [35].","section":"References"}],"recommendation":"major_revision","confidential_remarks":"This is a well-written proceedings paper that is honest about its preliminary nature, and the authors are to be credited for not quoting final numbers and for clearly stating that the continuum extrapolation is left for a future publication. The reason I recommend major revision rather than minor revision is that the paper's central claim of 'stability between all fit options and general agreement with previous extractions' is load-bearing and currently rests on an unquantified hand-assigned 0.1% discretization systematic and on a comparison made in r1 units that may not survive a physical-unit comparison. Both issues are fixable within the scope of a proceedings contribution: the authors can either add a quantitative estimate of the one-loop improvement effect from their unpublished calculation, or explicitly soften the stability claim to 'preliminary' pending the one-loop improvement and continuum extrapolation. I would also encourage them to report the physical-unit comparison in the text rather than only in r1 units, since the r1-scale difference between the (2+1)- and (2+1+1)-flavor analyses is a known source of systematic shift."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nRead the TUMQCD proceedings on strong coupling in 2+1+1 QCD. It is a preliminary report, and it reads like one: no final quoted value, explicit acknowledgment that continuum extrapolation and one-loop improvement are still to come. That is a strength. The paper does the first static-energy-based extraction of Lambda_MS with dynamical charm, using the finest MILC ensemble and two renormalon strategies (force integration and MRS) with a two-loop charm mass correction. The new element is the handling of delta_V_m and the check that Nf=4 and Nf=3+1 descriptions agree.\n\nThe reader's conditional verdict is right. The fits are internally consistent, the residual plots look flat, and the AIC averaging is standard. The paper is careful not to quote numbers, which remains appropriate because the analysis is incomplete.\n\nThe soft spots are as advertised. The 0.1% extra systematic for missing one-loop improvement is hand-assigned, and since the fitted window on the finest ensemble is r/a around 3-4, the discretization control depends heavily on that number plus the exclusion of on-axis points. The stress-test note is fair: the actual size of the one-loop correction at the included off-axis separations is not shown, so the 0.1% could under-cover the bias. That said, the paper does not claim a final precision; it claims stability across fit options and rough agreement with prior TUMQCD and FLAG. The displayed spread of r1 Lambda_MS around 0.46-0.50 is consistent with that. The missing continuum extrapolation and the restriction to two-loop accuracy for the 3+1 fits are acknowledged, and the charm correction truncated at two loops is a real limitation but not a hidden one.\n\nThe only point I would push back on is the word 'stability'. With three ensembles, no continuum limit, and a hand-assigned discretization error, 'stability' means 'no obvious tension within the large error bars'. That is a fair feasibility statement, but it is not yet a determination. The authors know this.\n\nWho is this for? Lattice practitioners working on alpha_s and the static energy; anyone tracking FLAG averages. It deserves publication as a proceedings, and a serious referee would check the one-loop improvement calculation and the size of the discretization systematic once the final paper appears. Recommend: accept for the proceedings; do not treat the numerical results as final.","headline":"First 2+1+1-flavor static-energy extraction of Lambda_MS; preliminary, honest about its gaps, and the stability claim is plausible but the 0.1% discretization systematic deserves a hard look in the final.","tokens_in":11050,"tokens_out":1921,"would_cite":false,"duration_ms":18577,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["12.38.Gc"],"model":"deepseek-v4-flash","headline":"Four-flavor lattice QCD yields a stable strong-coupling value.","keywords":["strong coupling","static energy","lattice QCD","charm quark","renormalon","Lambda_MS","MILC ensembles","static potential"],"falsifier":"Complete the one-loop lattice perturbation theory calculation of the static potential with HISQ fermions (the in-preparation Ref. [35]) and redo the fits with the one-loop improved distance: if the central value of $r_1\\Lambda_{\\overline{\\mathrm{MS}}}$ shifts by more than the 0.1% systematic error that was added to the shortest-distance points to compensate its absence, the quoted error budget would be too small.","tokens_in":9836,"feed_emoji":"⚛️","tokens_out":10144,"duration_ms":79751,"temperature":0.7,"pith_summary":"This proceedings paper reports a first lattice determination of $\\Lambda_{\\overline{\\mathrm{MS}}}$ (the quantity behind $\\alpha_s(M_Z)$) from the static energy in (2+1+1)-flavor QCD, using the MILC ensembles down to lattice spacing 0.03216 fm. It argues that the short-distance lattice static energy can be matched to the perturbative static potential once the finite charm mass is included, and that the extracted $\\Lambda_{\\overline{\\mathrm{MS}}}$ is stable across two renormalon treatments and two fit strategies. The authors find general agreement with previous TUMQCD 2+1-flavor extractions and the latest FLAG average, which matters because the strong coupling is a fundamental Standard Model parameter and this is a new, fully dynamical four-flavor route to it. The results are preliminary: they are presented in $r_1$ units, no final numbers are quoted, and the continuum extrapolation is left for the final publication.","feed_headline":"Four-flavor lattice QCD steadies the strong-coupling value","feed_subtitle":"A static-energy extraction with dynamical charm matches earlier 2+1-flavor results and the FLAG average.","key_machinery":"The central object is the static energy $E_0(r)$ of a static quark-antiquark pair, with its perturbative expansion in the strong coupling including ultrasoft logarithms. The two load-bearing tools are the force-integration form $\\int_{r_*}^r dr'\\,F^{(N_f)}(r')+\\delta V_m^{(N_f)}(r)$, which replaces the renormalon-affected constant by an integration constant, and the minimal renormalon subtraction (MRS) prescription, which sums the leading factorial growth of the perturbative coefficients; both are combined with the tree-level improved distance $r_I$ that removes the leading lattice cutoff artifacts. The charm-quark decoupling is implemented through the correction $\\delta V_m$, known up to $\\alpha_s^3$, which makes the $N_f=3+1$ fits possible up to $r_{\\max}\\simeq0.13~\\mathrm{fm}$.","core_discovery":"Using Coulomb-gauge Wilson-line correlators on MILC (2+1+1)-flavor ensembles, the authors compute the static energy $E_0(r)$ and compare it with the perturbative static-energy expansion, adding the finite-charm-mass correction $\\delta V_m$ known to two loops in perturbation theory. To handle the renormalon ambiguity in the additive constant, they use either the force-integrated static energy or the minimal renormalon subtraction (MRS) prescription, and they extract $\\Lambda_{\\overline{\\mathrm{MS}}}$ from correlated two-parameter fits in $r_1$ units, with a model average over fit ranges weighted by the Akaike information criterion. They find that both the short-distance $N_f=4$ fits and the $N_f=3+1$ fits with a massive charm describe the data well up to $r_{\\max}\\approx0.1$--$0.13~\\mathrm{fm}$, and that the resulting $\\Lambda_{\\overline{\\mathrm{MS}}}$ values are stable between all fit options and consistent with the TUMQCD 2+1-flavor results and the FLAG 2024 average. Because the analysis is preliminary, the paper deliberately refrains from quoting final numbers and defers the continuum extrapolation to a subsequent publication.","pith_inferences":["Because the 0.1% systematic on the shortest-distance points is a placeholder for an unfinished one-loop calculation, the final publication could revise the weight of short-distance data; a shift in the improved distance is the most plausible route for the preliminary stability to fail.","If the final continuum extrapolation keeps the agreement with FLAG, the static-energy method will have demonstrated competitive four-flavor precision, providing a cross-check of the FLAG average that is independent of other observables.","The mild dependence of $r_1\\Lambda_{\\overline{\\mathrm{MS}}}$ on light-quark mass at fixed lattice spacing (grouped points in the right panel of Fig. 4) could be a residual discretization effect or a genuine quark-mass dependence that a continuum extrapolation with more ensembles will have to resolve.","A test the paper does not yet perform is to compare the $N_f=4$ and $N_f=3+1$ extractions after converting to a common scheme via perturbative decoupling; if the two values disagree beyond the quoted AIC-weighted errors, the charm-mass treatment rather than the renormalon prescription would be the suspect."],"forward_implications":["If the stability survives the final continuum extrapolation, $\\alpha_s(M_Z)$ from the (2+1+1)-flavor static energy will provide a new independent lattice determination with a fully dynamical charm quark.","The success of the $N_f=3+1$ fits with a two-loop charm correction supports the decoupling picture in which charm becomes a heavy quark near $r\\approx0.15~\\mathrm{fm}$, extending the perturbative range beyond what a four-massless-quark description allows.","Using the updated $r_1$ scale from the kaon decay constant (Ref. [40]) would bring the (2+1+1)- and (2+1)-flavor extractions into closer agreement in physical units than the current $r_1=0.3037(25)~\\mathrm{fm}$ does.","Once the final publication releases the quoted $\\Lambda_{\\overline{\\mathrm{MS}}}$, the same fit machinery can be applied to the coarser ensembles to perform a continuum extrapolation, the remaining step to a final $\\alpha_s(M_Z)$ number.","The MRS-based extractions agree with the force-integrated ones, suggesting that the renormalon treatment is not a dominant source of systematic error for this observable."],"supporting_citations":[{"why":"Supplies the three-loop static potential and leading ultrasoft log resummation that define the perturbative static-energy expansion used in the fits.","marker":"[2–7]"},{"why":"Provides the finite-charm-mass correction $\\delta V_m$ to the static potential, the key ingredient for the $N_f=3+1$ fits.","marker":"[24]"},{"why":"MILC (2+1+1)-flavor HISQ ensembles on which the static energy is computed.","marker":"[29–31]"},{"why":"Gives the static energy in (2+1+1)-flavor lattice QCD with scale setting and charm effects, including the $r_1=0.3037(25)$ fm scale used here.","marker":"[33]"},{"why":"The previous TUMQCD 2+1-flavor static-energy extraction that this work is compared against, using the same fit strategy.","marker":"[17]"},{"why":"FLAG review 2024 providing the reference average for the strong coupling and the charm-quark mass $m_c(m_c)$.","marker":"[21]"},{"why":"Introduces the minimal renormalon subtraction prescription and truncation-uncertainty control used in the MRS fits.","marker":"[28]"},{"why":"RunDec library used to run the coupling and to relate $\\Lambda_{\\overline{\\mathrm{MS}}}$ across flavors via perturbative decoupling.","marker":"[38]"},{"why":"In-preparation one-loop lattice perturbation theory for the static potential with HISQ quarks; its absence motivates the added 0.1% systematic on short-distance points.","marker":"[35]"}],"fun_headline_variants":["Preliminary 4-flavor QCD pins strong coupling","Charm-aware lattice QCD stabilizes α_s","Four-flavor static energy matches known α_s","Lattice QCD with charm confirms strong coupling","New 2+1+1-flavor static energy bolsters α_s"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The extraction assumes that the two-loop truncated charm-mass correction together with the tree-level improved distance describes the lattice static energy at separations up to roughly 0.1–0.13 fm within the quoted errors, so that the remaining perturbative and discretization uncertainties are smaller than the statistical ones.","fun_headline_variants_meta":{"raw":{"variants":["Preliminary 4-flavor QCD pins strong coupling","Charm-aware lattice QCD stabilizes α_s","Four-flavor static energy matches known α_s","Lattice QCD with charm confirms strong coupling","New 2+1+1-flavor static energy bolsters α_s"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00023,"raw_usage":{"total_tokens":1474,"prompt_tokens":926,"completion_tokens":548,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":542,"completion_tokens_details":{"reasoning_tokens":467}},"tokens_in":542,"tokens_out":548,"duration_ms":5744,"temperature":1.0,"reasoning_tokens":467,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-09T15:14:29.846151+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Complete the one-loop lattice perturbation theory calculation of the static potential with HISQ fermions (the in-preparation Ref. [35]) and redo the fits with the one-loop improved distance: if the central value of $r_1\\Lambda_{\\overline{\\mathrm{MS}}}$ shifts by more than the 0.1% systematic error that was added to the shortest-distance points to compensate its absence, the quoted error budget would be too small.","supporting_citations":[{"cited_title":"Perturbative QCD Potential, Renormalon Cancellation and Phenomenological Potentials","cited_arxiv_id":"hep-ph/0109122","evidence_quote":"Provides the finite-charm-mass correction $\\delta V_m$ to the static potential, the key ingredient for the $N_f=3+1$ fits."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"In-preparation one-loop lattice perturbation theory for the static potential with HISQ quarks; its absence motivates the added 0.1% systematic on short-distance points."}],"review_version":1}