{"id":"b1fd58ff-738b-49e3-bd55-84f5a172c22d","arxiv_id":"2411.15278","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":9,"one_line_summary":"An extension of the authors' previous Regge fits shows that eikonal unitarization, but not U-matrix unitarization, changes its extracted Pomeron parameters when low-|t| differential cross-section data are included up to |t| = 0.2 GeV².","lead":"This paper re-fits models of high-energy proton scattering after extending the data range for differential cross sections from a momentum transfer of 0.1 to 0.2 GeV squared. It finds that the eikonal unitarization scheme is sensitive to this extra data, while the U-matrix scheme is not, and reports a very small Pomeron slope in the eikonal case.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Central sensitivity claim rests on an unseen comparison: no |t|≤0.1 GeV² baseline, Δχ², or significance for Δα'_P is given, and α'_P is degenerate with aP.","rationale":"I read the manuscript as a phenomenological extension of Ref. [1]: same formalism, same ensembles, but dσ/dt data now included up to |t|=0.2 GeV². The central claim is that the eikonal unitarization scheme is sensitive to the additional large-|t| data, as evidenced by α'_P dropping to ~0.011 GeV⁻² in both ensembles, whereas U-matrix is stable. For that claim to hold, the difference between the present fit and the Ref. [1] fit must be real and attributable to the added data. The paper does not demonstrate either: it provides no restricted fit, no Table from [1], and no statistical measure of the shift. In addition, the small α'_P in the eikonal fits is accompanied by a small vertex scale aP, so α'_P and aP are mutually compensating; the absence of correlation contours makes the interpretation fragile. This is not an internal inconsistency or a claim outside consensus—small α'_P appears in screened-Regge models [4,5,28–31]—but it is a missing-evidence problem in the manuscript. I therefore keep the reader's CONDITIONAL verdict: the paper should either include the |t|≤0.1 baseline comparison with uncertainties or soften the statement to a qualitative observation. I partially agree with the reader's weakest_assumption: the fixed secondary-Reggeon slopes are a secondary risk, but the primary load-bearing gap is the unseen baseline and the α'_P–aP degeneracy.","tokens_in":6121,"tokens_out":8806,"duration_ms":88580,"concrete_test":"Refit Ensembles A and T with the same code and data but restrict dσ/dt to |t|≤0.1 GeV²; then extend to |t|≤0.2 GeV² and compute Δα'_P = α'_P(≤0.2) − α'_P(≤0.1) with its profile-likelihood uncertainty (profiling aP). If |Δα'_P|/σ is below ~2–3, the sensitivity claim is not statistically established. As a cross-check, refit the eikonal scheme with aP fixed to the U-matrix A value (~40 GeV⁻²); if α'_P then returns to ~0.26 GeV⁻², the small slope is a degeneracy artifact rather than a robust data constraint.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central result—that the eikonal scheme is sensitive to dσ/dt data for |t|>0.1 GeV² and that both ensembles yield α'_P≈0.011 GeV⁻²—is supported only by a qualitative comparison with Ref. [1]. Section III states that Ensemble A 'now favors a small value of α′_P', but no fit restricted to |t|≤0.1 GeV² is reproduced, no parameter values from Ref. [1] are quoted, and no Δχ² or pull for the shift in α'_P is computed. This matters because α'_P is not independently identified: in the eikonal fits aP≈0.47–0.53 GeV⁻² (Table I, Eq. (15)), while the U-matrix Ensemble A fit prefers aP≈40 GeV⁻²; at |t|≤0.2 GeV² the vertex scale aP generates t-dependence that can be traded against α'_P. Without a profile likelihood in (α'_P, aP) or a nested t-range comparison, the reported small α'_P and the claimed sensitivity to |t|>0.1 GeV² could be an artifact of parameter degeneracy rather than a data-driven effect. The conclusion is therefore plausible but under-supported.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper extends the authors' previous global analysis of pp and ppbar elastic scattering to include dσ/dt data up to |t| = 0.2 GeV^2, comparing eikonal and U-matrix unitarization schemes. It reports fits to two ensembles (ATLAS-based and TOTEM-based) in a Regge model with Pomeron, Odderon, and secondary Reggeons, and claims that the eikonal scheme is sensitive to the inclusion of dσ/dt data with |t| > 0.1 GeV^2, yielding a small Pomeron trajectory slope α'_P ≈ 0.011 GeV^-2 in both ensembles, whereas the U-matrix scheme is stable. The paper presents Table I of best-fit parameters and Figure 1 comparing total cross sections, ρ, and differential cross sections.","tokens_in":6555,"tokens_out":5652,"duration_ms":52156,"significance":"If substantiated, the result would be relevant to the long-standing question of the soft Pomeron slope and to scheme dependence in unitarization. The paper's explicit analytic formalism, the simultaneous treatment of σ_tot, ρ, and dσ/dt in two modern LHC data ensembles, and the clean separation of ATLAS and TOTEM data are strengths. However, the central sensitivity claim currently rests on a qualitative comparison with Ref. [1] and does not provide the statistical evidence needed to distinguish a genuine data effect from parameter degeneracy or model assumptions. The central thesis is defensible but requires additional quantitative support rather than a fundamentally flawed derivation.","major_comments":[{"comment":"The central claim that eikonal unitarization is sensitive to dσ/dt data for |t| > 0.1 GeV^2 is not backed by a quantitative comparison. The paper reports α'_P ≈ 0.011 GeV^-2 for both ensembles in the eikonal scheme, but it does not reproduce the Ref. [1] fits restricted to |t| ≤ 0.1 GeV^2, quote the corresponding parameter values, or give the change in χ^2 (or a pull) for the shifts in α'_P and aP. Without a nested fit over t-ranges or an equivalent statistical test, the reader cannot determine whether the small α'_P is a significant data-driven effect or a consequence of parameter correlations.","section":"Section III, Table I and final paragraph"},{"comment":"α'_P appears degenerate with the vertex parameter aP. In the eikonal fits, aP = 0.47 ± 0.11 GeV^-2 (Ensemble A) and 0.53 ± 0.24 GeV^-2 (Ensemble T); at |t| ~ 0.2 GeV^2 the vertex factor (1 − t/aP)^-1 produces a much stronger t-dependence than α'_P ln(s/s0), while the U-matrix Ensemble A solution with aP ≈ 40 GeV^-2 and α'_P ≈ 0.26 GeV^-2 shows a different balance. A profile likelihood in (α'_P, aP) or at least the parameter correlation matrix is needed to show that the reported small α'_P is determined by the data rather than by the chosen functional form of βP(t).","section":"Table I and Eq. (15)"},{"comment":"The fixed inputs α'_+ = α'_− = 0.9 GeV^-2, r_+ = r_− = 4.0 GeV^-2, and ξ_O = −1 are adopted without stability tests. The sensitivity claim concerns precisely the low-|t| region where these fixed secondary-Reggeon and Odderon inputs contribute, so the robustness of the eikonal result should be checked by repeating the fits with conservative variations of these parameters or by reporting their correlations with α'_P. Without such a check, the reported sensitivity could be an artifact of the model space rather than a property of the data.","section":"Section II, paragraph after Eq. (17)"}],"minor_comments":[{"comment":"The text says α'_+ and α'_− are fixed at 0.9 GeV^-1; the units should be GeV^-2.","section":"Section II"},{"comment":"The phrase 'χO(s,b) represents the Odderon's phase factor' is imprecise; χO is the transformed Born amplitude and ξO = −1 is the phase factor.","section":"Eq. (17)"},{"comment":"The quoted uncertainties are not defined; specify whether they are 1σ errors from the χ^2 minimum and how they relate to the 90% confidence intervals described in Section III.","section":"Table I"},{"comment":"The ensembles are described in terms of TOTEM/ATLAS dσ/dt data, but the text also refers to PDG σ_tot and ρ data; clarify which σ_tot and ρ points are assigned to each ensemble.","section":"Section III, ensemble definitions"},{"comment":"The caption is minimal; specify the t-intervals shown, the data sets in each panel, and which curves correspond to the eikonal and U-matrix schemes.","section":"Figure 1"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is a short conference write-up. The missing baseline fits and profile likelihoods are likely feasible within the existing framework and should be requested before publication. I see no concerns about the integrity of the analysis, but the paper relies heavily on the authors' own prior work, Ref. [1], without making the comparison self-contained."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a proceedings-style extension of the authors' earlier global fit, widening the dσ/dt range from |t| ≤ 0.1 to |t| ≤ 0.2 GeV². The interesting outcome is that the eikonal and U-matrix unitarization schemes behave very differently: the eikonal fits drive α'_P to ~0.011 GeV⁻² in both the ATLAS and TOTEM ensembles, while U-matrix keeps larger values. That is a genuinely notable scheme dependence.\n\nWhat the paper does well: the formalism is explicit, the two data ensembles are cleanly separated, the χ²/ν values are reported, and the fixed secondary-Reggeon parameters are stated with a rationale. The authors are upfront about the TOTEM/ATLAS tension. As a phenomenological exercise, it is competent.\n\nThe soft spot is the central claim. The abstract and Section III say the eikonal scheme is “sensitive” to dσ/dt data for |t| > 0.1 GeV², but the paper never shows a fit restricted to the old range. No baseline parameter values from Ref. [1] are quoted, no Δχ² or significance for the shift in α'_P is computed. The only evidence is a comparison to memory. That is not enough to establish sensitivity.\n\nThere is also a degeneracy issue. In the eikonal fits, aP is ~0.5 GeV⁻² with |t| up to 0.2 GeV², so (1 − t/aP)⁻¹ has real t-dependence that can mimic a small α'_P. A profile likelihood in (α'_P, aP) or a nested t-range fit would settle whether the small slope is data-driven or a fitting artifact. The quoted errors on α'_P (0.004–0.005) are not a substitute, because they are within a single fit, not across ranges.\n\nThe final remark connecting small α'_P to a perturbatively calculable soft Pomeron is speculative and goes beyond the evidence. I would keep it as a remark, not a conclusion.\n\nWho is this for? Specialists in soft-scattering phenomenology who want to see one more data point in the eikonal-versus-U-matrix debate. It is a useful addendum to Ref. [1], not a standalone strong result.\n\nRecommendation: send it to peer review as a short paper, but a serious referee should require (1) a reproduction of the |t| ≤ 0.1 GeV² fits, (2) a quantitative comparison, and (3) a check of the α'_P–aP degeneracy. With those, the sensitivity claim could become credible; without them, it is plausible but unproven.","headline":"A legitimate but under-supported sensitivity study: the eikonal α'_P ≈ 0.011 GeV⁻² result needs a proper baseline comparison and a check against degeneracy with aP before it can be called data-driven.","tokens_in":7034,"tokens_out":3526,"would_cite":false,"duration_ms":33557,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["12.40.Nn","13.85.Lg","13.85.-t"],"model":"deepseek-v4-flash","headline":"This paper reports that adding differential cross-section data out to 0.2 GeV² makes eikonal unitarization fits return a nearly flat Pomeron trajectory, slope about 0.011 GeV⁻², in both ATLAS- and TOTEM-based ensembles, while U-matrix…","keywords":["elastic pp scattering","eikonal unitarization","U-matrix unitarization","Pomeron trajectory","Odderon","Reggeon exchange","LHC differential cross sections"],"falsifier":"Refit Ensembles A and T with the secondary-Reggeon slopes $\\alpha'_{\\pm}$ and vertex slopes $r_{\\pm}$ freed, and check whether the eikonal scheme still returns $\\alpha'_P \\approx 0.011\\,\\mathrm{GeV}^{-2}$ in both ensembles; if the small slope moves by more than its quoted uncertainties, the central claim is an artifact of fixed inputs. A second check is to replace the power-like proton-Pomeron vertex of Eq. (15) with an exponential form and see whether the scheme sensitivity persists.","tokens_in":5925,"feed_emoji":"⚛️","tokens_out":11593,"duration_ms":94173,"temperature":0.7,"pith_summary":"This paper asks whether the extracted Pomeron and Odderon parameters depend on how much of the elastic differential cross section enters the fit. It extends an earlier global analysis of proton-proton and proton-antiproton scattering from momentum transfers $|t| \\le 0.1$ GeV$^{2}$ to $|t| \\le 0.2$ GeV$^{2}$, using two data ensembles built around ATLAS and TOTEM measurements and two unitarization schemes, eikonal and $U$-matrix. The central finding is that the eikonal scheme is sensitive to the added $|t| > 0.1$ GeV$^{2}$ data: both ensembles then prefer a nearly flat Pomeron trajectory, $\\alpha'_P \\approx 0.011\\,\\mathrm{GeV}^{-2}$, close to screened-Regge expectations. The $U$-matrix scheme, by contrast, reproduces the previous results with little change, and the Odderon phase factor $\\xi_O = -1$ remains favored. The authors read the small eikonal slope as compatible with treating the soft Pomeron perturbatively in the context of Gribov's Reggeon calculus.","feed_headline":"Eikonal unitarization collapses the soft Pomeron slope to ~0.011","feed_subtitle":"Adding LHC differential data out to 0.2 GeV² drives a near-flat trajectory.","key_machinery":"The carrier of the argument is the pair of unitarization relations in impact-parameter space. Starting from Born amplitudes $\\chi^{pp}_{\\bar{p}p}(s,b)$ built from Pomeron, Odderon, and secondary Reggeon exchanges, the eikonal scheme constructs the physical amplitude as $H = i(1 - e^{i\\chi})$, while the $U$-matrix scheme uses $H = \\chi/(1 - i\\chi/2)$, and both are Fourier-Bessel transformed back to momentum space to compute $\\sigma_{\\rm tot}$, $\\rho$, and $d\\sigma/dt$. The Pomeron trajectory in Eq. (13) includes a pion-loop term $h(\\tau)$, and the proton vertices for Pomeron and Odderon are power-like rather than exponential. The two analytic re-summations respond differently when the differential cross-section range is widened: eikonalization amplifies the influence of the new $|t| > 0.1$ GeV$^{2}$ points and drives $\\alpha'_P$ down to about $0.011$ GeV$^{-2}$, whereas the $U$-matrix relation keeps the fitted trajectory close to its previous value.","core_discovery":"The paper's central claim is that the eikonal unitarization scheme is sensitive to the input $d\\sigma/dt$ data for $|t| > 0.1$ GeV$^{2}$ in both Ensembles A (ATLAS) and T (TOTEM), yielding a very small Pomeron slope $\\alpha'_P \\approx 0.011\\,\\mathrm{GeV}^{-2}$ in both ensembles. Under the $U$-matrix scheme the same extended data leave the parameters close to those of the earlier $|t| \\le 0.1$ GeV$^{2}$ analysis, with the previously favored Odderon phase factor $\\xi_O = -1$ retained. The authors present this as an extension of their earlier work, and they interpret the small eikonal slope as aligned with screened-Regge models and with the possibility of treating the soft Pomeron in a perturbative QCD framework.","pith_inferences":["An unstated consequence of the small eikonal slope is that the soft Pomeron may not be a simple Regge pole; the fitted trajectory could be an effective screened quantity, so comparisons with nonperturbative QCD calculations should distinguish bare and screened trajectories.","Because the two schemes diverge most in the interval $0.1 < |t| < 0.2$ GeV$^{2}$, that window is a natural discriminator, and higher-statistics LHC measurements there could decide which unitarization is closer to the data.","The fixed secondary-Reggeon slopes and vertex slopes are the main modeling assumptions; an independent fit that frees them would show whether the eikonal sensitivity is genuinely data-driven or an artifact of those constraints.","Applying the same two-ensemble procedure to a wider momentum range, say $|t| \\le 0.3$-$0.4$ GeV$^{2}$, would test whether the eikonal $\\alpha'_P$ continues to decrease or stabilizes."],"forward_implications":["Under the eikonal scheme, both the ATLAS- and TOTEM-based ensembles return a nearly flat Pomeron trajectory, $\\alpha'_P \\approx 0.011\\,\\mathrm{GeV}^{-2}$, bringing the extracted trajectory close to values obtained in screened-Regge models.","The eikonal fits place most of the cross-section growth in the Pomeron intercept, $\\epsilon \\approx 0.117$-$0.123$, whereas the $U$-matrix fits return a larger slope and, for the ATLAS ensemble, a smaller intercept.","Extending $d\\sigma/dt$ to $|t| = 0.2$ GeV$^{2}$ leaves the $U$-matrix parameters essentially unchanged, so the earlier conclusions about the Odderon phase, $\\xi_O = -1$, remain intact under that scheme.","The scheme dependence means future Pomeron extractions must state which unitarization prescription was used; eikonal and $U$-matrix parameter sets are not interchangeable."],"supporting_citations":[{"why":"It is the earlier global analysis whose formalism, statistical methods, and |t| ≤ 0.1 GeV² baseline results this paper extends.","marker":"[1]"},{"why":"These references supply the Pomeron trajectory form, including the pion-loop term h(τ) used in Eq. (13).","marker":"[2–7]"},{"why":"They are the screened-Regge analyses that return very small Pomeron slopes, which the paper compares with its eikonal result, and they also provide fixed secondary-Reggeon parameter values.","marker":"[4, 5]"},{"why":"It is the PDG compilation of total cross-section and ρ data used to build both Ensembles A and T.","marker":"[11]"},{"why":"These TOTEM papers provide the differential cross-section data at 7, 8, and 13 TeV that define Ensemble T.","marker":"[12–17]"},{"why":"These ATLAS papers provide the differential cross-section data at 7, 8, and 13 TeV that define Ensemble A.","marker":"[18–20]"},{"why":"It is the earlier determination of the secondary-Reggeon trajectory and vertex slopes that the fits hold fixed.","marker":"[25]"}],"fun_headline_variants":["Eikonal scheme shrinks Pomeron slope to 0.011","Extended data flattens Pomeron trajectory in eikonal model","Eikonal unitarization yields near-zero Pomeron slope","New |t| data forces Pomeron slope down to 0.011","Soft Pomeron slope collapses in eikonal scheme"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The fits assume that the fixed secondary-Reggeon slopes $\\alpha'_{\\pm} = 0.9\\,\\mathrm{GeV}^{-2}$, the fixed vertex slopes $r_{\\pm} = 4.0\\,\\mathrm{GeV}^{-2}$, and the specific vertex forms of Eqs. (12) and (15) are correct; if those modeling choices are wrong, the reported eikonal sensitivity and the very small Pomeron slope could be artifacts of the model rather than features of the data.","fun_headline_variants_meta":{"raw":{"variants":["Eikonal scheme shrinks Pomeron slope to 0.011","Extended data flattens Pomeron trajectory in eikonal model","Eikonal unitarization yields near-zero Pomeron slope","New |t| data forces Pomeron slope down to 0.011","Soft Pomeron slope collapses in eikonal scheme"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000151,"raw_usage":{"total_tokens":1111,"prompt_tokens":765,"completion_tokens":346,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":381,"completion_tokens_details":{"reasoning_tokens":256}},"tokens_in":381,"tokens_out":346,"duration_ms":3530,"temperature":1.0,"reasoning_tokens":256,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T14:37:21.792618+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Refit Ensembles A and T with the secondary-Reggeon slopes $\\alpha'_{\\pm}$ and vertex slopes $r_{\\pm}$ freed, and check whether the eikonal scheme still returns $\\alpha'_P \\approx 0.011\\,\\mathrm{GeV}^{-2}$ in both ensembles; if the small slope moves by more than its quoted uncertainties, the central claim is an artifact of fixed inputs. A second check is to replace the power-like proton-Pomeron vertex of Eq. (15) with an exponential form and see whether the scheme sensitivity persists.","supporting_citations":[{"cited_title":"Maneyro, E","cited_arxiv_id":null,"evidence_quote":"It is the earlier global analysis whose formalism, statistical methods, and |t| ≤ 0.1 GeV² baseline results this paper extends."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"It is the PDG compilation of total cross-section and ρ data used to build both Ensembles A and T."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"It is the earlier determination of the secondary-Reggeon trajectory and vertex slopes that the fits hold fixed."}],"review_version":1}