{"id":"d9fb2bc0-94ea-4179-8edb-8d3a77631a5b","arxiv_id":"2507.17704","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"Using a global NNLO+NNLL fit with a stretched-exponential non-perturbative jet function, the authors describe the near-side electron-positron EEC and extract a quark-jet transition scale of about 2.3 GeV, lower than the scale previously estimated for gluon jets.","lead":"This paper models the small-angle energy-energy correlator in electron-positron collisions by combining NNLO perturbative QCD with a non-perturbative jet function fitted to data from eight experiments spanning 29 to 91.2 GeV. It reports a unified description of the perturbative-to-hadronization transition and extracts a characteristic scale near 2.3 GeV, with implications for quark versus gluon hadronization.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 2.31 GeV scale is not yet direct evidence for a quark-specific transition: the e+e- fit imposes j_q,np = j_g,np, so a1 is a flavor-averaged effective parameter, and comparison to the LL pp fit cannot isolate flavor from perturbative-accuracy or jet-composition differences.","rationale":"The reader's verdict is CONDITIONAL and I find the same load-bearing concern, so no change is needed. The paper is a serious global analysis: the theoretical framework (NNLO fixed order, NNLL resummation, b* prescription) is standard, the data selection is documented, and the global fit quality (chi2/Ndata = 1.38) shows that the effective NP jet function describes the measured EEC across the chosen energy range. That is genuine evidence that the ansatz is a useful phenomenological model. The problem is the interpretive leap from this successful effective fit to 'the first direct evidence of flavor dependence.' The in-scope text itself says j_q,np = j_g,np is imposed because e+e- data cannot separately constrain the two functions, so a1 = 2.31 GeV is an average over the e+e- flavor mixture, not a measured quark quantity. Comparing that number to a1 = 3.8 GeV from a LL pp fit cannot isolate flavor: the two extractions differ in perturbative order, in the observable's phase-space definition, and in the flavor composition of the jet sample. The authors' own call for a future combined NNLL fit with separate quark and gluon NP functions is the correct test and effectively concedes the present result is indirect. I would keep the verdict at CONDITIONAL: accept the data description and the extracted effective model, but require the joint flavor-resolved fit before endorsing the flavor-dependence claim as direct evidence.","tokens_in":14300,"tokens_out":7672,"duration_ms":90638,"concrete_test":"Perform a simultaneous NNLL fit of the eight e+e- datasets listed in Table I and the CMS pp jet EEC dataset of Ref. [55], using the framework of Ref. [37], with independent non-perturbative functions j_q,np(b) = exp[-(a1_q b)^a2_q] and j_g,np(b) = exp[-(a1_g b)^a2_g], with quark/gluon fractions fixed from NNLO cross sections. If the 68% confidence intervals for a1_q and a1_g overlap, the claimed flavor dependence is not established; if a1_q is constrained near 2.3 GeV and a1_g near 3.8 GeV, the claim survives. This is the direct test the authors identify as future work.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The headline result, that a1 = 2.31 GeV is a quark-jet transition scale distinct from the gluon-dominated pp value of 3.8 GeV, and that this difference is 'the first direct evidence of flavor dependence in the EEC', depends on two assumptions that the fit does not test. First, Eq. (6) multiplies the perturbative quark and gluon jet functions by the same non-perturbative function j_np(b) = exp[-(a1 b)^a2]; the authors state explicitly that e+e- data cannot separately constrain j_q,np and j_g,np. The fitted a1 is therefore an effective flavor-averaged parameter, not a quark-specific scale. Second, the comparison value 3.8 GeV comes from a LL fit to pp inclusive-jet data (Ref. [37]) at lower perturbative accuracy and with a jet sample that is only 'mostly' gluon-dominated; perturbative-order differences, b* and scale choices, or quark admixture in the pp sample could generate the same 1.5 GeV shift without any genuine flavor dependence. The paper's own proposed 'future combined NNLL fit' to separately constrain the two NP functions concedes that the present comparison is indirect. The data description is credible, but the flavor-dependence claim needs that joint fit to land.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies the collinear limit of the electron-positron energy-energy correlator (EEC) and describes the transition from the perturbative to the non-perturbative regime. The authors factorize the EEC in position space and introduce a non-perturbative jet function j_np(b) = exp[-(a1 b)^a2] multiplying the perturbative quark and gluon jet functions. Using this framework at NNLO+NNLL accuracy, they perform a global fit to eight e+e- datasets spanning Q = 29.0-91.2 GeV, obtaining chi2/Ndata = 1.38 over 257 points. The fit extracts a1 = 2.31 GeV and a2 = 1.06, and the paper claims this a1 is a characteristic quark-jet transition scale distinct from the gluon-dominated value a1 = 3.8 GeV extracted from pp EEC-in-jet data, presenting this as the first direct evidence of flavor dependence in the EEC.","tokens_in":14622,"tokens_out":5804,"duration_ms":58605,"significance":"If the result holds, the paper provides a useful unified description of the EEC over a wide range of center-of-mass energies and a quantitative handle on hadronization effects in the collinear limit. The global fit quality is good, the replica method for statistical uncertainties is well described, and the position-space factorization in the supplementary material is carefully laid out. The central modeling assumption - a multiplicative non-perturbative jet function with a simple two-parameter form - is physically motivated and has some predictive power, for example the geometric scaling dΣ/dz ~ z^0 at small qT. However, the headline flavor-dependence claim is not directly established by the analysis presented, because the fit enforces equality of the quark and gluon non-perturbative functions and the comparison to the pp result is across different perturbative accuracies and environments. The work is therefore a solid phenomenological contribution whose most exciting conclusion needs additional support or a more cautious interpretation.","major_comments":[{"comment":"The claim that a1 = 2.31 GeV is a quark-jet transition scale and that its difference from the pp value 3.8 GeV constitutes 'the first direct evidence of flavor dependence in the EEC' is not supported by the present analysis. In Eq. (6) the authors impose j_q,np(b) = j_g,np(b) and explicitly state that e+e- data cannot separately constrain the two non-perturbative jet functions; the fitted a1 is therefore an effective flavor-averaged parameter rather than a quark-specific scale. Moreover, the comparison value a1 = 3.8 GeV from Ref. [37] comes from a leading-logarithmic fit to EEC in inclusive jets in pp collisions, so the comparison mixes different perturbative orders (LL vs. NNLO+NNLL), different observables (full e+e- EEC vs. EEC-in-jet), and a jet sample that is only 'mostly' gluon-dominated. The 1.5 GeV shift could be produced by any of these differences without genuine flavor dependence. The authors should either soften the wording to 'an indication consistent with flavor dependence' or perform a controlled comparison, such as a matched-accuracy fit to the pp data or a sensitivity study with j_q,np ≠ j_g,np.","section":"Abstract, Numerical Results, Conclusions"},{"comment":"The extraction of a1 and a2 relies on the assumption that the two constant K-factors A and B in Eq. (9) absorb all missing higher-order corrections and that the non-perturbative physics is fully captured by the multiplicative ansatz j_np(b). The paper itself notes that the fitted K-factors indicate 'a non-trivial z-dependence that cannot be fully captured by constant K-factors,' which means the central parameters are correlated with the K-factor modeling choice. A robustness test, for example allowing a mild z-dependent K-factor or varying the matching between the resummed and non-singular contributions, would help establish that the extracted a1 is a stable physical scale rather than an artifact of the fixed form of the K-factors. Without such a test, the quantitative comparison to the pp value of 3.8 GeV is on weaker footing.","section":"Global Analysis, Eq. (9), Table II"}],"minor_comments":[{"comment":"Reference [61] is incomplete: it lists 'arXiv:2507.xxxxx' and 'to appear'; the arXiv number and full citation should be provided before publication.","section":"References"},{"comment":"In Eq. (8), the expression 'a1/4' is ambiguous in the typeset version; the power of a1 should be written explicitly (e.g., a1/4 or a1^{1/4}) to avoid confusion.","section":"Eq. (8)"},{"comment":"The statement that the model describes 'the entire near-side region (0°<χ<90°)' should be qualified by the fact that the first point of each dataset is excluded and that data do not extend into the free-hadron region qT ≲ 1 GeV.","section":"Global Analysis - Data Selection"},{"comment":"The sentence 'Because the EEC in e+e− collisions is quark jet dominated, this implies a quark jet transition scale around 2.3 GeV' is a logical jump; it should be phrased as an interpretation consistent with quark dominance rather than a direct implication of the analysis.","section":"Numerical Results"},{"comment":"The choice bmax = 2e^{-γE} GeV^{-1} is fixed, but the paper does not include an uncertainty from this choice in the theoretical error budget; a brief discussion of the sensitivity to bmax would improve the robustness assessment.","section":"Theoretical Framework"}],"recommendation":"major_revision","confidential_remarks":"The paper's flavor-dependence claim is likely to attract wide attention, but as written it overstates what the current analysis can establish. The authors should be encouraged to either hedge the claim or add a same-accuracy pp fit, which would materially strengthen the paper. Also, the incomplete reference [61] should be corrected before resubmission."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The fit is good and the e+e- data description is a useful advance, but the abstract's 'first evidence of flavor dependence' is stronger than what the analysis actually establishes. The number a1=2.31 GeV is an effective parameter from a fit that enforces the same non-perturbative function for quark and gluon jets, so it cannot by itself isolate a quark-specific transition scale.\n\nWhat the paper does well: it gives the first global NNLO+NNLL description of the near-side e+e- EEC from 29 to 91.2 GeV using a stretched-exponential NP jet function, with chi2/Ndata=1.38 over 257 points. The treatment of fixed-order matching, scale variation, and MC replicas is thorough. The fit finds a2=1.06, close to linear b-dependence, and the framework reduces to the known leading power correction in the appropriate limit. These are real, useful results for the hadronization and alpha_s extraction community.\n\nWhere the soft spots are: the flavor-dependence claim. The authors state they cannot separate j_q,np and j_g,np and therefore set them equal. So the fitted a1 is an average over the jet sample, not a pure quark scale. Comparing that with the pp jet result of 3.8 GeV from a LL fit to CMS data conflates possible flavor differences with differences in perturbative accuracy, energy, and quark admixture. The paper's own suggestion of a future combined NNLL fit is an admission that this comparison is indirect. Similarly, the NP form exp[-(a1 b)^a2] is a model ansatz; the extracted scale is meaningful only within that model. The constant K-factors A~0.86 and B~1.24 are somewhat sizeable, indicating some missing higher-order sensitivity, though they do not undermine the good global fit.\n\nWho should read this: anyone working on EEC, hadronization, or alpha_s extraction. The e+e- data description and the NP parameterization are worth having. The paper deserves peer review, but I would ask the authors to soften the 'first direct evidence' language and to address the equality assumption, either by a sensitivity study or by presenting constraints from a joint e+e-/pp fit.","headline":"A solid global fit of the e+e- EEC that overreaches in calling its effective NP scale direct evidence for quark-gluon flavor dependence.","tokens_in":15153,"tokens_out":3371,"would_cite":true,"duration_ms":36337,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A single non-perturbative jet function describes the full near-side energy-energy correlator in $e^+e^-$ collisions, placing the quark-jet hadronization transition at about 2.3 GeV.","keywords":["energy-energy correlator","collinear limit","non-perturbative QCD","hadronization","e+e- annihilation","NNLO+NNLL resummation","jet function","flavor dependence"],"falsifier":"Fit the same eight datasets with a different non-perturbative ansatz\\,--\\,separate $a_1^q$ and $a_1^g$ for quark and gluon jets, or a power-series correction in $b$\\,--\\,and check whether a comparable global fit still requires a quark scale near 2.3 GeV. A sharper test is to apply the framework to track-based EEC data from the LEP era: if the data force a materially different $a_1$ or $a_2$, or a joint NNLL fit of $e^+e^-$ and LHC jet data returns a common $a_1$ for both flavors, the claimed 2.3-versus-3.8 GeV flavor dependence does not survive.","tokens_in":14097,"feed_emoji":"⚛️","tokens_out":11941,"duration_ms":113717,"temperature":0.7,"pith_summary":"The paper tries to establish that the collinear energy-energy correlator in $e^+e^-$ annihilation can be described across the whole near-side region ($0^\\circ<\\chi<90^\\circ$) by one unified framework: fixed-order NNLO plus NNLL resummation, multiplied by a non-perturbative jet function acting in position space. Fitting the parameters of that jet function to eight legacy datasets at center-of-mass energies from 29.0 to 91.2 GeV gives a good global description, with $\\chi^2/N_{\\rm data}=1.38$ over 257 data points. The fit locates the parton-to-hadron transition for quark jets at a transverse momentum scale $a_1 = 2.31$ GeV, clearly below the $3.8$ GeV scale previously extracted from gluon-dominated jets in $pp$ collisions. This difference is what the authors present as the first direct evidence of flavor dependence in the energy-energy correlator. If the result holds, it gives a concrete, data-anchored description of exactly where perturbative QCD ends and hadronization begins inside a jet.","feed_headline":"Electron-positron energy correlator turns non-perturbative at 2.3 GeV","feed_subtitle":"A global fit to e+e− data from 29 to 91 GeV finds the quark-jet scale is 2.3 GeV, below the gluon-jet scale of 3.8 GeV.","key_machinery":"The load-bearing object is the non-perturbative jet function $j_{\\rm np}(b)=\\exp[-(a_1 b)^{a_2}]$, inserted in position space as a multiplicative correction to the resummed EEC jet function at the initial scale $\\mu_J^i=\\mu_{b^*}$, where $\\mu_{b^*}=2e^{-\\gamma_E}/b_*$ and the $b_*$ prescription regulates the Landau pole. In this representation the non-perturbative transverse-momentum physics becomes a simple product rather than a convolution, and the shape parameters $a_1,a_2$ are fixed by a global $\\chi^2$ fit together with two $K$-factors $A$ and $B$. The same machinery provides the resummation of $\\ln z$ logarithms through NNLL via the time-like DGLAP evolution of the position-space jet function, matched to fixed-order NNLO results for the non-singular piece. The near-linear exponent $a_2\\simeq 1.06$ also reproduces the known leading power correction in the small-$b$ limit, tying the modeled profile to earlier power-correction analyses.","core_discovery":"The central claim is that the non-perturbative physics of the near-side EEC factorizes into a single multiplicative profile in position space, $j_{\\rm np}(b)=\\exp[-(a_1 b)^{a_2}]$, attached to the perturbative jet function at its initial scale. The global fit returns $a_1=2.310$ GeV and $a_2=1.059$, together with two $K$-factors, and reproduces the measured EEC at all eight energies in the full near-side angular range. Because $e^+e^-$ events are quark-jet dominated, the paper interprets $a_1$ as the characteristic transition scale of the quark jet function and contrasts it with the $3.8$ GeV scale assigned to gluon-dominated jets from earlier $pp$ analyses. That contrast, the authors argue, constitutes the first direct evidence of quark-versus-gluon flavor dependence in the energy-energy correlator, with the transition peak in the data appearing near $Q\\sin(\\chi/2)\\simeq 2.8$ GeV, comparable to $a_1$.","pith_inferences":["If the quark scale is genuinely about 2.3 GeV, jet samples with different quark fractions should show an effective transition scale between 2.3 and 3.8 GeV that tracks the fraction; this is a testable prediction for LHC jet EEC measurements but is not derived in the paper.","The same $b$-space profile should reappear in the back-to-back limit and in light-ray energy correlators, so a unified fit across those observables could either confirm the universality of the profile or reveal environment-dependent hadronization corrections.","The near-linear exponent ($a_2\\simeq 1$) suggests that a single soft scale, rather than a tower of power corrections, dominates the hadronization correction; if so, the ansatz could absorb renormalon-type ambiguities in $\\alpha_s$ extractions from event shapes, though the paper does not pursue this.","Track-based EEC data from the LEP era, with finer angular resolution, should show the same transition peak near $Q\\sin(\\chi/2)\\simeq 2.8$ GeV; if that peak moves with the track selection, the flavor-scale interpretation would need revisiting."],"forward_implications":["One unified NNLO+NNLL framework with a fitted non-perturbative jet function describes the full near-side EEC across $Q=29.0$\\,--\\,$91.2$ GeV with $\\chi^2/N_{\\rm data}=1.38$.","The quark-dominated $e^+e^-$ data yield a transition scale $a_1=2.31$ GeV, compared with $3.8$ GeV for gluon-dominated jets in $pp$ collisions, which the paper presents as the first direct evidence of flavor dependence in the EEC.","The extracted exponent $a_2=1.06$ is close to the value found in the EEC-in-jet analysis and to the back-to-back value $a_2=1.15$, suggesting a common non-perturbative profile across different EEC limits.","The same non-perturbative jet function can be applied to track-based EEC measurements, to $pp$ and heavy-ion data, and to $ep$ collisions, providing cross-environment tests of hadronization universality.","Combining $e^+e^-$ and LHC data in a future NNLL fit would allow separate constraints on quark and gluon non-perturbative functions."],"supporting_citations":[{"why":"Supplies the collinear factorization and the RG equations for hard and jet functions that define the resummation framework.","marker":"[12]"},{"why":"Provides the $b$-space non-perturbative jet-function framework and the $a_1=3.8$ GeV gluon-jet scale used for the flavor comparison.","marker":"[37]"},{"why":"Supplies the numerical three-jet NNLO result used as part of the fixed-order EEC input.","marker":"[65]"},{"why":"Provides the NNLO+NNLL EEC calculation used for the non-singular matched contribution.","marker":"[66]"},{"why":"Motivates the $Q\\ge 29$ GeV data selection and the treatment of experimental uncertainties in the global fit.","marker":"[78]"},{"why":"Gives the back-to-back EEC analysis whose extracted exponent $a_2=1.15$ is compared with the collinear result to argue universality.","marker":"[19]"},{"why":"Introduces the $b_*$ prescription used to regulate the Landau pole in the position-space resummation.","marker":"[75]"},{"why":"Supports the large-distance behavior of the transverse-momentum-dependent functions underlying the non-perturbative profile.","marker":"[76]"},{"why":"Is the highest-energy dataset (91.2 GeV) anchoring the global fit.","marker":"[41]"},{"why":"Provides a second 91.2 GeV dataset with full uncertainty information used in the fit.","marker":"[39]"}],"fun_headline_variants":["EEC in e+e- turns non-perturbative at 2.3 GeV for quark jets","First evidence of quark-gluon flavor dependence in EEC at 2.3 GeV","EEC flavor split: quark jet 2.3 GeV, gluon jet 3.8 GeV","Quark jet EEC scale 2.3 GeV vs gluon's 3.8 GeV"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The conclusion that the EEC transition is flavor dependent rests on the assumption that non-perturbative hadronization effects factor exactly as one multiplicative exponential profile $\\exp[-(a_1 b)^{a_2}]$ shared by quark and gluon jets and fixed across all energies; if the true correction has a different shape, or the forced equality $j_{q,\\rm np}=j_{g,\\rm np}$ hides a flavor difference, the extracted $2.31$ GeV scale is an artifact of the ansatz rather than a physical quark transition scale.","fun_headline_variants_meta":{"raw":{"variants":["EEC in e+e- turns non-perturbative at 2.3 GeV for quark jets","First evidence of quark-gluon flavor dependence in EEC at 2.3 GeV","EEC flavor split: quark jet 2.3 GeV, gluon jet 3.8 GeV","Quark jet EEC scale 2.3 GeV vs gluon's 3.8 GeV"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000831,"raw_usage":{"total_tokens":3676,"prompt_tokens":1038,"completion_tokens":2638,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":654,"completion_tokens_details":{"reasoning_tokens":2535}},"tokens_in":654,"tokens_out":2638,"duration_ms":18109,"temperature":1.0,"reasoning_tokens":2535,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T18:19:50.519123+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Fit the same eight datasets with a different non-perturbative ansatz\\,--\\,separate $a_1^q$ and $a_1^g$ for quark and gluon jets, or a power-series correction in $b$\\,--\\,and check whether a comparable global fit still requires a quark scale near 2.3 GeV. A sharper test is to apply the framework to track-based EEC data from the LEP era: if the data force a materially different $a_1$ or $a_2$, or a joint NNLL fit of $e^+e^-$ and LHC jet data returns a common $a_1$ for both flavors, the claimed 2.3-versus-3.8 GeV flavor dependence does not survive.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Introduces the $b_*$ prescription used to regulate the Landau pole in the position-space resummation."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Is the highest-energy dataset (91.2 GeV) anchoring the global fit."}],"review_version":1}