{"id":"46c451fb-3499-44d6-bc0a-4a0d61f91ebb","arxiv_id":"2607.16907","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A geometric-scaling model with a crossing-odd amplitude and a maximal-Odderon correction can reproduce low-energy rho data and accommodate the TOTEM 13 TeV rho_pp measurement.","lead":"Using a geometric-scaling model of proton scattering, the paper derives simple formulas connecting the rho parameter to total cross-sections and shows that a small Odderon-shaped correction to antiproton-proton scattering can explain the low rho value measured by TOTEM at 13 TeV. It offers a minimal, model-dependent way to reconcile the debated Odderon hypothesis with precision LHC forward-scattering data.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Stated Odderon parameters raise rho_pp at 13 TeV, opposite to the TOTEM deficit","rationale":"The reader's weakest_assumption focuses on the untested C-odd geometric-scaling Ansatz (Eq. 6). That is a legitimate concern about theoretical foundations, but it is not the most load-bearing issue for the central claim. The paper's own numerical example, as defined by Eqs. (16)-(19) with A=0.08, s3=1 TeV, q=-0.2, moves ρ_pp in the wrong direction: the additional terms in the numerator of Eq. (18) are positive, increasing ρ_pp at 13 TeV from ~0.140 to ~0.148, while the data demand a decrease to ~0.10. This is an internal inconsistency in the quantitative claim, independent of whether Eq. (6) holds. Even if the sign of the f terms were flipped, the magnitude of the shift (~0.007) is an order of magnitude too small to account for the ~0.04 discrepancy. Therefore the abstract's assertion that the modification accommodates the 13 TeV ρ_pp data is not supported by the presented equations. This is a concrete, checkable failure of the central claim, warranting rejection unless the authors can supply a corrected parametrization and/or fit that actually lowers ρ_pp to the measured value.","tokens_in":8560,"tokens_out":29247,"duration_ms":250218,"concrete_test":"Recompute ρ_pp at √s=13 TeV from Eq. (18) with A=0.08 mb, s3=1 TeV, q=−0.2 mb and compare to the value plotted in Fig. 2 and to the TOTEM/ATLAS measured 0.098±0.01. If the computed value is above ~0.14, the claimed accommodation fails. Then scan A∈[−1,1] mb and s3∈[1,1000] GeV to find any parameter set that brings ρ_pp below 0.11; if none exists, the central phenomenological claim is unsupported.","verdict_should_be":"REJECT","load_bearing_attack":"The central numerical claim is not supported by the paper's own equations. With the stated choices A=0.08 mb, s3=1 TeV, q=-0.2 mb, the extra terms in Eq. (18), +(π/8)f'' + (1/(2π))f, are positive and increase ρ_pp. Using the COMPETE values: at √s=13 TeV, R^2≈55.108 mb, dR^2/dy≈4.797 mb, Q^2≈−0.1994 mb (from q=−0.2), so the unmodified ρ_pp is (π/2 dR^2/dy − Q^2)/(R^2 + (π/2)dQ^2/dy) ≈ (7.535+0.1994)/55.107 = 0.1403. The addition gives π/8·0.16 + (1/(2π))·2.105 ≈ 0.063+0.335 = 0.398 mb, yielding ρ_pp≈(7.534+0.199+0.398)/55.107≈0.1476—higher, not lower. Even if the sign were reversed, the shift would be only ~0.007 mb, far too small to bridge the gap to TOTEM/ATLAS (ρ≈0.098), which require a reduction of ~0.04. Thus the abstract's claim that this modification 'allows to accommodate ρ_pp 13 TeV data' is contradicted by the stated parametrization.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper extends geometric scaling ideas to the crossing-odd elastic amplitude by postulating T^-_el(s,t) = -s Q^2(-is) Ψ(|t|Q^2(-is)), and derives simple expressions for the total cross-sections and ρ parameters in terms of the interaction radii R^2 and Q^2 (Eqs. (9)-(12)). Using the COMPETE parametrization of σ_tot^{pp,pbarp} as input, the author states that the low-energy ρ data are reproduced. To address the 13 TeV TOTEM/ATLAS ρ_pp deficit, a maximal-Odderon term f(y)=A ln^2(s/s3) is added to σ_tot^{pbarp}; with A=0.08 mb, s3=1 TeV, q=-0.2 mb, the paper claims that ρ_pp moves down to the TOTEM/ATLAS values while total cross-sections are almost unchanged. The core claim is that this modification allows the Odderon interpretation of the 13 TeV data.","tokens_in":9035,"tokens_out":15919,"duration_ms":139773,"significance":"If correct, the paper would provide a simple analytic framework connecting geometric scaling, analyticity, and the Odderon, with explicit formulae that can be checked against data. The derivation of the forward relations is transparent and the algebra is easy to follow. However, the central numerical demonstration is incorrect, and the independent predictive content is weaker than claimed because the COMPETE input is already fitted to ρ data. The geometric-scaling form of the C-odd amplitude is not actually tested by forward data. These issues undermine the main conclusion as it stands.","major_comments":[{"comment":"The central numerical claim is contradicted by the paper's own equations. For the stated values (A=0.08 mb, s3=1 TeV, q=-0.2 mb) the extra term in the ρ_pp numerator of Eq. (18) is +(π/8)f'' + f/(2π). At √s=13 TeV, using COMPETE inputs, R^2≈55.12 mb, dR^2/dy≈4.80 mb, Q^2≈-0.199 mb, f≈2.10 mb, f''=0.16 mb. The unmodified ρ_pp is about 0.140, and the added term +0.398 mb raises it to about 0.148, not lowers it. The TOTEM/ATLAS value is ≈0.098, requiring a reduction of ≈0.04. Even with a reversed sign the shift is only -0.007, far too small. Thus the abstract's claim that this modification 'allows to accommodate ρ_pp 13 TeV data' is not supported by the stated parametrization.","section":"Odderon, Eqs. (18)-(19), Fig. 2"},{"comment":"The 'reproduction' of the low-energy ρ parameters is largely circular. The COMPETE parametrization (13) was fitted to data that include the ρ measurements, and the integration constant q in Eq. (15) is also adjusted to the same data. Therefore the agreement in Fig. 1 is partly inherited from the input. The text calls Eq. (12) 'parameter free', but q is a free parameter. The authors should clarify what genuinely new predictive content Eq. (12) has, for example by showing a prediction for energies not included in the COMPETE fit, or by testing the relation (12) with an independent σ_tot parametrization.","section":"Phenomenology, Eqs. (13)-(15)"},{"comment":"The forward data used in the paper cannot validate the geometric-scaling Ansatz (6) for the C-odd amplitude. At t=0 only the normalization Ψ(0)=1 enters, so Eqs. (11)-(12) test the analytic behavior of Q^2(y), not the scaling variable |t|Q^2. Therefore the statement 'This result proves that parametrization (6) is a highly probable possibility' is an overreach. A test of the scaling form requires the t-dependence of the C-odd amplitude, which is not analyzed here. The paper should either present such a test or soften the claim to say that the forward data are consistent with the analytic continuation (8) of the C-odd input.","section":"Geometric scaling / Phenomenology, Eq. (6)"}],"minor_comments":[{"comment":"The parameter s3 is quoted as 1 TeV, but s in the COMPETE parametrization is in GeV^2. Please specify whether s3 means (1 TeV)^2 or 1 TeV in mass units. This ambiguity affects the numerical results and the statement that σ_pbarp changes by '2–3 mb' at LHC energies.","section":"Odderon, Eq. (19)"},{"comment":"The text says for pbarp above 1 TeV the ρ parameter 'overshoots' the COMPETE parametrization. With the stated positive f and Eq. (18), the ρ_pbarp numerator changes by (π/8)f'' - f/(2π), which is negative for the chosen parameters, so ρ_pbarp is lower, not higher. Please check the figure and the description.","section":"Odderon, after Eq. (18)"},{"comment":"Calling Eq. (12) 'parameter free' is misleading because Q^2 contains the integration constant q from Eq. (15), which is fit to data. The relations are model-dependent through the choice of the COMPETE parameters and q.","section":"Eq. (12)"},{"comment":"The transformation (16) is called a 'gauge' freedom, but it changes the physical ρ parameters and modifies σ_pbarp, so it is not a gauge symmetry in the usual sense. Consider using a different term such as 'reparametrization'.","section":"Eq. (16)"}],"recommendation":"major_revision","confidential_remarks":"The algebraic framework in Eqs. (9)-(12) may still have value, but the paper cannot be accepted with the present numerical demonstration: the stated Odderon parameters move ρ_pp in the wrong direction and by far too little. The authors need to redo the phenomenological analysis, either with a proper fit or with a clear parameter scan, and temper the claims about geometric scaling of the C-odd amplitude."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear [Colleague],\n\nThe new thing here is the crossing-odd geometric-scaling Ansatz, Eq. (6), and the clean derivation of the rho/sigma relations in Eqs. (11)-(12). That part is solid and worth a look. The low-energy Reggeon description works, as the author notes, and the idea of a separate interaction radius Q^2(s) for the C-odd amplitude is a genuinely new tool.\n\nThe problem is the Odderon section. The author claims that f(y)=A ln^2(s/s3) with A=0.08 mb, s3=1 TeV, q=-0.2 mb allows them to 'touch' the TOTEM 13 TeV rho_pp data. But plugging those numbers into Eq. (18) gives the opposite: the extra terms +(pi/8)f'' + (1/(2pi))f are positive, raising rho_pp from about 0.140 to about 0.148, further away from the TOTEM/ATLAS value of ~0.098. I checked the algebra; the sign in the transformation (16) is correct. So the paper's central numerical claim is not supported by its own equations. Unless I'm misreading the figure, the dashed line in Fig. 2 must be going up, not down.\n\nThere's also a secondary issue: even if the sign were flipped, the shift is only ~0.007, while the gap to the data is ~0.04. So the proposed Odderon term, at least in this form, cannot accommodate the low rho_pp. The author also uses COMPETE, which already includes rho data in its fit, so the low-energy 'reproduction' is partly inherited rather than predicted. That's a circularity worth acknowledging, though not fatal.\n\nThe paper is honest about its limitations—it calls the C-odd GS assumption a test—but the Odderon conclusion rests on a numerical error. The author needs to redo the analysis with proper error propagation and correct the sign before this can be taken seriously. If fixed, the C-odd GS Ansatz might be a useful addition to the Odderon toolbox.\n\nWho is this for? People working on soft QCD and the Odderon puzzle. It's a short paper with a novel idea but a broken central claim. I'd send it to referees only after the author fixes the sign issue; in its current form it's a cautionary example of a sign error, not a contribution to the Odderon debate.\n\nRecommendation: reject in current form, but encourage a resubmission after correction.\n\nBest,\n[You]","headline":"Nice new Ansatz, but the Odderon accommodation claim is off by a sign—the stated parameters increase rho_pp instead of decreasing it.","tokens_in":9474,"tokens_out":8065,"would_cite":false,"duration_ms":63022,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["13.85.-t","13.85.Lg"],"model":"deepseek-v4-flash","headline":"Extending geometric scaling to the crossing-odd amplitude gives parameter-free rho relations, and adding a maximal-Odderon term accommodates the low 13 TeV proton-proton rho value.","keywords":["geometric scaling","Odderon","rho parameter","elastic proton-proton scattering","crossing symmetry","total cross section","C-odd amplitude","interaction radius"],"falsifier":"A decisive check is to measure the rho parameter or the total cross-section difference for proton-antiproton scattering at several TeV energies: the maximal-Odderon term predicts rho_pbarp to rise noticeably and sigma_pbarp to exceed sigma_pp by roughly 2-3 mb at LHC energies. If the measured values follow the unmodified parametrization instead, the proposed Odderon explanation fails. A second decisive check is to compare the t-dependence of the C-odd amplitude extracted from the forward relation with future differential cross-section data; if the scaling function Psi does not describe the dip","tokens_in":8467,"feed_emoji":"⚛️","tokens_out":8370,"duration_ms":74038,"temperature":0.7,"pith_summary":"This paper argues that geometric scaling, the idea that elastic scattering depends on energy through a single interaction radius, can be extended to the crossing-odd amplitude, giving it its own radius Q(s). From this, it derives closed formulas for the rho parameter (the ratio of the real to the imaginary forward amplitude) in terms of two interaction radii and their energy derivatives. With a standard fit to total cross sections, these formulas reproduce measured rho values for proton-proton and proton-antiproton scattering up to about 1 TeV, but undershoot the 13 TeV proton-proton point. The paper then adds a small maximal-Odderon term, proportional to ln-squared energy, to the antiproton cross-section and shows it shifts the 13 TeV prediction down to the measured value while altering total cross-sections by only a few millibarns. If correct, this supports the claim that a C-odd exchange, the Odderon, is present at LHC energies.","feed_headline":"Odderon term absorbs 13 TeV proton rho gap","feed_subtitle":"Extending geometric scaling to the crossing-odd signal ties rho to two interaction radii; an ln-squared correction lands on the LHC points.","key_machinery":"The central object is the geometric-scaling ansatz for the C-odd amplitude, T^-_el(s,t) = -s Q^2(-is) Psi(|t| Q^2(-is)), introduced as the odd counterpart of the even scaling amplitude. The workhorse maneuver is the analytic expansion -is = exp(y - i pi/2), which replaces the radius Q^2(-is) by Q^2(y) - (i pi/2) dQ^2/dy. This splits the amplitude into real and imaginary parts, so the rho parameter and total cross sections become algebraic functions of R^2, Q^2, and dR^2/dy. The paper then exploits a residual gauge freedom in Q^2 to insert an Odderon-shaped function f(y)=A ln^2(s/s3) into the antiproton cross-section while leaving the proton cross-section nearly unchanged.","core_discovery":"On the paper's own claims, the forward proton-proton and proton-antiproton amplitudes can each be split into crossing-even and crossing-odd pieces that both obey geometric scaling with separate interaction radii R^2 and Q^2. Analytic continuation of the energy variable converts the amplitude's phase into a derivative operator, yielding simple parameter-free relations between the rho parameter, the total cross sections, and the two radii. Fixing the radii from a standard parametrization of the sum and difference of the two total cross sections reproduces the low-energy rho data; only the 13 TeV proton-proton point is missed. Adding the maximal-Odderon function f(A ln^2) to the antiproton tota","pith_inferences":["The Odderon term is added by hand with parameters chosen rather than fitted; a global fit of the combined parametrization to all forward data would either sharpen the claimed magnitude or expose tensions with existing points.","The gauge freedom in the derivation means the same physical shift could be redistributed between proton and antiproton channels; if future data prefer a symmetric adjustment, the qualitative conclusion survives but the specific 2-3 mb prediction would not.","One could test assumption (6) directly by checking whether the t-dependence of elastic scattering at ISR energies, where C-odd Reggeon exchanges are sizable, follows the same scaling-law form with a single Q^2.","Because the paper only uses forward kinematics, the same C-odd scaling function should show up in the dip and bump structure of differential cross sections; extracting Psi there would provide an independent consistency check."],"forward_implications":["If the ansatz is right, no new model of the even amplitude is needed at 13 TeV; the rho deficit is naturally attributed to a C-odd, Odderon-like contribution.","The C-odd scaling function Psi and radius Q^2 make concrete predictions for the difference between pp and pbarp differential cross sections, testable in future runs or at facilities with antiproton beams.","The derivative expansion gives an analytic alternative to dispersion relations: future parametrizations of the total cross sections directly determine rho, bypassing numerical dispersion integrals.","Once the Odderon parameters are fixed, the same term predicts the size of the pp - pbarp total cross-section difference at LHC energies, turning the rho measurement into a quantitative Odderon probe.","The rho values for proton-antiproton scattering above 1 TeV, where no data exist, provide a sharp falsifiable prediction of the modified scenario."],"fun_headline_variants":["Odderon fills 13 TeV proton rho gap","Two radii plus Odderon fixes rho at 13 TeV","Geometric scaling + Odderon nails LHC rho","Odderon tweak to ppbar closes rho gap","Crossing-odd term in ppbar explains 13 TeV rho"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The whole rho-parameter machinery depends on the untested guess that the crossing-odd amplitude scales geometrically exactly like the even one, T^-_el(s,t) = -s Q^2(-is) Psi(|t| Q^2(-is)); the paper itself labels this a test.","fun_headline_variants_meta":{"raw":{"variants":["Odderon fills 13 TeV proton rho gap","Two radii plus Odderon fixes rho at 13 TeV","Geometric scaling + Odderon nails LHC rho","Odderon tweak to ppbar closes rho gap","Crossing-odd term in ppbar explains 13 TeV rho"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000284,"raw_usage":{"total_tokens":1469,"prompt_tokens":659,"completion_tokens":810,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":403,"completion_tokens_details":{"reasoning_tokens":733}},"tokens_in":403,"tokens_out":810,"duration_ms":7159,"temperature":1.0,"reasoning_tokens":733,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-01T19:34:06.967281+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A decisive check is to measure the rho parameter or the total cross-section difference for proton-antiproton scattering at several TeV energies: the maximal-Odderon term predicts rho_pbarp to rise noticeably and sigma_pbarp to exceed sigma_pp by roughly 2-3 mb at LHC energies. If the measured values follow the unmodified parametrization instead, the proposed Odderon explanation fails. A second decisive check is to compare the t-dependence of the C-odd amplitude extracted from the forward relation with future differential cross-section data; if the scaling function Psi does not describe the dip","supporting_citations":[],"review_version":1}