{"id":"d247c8b7-1dfc-4499-afb5-9bd96d4ec9bf","arxiv_id":"2411.15275","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":11,"one_line_summary":"A two-channel eikonal fit to low-|t| pp and ppbar data yields a small Odderon contribution (delta_rho <= 0.004) with sign opposite to pQCD, an order of magnitude below TOTEM's claim.","lead":"This paper fits proton-proton and proton-antiproton elastic scattering data at very low momentum transfer with a model that includes both the usual Pomeron and a C-odd Odderon exchange. It finds that the data prefer a small Odderon contribution, much smaller than the value used for the TOTEM Odderon discovery claim, and with a sign opposite to the perturbative QCD prediction.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The sign and smallness of the extracted Odderon contribution depend on an untested assumption that βO(t) is nonzero at t=0; footnote 2 concedes that a node at t=0 flips the sign, making the headline conclusion conditional on this form factor.","rationale":"The reader's weakest assumption identified the two-channel eikonal scheme and the fixed intercept αO(t)=1 as the main model-dependence. I find a narrower and more load-bearing issue: the assumed t=0 behavior of the Odderon coupling. Eq. (7) fixes βO(t) to a nonzero constant at t=0, and the paper's own footnote 2 states that if this coupling vanishes at t=0 the dominant C-odd contribution at the forward point comes from the Pomeron–Odderon cut with the opposite sign. Because the headline lessons include a specific sign opposite to pQCD and a small δρ, and because δρ is defined at t=0, this untested form-factor assumption directly controls the central conclusion. The reported χ² improvement (560 vs 726) is substantial and supports the presence of some C-odd contribution, so I do not reject the paper; but the sign and smallness claims are conditional on the βO(t) shape. A decisive check is to refit with a C-odd vertex that vanishes at t=0 and compare the extracted δρ and sign. This does not change the reader's CONDITIONAL verdict, but it sharpens the specific condition that must be verified.","tokens_in":3963,"tokens_out":6192,"duration_ms":66169,"concrete_test":"Refit the same data ensemble with βO(t) = βO(0) t e^{Dt/2} (or another C-odd proton form factor that vanishes at t=0), keeping the same χ² penalty and eikonal framework, and recompute δρ at 13 TeV plus the sign of the C-odd contribution to Re A at t=0. If the sign remains opposite to pQCD and δρ stays ≤ 0.004, the concern is resolved; if either changes, the paper's sign and smallness conclusions are specific to the exponential vertex and must be reworded.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claims — the Odderon sign opposite to pQCD and δρ ≤ 0.004 — rely on Eq. (7), where the C-odd proton vertex is βO(t) = βO(0) e^{Dt/2}, i.e. nonzero at t=0. The fit never tests whether βO vanishes or decreases strongly at t=0, and footnote 2 explicitly admits that in this case the dominant t=0 C-odd amplitude comes from the Pomeron–Odderon cut and 'has the opposite sign.' Since all fitted data are at finite |t| (the CNI region), the t=0 extrapolation is exactly where βO(0) and δρ are defined. Thus the quoted sign is not a model-independent extraction; it is a property of the chosen exponential form. The paper also quotes no uncertainty on δρ and reports large TOTEM normalization factors (N13 = 1.15), but the form-factor node is the more direct threat to the sign claim.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper analyzes proton-proton and proton-antiproton elastic scattering data in the Coulomb-nuclear interference region (|t| < 0.1 GeV^2, sqrt(s) = 50 GeV to 13 TeV) using a two-channel eikonal model that adds a C-odd Odderon exchange to the dominant C-even Pomeron. The authors report that including the Odderon improves the global chi^2 from 726 to 560 for 504 degrees of freedom, yielding a best-fit Odderon coupling beta_O(0) = 0.90 ± 0.18, with a slope D = A/2 fixed to half the Pomeron vertex slope. The central conclusion is that the required C-odd contribution to the forward real-to-imaginary ratio at 13 TeV is small, delta_rho <= 0.004, i.e. about ten times smaller than the value originally claimed by TOTEM, and that the sign of the extracted Odderon amplitude is opposite to the perturbative QCD three-gluon exchange prediction. The paper also finds large normalization rescaling factors for TOTEM data (up to N13 = 1.15).","tokens_in":4233,"tokens_out":2628,"duration_ms":24657,"significance":"If the result is robust, it would significantly constrain the size and sign of a possible high-energy Odderon contribution, and would provide a concrete quantitative bound that can be compared with model predictions. The paper's use of a two-channel eikonal to account for screening of the Odderon by Pomeron exchanges is a valuable feature, and the global fit includes both TOTEM and ATLAS/ALFA data with explicit normalization penalties. However, the strength of the claim is limited by the absence of a statistical significance test for the chi^2 improvement, by the very large normalization rescaling of TOTEM data, and by the fact that the sign and smallness of delta_rho depend on an untested assumption about the t-dependence of the Odderon-proton vertex.","major_comments":[{"comment":"The paper reports a chi^2 improvement from 726 to 560 when the Odderon is introduced, but no significance test (e.g., a likelihood-ratio or F-test accounting for the added parameters beta_O(0) and D, together with the free TOTEM normalization factors) is provided. Since the normalization factors themselves can absorb systematic offsets, the reader cannot judge whether the improvement is statistically meaningful. This is load-bearing for the central claim that the Odderon term is required by the data.","section":"Section III, Eq. (1), Table I"},{"comment":"The TOTEM normalization factors N7 = 1.077, N8 = 1.121, and N13 = 1.15 rescale the TOTEM data by up to 15%, which is far larger than the typical normalization uncertainties quoted by the experiments. With the 13 TeV TOTEM data multiplied by 1.15, the chi^2 improvement may be driven more by rescaling than by a physical Odderon contribution. The authors should demonstrate that the conclusion survives when the normalizations are constrained to their nominal values (or when the penalty terms are weighted more strongly), and should discuss the compatibility of N13 = 1.15 with the published TOTEM luminosity and normalization uncertainties.","section":"Section III, Table I and Fig. 1"},{"comment":"The sign of the Odderon contribution and the bound delta_rho <= 0.004 rely on the assumed form beta_O(t) = beta_O(0) e^{Dt/2}, which is nonzero at t = 0. The footnote concedes that if beta_O(t) vanishes or strongly decreases at t = 0, the dominant C-odd contribution at t = 0 comes from the Pomeron-Odderon cut and 'has the opposite sign.' Since all fitted data are at finite |t|, the t = 0 extrapolation is not tested by the fit. The paper should present fits with a node in beta_O(t) (e.g., beta_O(t) proportional to t or another form vanishing at t = 0) and report whether the sign and size of the extracted delta_rho are stable; as written, the quoted sign is a property of the chosen exponential vertex, not a model-independent extraction.","section":"Section IV and footnote 2"},{"comment":"The Odderon trajectory is fixed to alpha_O(t) = 1 and the screening is fixed to the specific two-channel eikonal form of Eq. (2). The paper tests only the dependence on the slope D, varying it from 0.1A to 0.9A, and does not explore alternative unitarization schemes or variations of alpha_O(0) and alpha'_O. The extracted beta_O(0) and the bound delta_rho <= 0.004 are therefore conditional on these model choices. The authors should either justify these choices in more detail or scan over a plausible range of alpha_O(0) and alpha'_O to quantify the resulting uncertainty on delta_rho.","section":"Section II and Section III"}],"minor_comments":[{"comment":"The bound delta_rho <= 0.004 is quoted without any uncertainty or confidence level; since beta_O(0) has a reported error, the final C-odd contribution should include a propagated uncertainty.","section":"Section IV"},{"comment":"There is a typographical error in the text following Eq. (7): 'beta_O(t)) = beta_O(0)e^{Dt/2}' contains a stray parenthesis; this should read 'beta_O(t) = beta_O(0)e^{Dt/2}'.","section":"Section II, Eq. (7)"},{"comment":"The paper states that ATLAS/ALFA 'confirmed' the TOTEM value of rho, but the ATLAS result is based on a different total cross-section value that is about 5% lower; it would be useful to state explicitly how the rho values compare after accounting for this difference.","section":"Section I"},{"comment":"The right panel of Fig. 1 shows the t-dependence at 13 TeV, but the vertical axis label is not visible in the reproduced figure; please ensure that the axis is labeled with the differential cross-section and its units.","section":"Section III, Fig. 1"}],"recommendation":"major_revision","confidential_remarks":"This is a short conference-proceedings style paper with strong quantitative claims. The core issue is that the headline results (the sign of the Odderon and delta_rho <= 0.004) depend on assumptions untested by the fit, and the statistical significance of the chi^2 improvement is not established. These are fixable with additional analysis, so I recommend major revision rather than rejection, provided the authors can address the concerns about significance testing, normalization sensitivity, and t=0 extrapolation."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Both the reader's report and the stress-test note land on the right spot. The paper's central claim—that a small Odderon with sign opposite to pQCD improves the low-|t| fit—is really a conditional statement, and the authors flag the condition in footnote 2. If βO(t) develops a node at t=0, the dominant C-odd contribution at t=0 comes from the Pomeron–Odderon cut and flips sign. Since the fitted data all sit at finite |t|, the t=0 extrapolation is doing all the work for δρ and for the sign. That is a load-bearing caveat, not a nuisance detail.\n\nWhat is genuinely new is applying the two-channel eikonal model to extract an Odderon term from the CNI region at collider energies, and the reported χ² improvement (726→560) is large. The paper also does something useful by treating TOTEM normalization factors as free parameters; the result that ATLAS normalizations sit near 1 while TOTEM needs N13=1.15 is worth knowing, even if the size of that rescaling invites caution. The comparison to the pQCD three-gluon sign is a legitimate external benchmark, but as the reader notes, the magnitude and sign are outputs of the same fit, not independent predictions.\n\nThe soft spots are mostly concentrated in what is not shown. No significance test is given for the added Odderon parameters, δρ is quoted as an upper limit with no uncertainty, and the trajectory is fixed at αO=1 with only the slope D varied (0.1A–0.9A). The D-independence of σtot and ρ is reassuring, but it does not address the node-in-βO scenario that footnote 2 concedes would flip the sign. That makes the headline conclusion—'sign opposite to pQCD, δρ≤0.004'—a property of the chosen exponential form, not a robust extraction.\n\nDespite these caveats, the paper is coherent and unusually honest for a conference proceeding: footnote 2 is exactly where too many authors would have buried the problem. The fit is plausible and the data handling is transparent. It deserves a serious referee—one who should ask for a node-βO fit, a proper likelihood treatment of the extra parameters, and uncertainties on δρ. I would bring it to a reading group if we are discussing Odderon phenomenology, and I would cite it once those caveats are addressed.\n\nSend it to peer review, with a recommendation for major revision rather than acceptance as is.","headline":"Serious and honest fit, but the Odderon sign and size are conditional on an untested t=0 form factor that the authors themselves concede in footnote 2.","tokens_in":4787,"tokens_out":2029,"would_cite":true,"duration_ms":20502,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Including a small Odderon exchange improves the fit to low-|t| elastic data, but its imprint on rho at 13 TeV is at most 0.004, ten times smaller than TOTEM's value.","keywords":["Odderon","elastic scattering","Coulomb-nuclear interference","two-channel eikonal model","rho parameter","Pomeron","LHC","low momentum transfer"],"falsifier":"Measure $\\rho$ for $pp$ and $\\bar p p$ at the same high energy with a total uncertainty below 0.002; if $|\\rho_{\\bar p p} - \\rho_{pp}|/2$ exceeds 0.004 at 13 TeV, the paper's central bound is falsified. A simpler check is to redo the fit with a single-channel eikonal or an alternative screening scheme and see whether the extracted $\\delta\\rho$ remains below 0.004.","tokens_in":3740,"feed_emoji":"⚛️","tokens_out":15330,"duration_ms":121507,"temperature":0.7,"pith_summary":"This paper tries to establish how large the Odderon—the charge-odd exchange that does not fall, or falls very slowly, with energy—can be in high-energy elastic proton scattering. The authors fit $pp$ and $\\bar p p$ data in the Coulomb-nuclear interference region, $|t| < 0.1$ GeV$^2$, over $\\sqrt{s} = 50$ GeV to 13 TeV, using a two-channel eikonal model that screens the Odderon by the Pomeron. Adding an Odderon with intercept $\\alpha_O(t) = 1$ lowers $\\chi^2$ from 726 to 560 for 504 degrees of freedom. The physical $C$-odd asymmetry in the forward real-to-imaginary ratio is $\\delta\\rho = (\\rho_{\\bar p p} - \\rho_{pp})/2 \\le 0.004$, an order of magnitude smaller than the value behind TOTEM's Odderon claim, and the needed sign is opposite to the perturbative QCD three-gluon exchange prediction. If correct, the Odderon exists at the LHC but is far weaker, and with a sign puzzle, than previously claimed.","feed_headline":"Odderon needed at LHC but 10 times weaker than TOTEM claimed","feed_subtitle":"Two-channel eikonal fit to low-|t| pp and ppbar data puts the C-odd rho shift at 0.004 or less.","key_machinery":"The carrying object is the two-channel eikonal amplitude (Eq. 2), built from an opacity $\\Omega(s,b) = \\Omega_P(s,b) + \\Omega_O(s,b)$. Each bare exchange is Fourier-Bessel transformed to impact parameter, and unitarization mixes two diffractive eigenstates through the coupling $\\gamma$; this is the mechanism that screens the seed Odderon by the C-even Pomeron. The Odderon input is $\\beta_O^2(t)\\, \\eta_O(t)\\, (s/s_0)^{\\alpha_O(t)}$ with the odd signature factor $\\eta_O(t) = -i e^{-i\\pi\\alpha_O(t)/2}$ and the trajectory fixed to the maximal QCD value $\\alpha_O(t) = 1$. The relative signs of the three unitarization terms in Eq. 2 control whether the physical $C$-odd contribution is suppressed and which sign it takes.","core_discovery":"The authors show that the global low-$|t|$ elastic dataset, including both TOTEM and ATLAS/ALFA measurements, is described better when a $C$-odd Odderon exchange with $\\alpha_O(t)=1$ is included in the two-channel eikonal amplitude: $\\chi^2 = 560$ for 504 degrees of freedom with the Odderon versus 726 without it. The best-fit Odderon-proton coupling is $\\beta_O(0) = 0.90 \\pm 0.18$, smaller than the Pomeron coupling, and after eikonal screening the final $C$-odd contribution to $\\rho$ at 13 TeV is $\\delta\\rho = (\\rho_{\\bar p p} - \\rho_{pp})/2 \\le 0.004$, not the $\\delta\\rho \\approx 0.04$ claimed by TOTEM. The required sign of the Odderon amplitude is opposite to that of the pQCD three-gluon exchange, and the paper suggests this can be reconciled if $\\beta_O(t)$ vanishes or strongly decreases at $t = 0$, in which case the dominant $C$-odd contribution at $t = 0$ comes from the Pomeron-Odderon cut with the opposite sign.","pith_inferences":["By extension, if the ATLAS/ALFA normalization is correct, the TOTEM normalizations needed here (1.077 to 1.15) suggest the apparent Odderon signal may be partly a normalization artefact; a single high-precision $\\rho$ measurement at 13 TeV with unified normalization would settle which dataset is right.","The same two-channel screening logic, applied to the diffractive dip region, predicts a specific $C$-odd asymmetry in $d\\sigma/dt$ between $pp$ and $\\bar p p$; measuring that asymmetry at the LHC or in a future collider would test whether the sign and size extracted here are correct.","A QCD determination of the Odderon intercept away from 1 would change the bound: a lower intercept makes the Odderon fade faster and pushes $\\delta\\rho$ lower, while a higher one would revive a TOTEM-sized effect."],"forward_implications":["The Odderon is not ruled out by low-$|t|$ data, but its physical imprint on the forward $\\rho$ parameter at 13 TeV is at most 0.004, an order of magnitude below the $\\delta\\rho = 0.04$ used in TOTEM's original Odderon claim.","The sign of the required $C$-odd amplitude is opposite to the bare perturbative three-gluon exchange, so the $t = 0$ $C$-odd effect would have to come from the Pomeron-Odderon cut if $\\beta_O(0)$ vanishes.","Including the Odderon improves the global fit from $\\chi^2 = 726$ to 560 for the same data, so future global analyses of elastic scattering should include a $C$-odd term even if its coupling is small.","The TOTEM normalizations come out well above unity, up to 1.15 at 13 TeV, so the absolute normalization of TOTEM data is a major driver of the extracted cross sections and $\\rho$ values."],"supporting_citations":[{"why":"Supplies the TOTEM 13 TeV total cross-section and $\\rho$ data that the low-$|t|$ fit must describe and that prompted the Odderon claim.","marker":"[1]"},{"why":"Supplies the ATLAS/ALFA 13 TeV data, whose lower total cross-section pulls the fitted $\\rho$ downward relative to TOTEM.","marker":"[3]"},{"why":"Provides the earlier global low-$|t|$ analysis whose dataset and normalization-parameter approach this paper extends with the Odderon.","marker":"[4]"},{"why":"Gives the pion-loop term $h(\\pi\\pi)$ inserted in the Pomeron trajectory used in Eq. (6).","marker":"[6]"},{"why":"Three references fixing the maximal QCD Odderon trajectory to $\\alpha_O(t) = 1$, an input fixed in the fit.","marker":"[7–9]"},{"why":"Three references giving the pQCD three-gluon exchange prediction whose sign the extracted Odderon contribution contradicts.","marker":"[10–12]"}],"fun_headline_variants":["Odderon improves fit but only a tenth of TOTEM's claim","Odderon contribution at rho is at most 0.004, not 0.04","TOTEM's Odderon claim ten times too large","Odderon real but rho shift at LHC < 0.004"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The bound depends on the specific two-channel eikonal screening formula and on the assumption that the Odderon grows with energy at the maximal QCD rate; change either, and the extracted Odderon coupling and the 0.004 bound move.","fun_headline_variants_meta":{"raw":{"variants":["Odderon improves fit but only a tenth of TOTEM's claim","Odderon contribution at rho is at most 0.004, not 0.04","TOTEM's Odderon claim ten times too large","Odderon real but rho shift at LHC < 0.004"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000662,"raw_usage":{"total_tokens":3040,"prompt_tokens":978,"completion_tokens":2062,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":594,"completion_tokens_details":{"reasoning_tokens":1976}},"tokens_in":594,"tokens_out":2062,"duration_ms":15559,"temperature":1.0,"reasoning_tokens":1976,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T14:38:21.930683+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure $\\rho$ for $pp$ and $\\bar p p$ at the same high energy with a total uncertainty below 0.002; if $|\\rho_{\\bar p p} - \\rho_{pp}|/2$ exceeds 0.004 at 13 TeV, the paper's central bound is falsified. A simpler check is to redo the fit with a single-channel eikonal or an alternative screening scheme and see whether the extracted $\\delta\\rho$ remains below 0.004.","supporting_citations":[{"cited_title":"Antchev et al","cited_arxiv_id":null,"evidence_quote":"Supplies the TOTEM 13 TeV total cross-section and $\\rho$ data that the low-$|t|$ fit must describe and that prompted the Odderon claim."},{"cited_title":"Aad et al., Eur","cited_arxiv_id":null,"evidence_quote":"Supplies the ATLAS/ALFA 13 TeV data, whose lower total cross-section pulls the fitted $\\rho$ downward relative to TOTEM."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the earlier global low-$|t|$ analysis whose dataset and normalization-parameter approach this paper extends with the Odderon."},{"cited_title":"Anselm and V.N","cited_arxiv_id":null,"evidence_quote":"Gives the pion-loop term $h(\\pi\\pi)$ inserted in the Pomeron trajectory used in Eq. (6)."}],"review_version":1}