{"id":"d2d46897-217b-46a8-b927-6a87f3074396","arxiv_id":"2608.12463","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"CP-odd spin-density-matrix observables and their optimal combination can probe top electric and chromo-electric dipole moments with projected reaches up to about 200 TeV at the HL-LHC, while the top-antitop discord asymmetry vanishes identically for these couplings.","lead":"This paper proposes using the reconstructed spin state of top-antitop pairs as a CP-violation search tool, extracting three CP-odd spin correlations and a statistically optimal combination that improves sensitivity to top electric and chromo-electric dipole moments. Detector-level simulations project reaches of 10-15 TeV at FCC-ee and 40-200 TeV at the LHC, and prove that a recently proposed quantum-discord asymmetry is blind to these couplings.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Detector-level reach projections rely on an unvalidated collapse of the background-subtracted limit Eq. (4.3) to the statistics-only Eq. (4.2); the paper's own SM-reference uncertainties are not shown to be subdominant.","rationale":"The reader's weakest assumption is exactly the most load-bearing soft spot: the quantitative projections depend on the unquantified collapse of Eq. (4.3) to Eq. (4.2). I agree with that identification, and I find additional support for it in the paper's own reported SM-reference uncertainties, which appear comparable to or larger than the expected statistical uncertainties of the physics samples. This concern affects the central quantitative claims (the 10-15 TeV FCC-ee reaches and the 40/200 TeV LHC reaches, and the comparison with T and sgnO1), while leaving the symmetry argument, the analytic density matrices, and the no-go theorem intact. The paper is transparent about the assumption and explicitly calls for future systematic studies, but as it stands the detector-level reach statements are optimistic. The reader's CONDITIONAL verdict is therefore appropriate, and my stress-test does not move it.","tokens_in":31388,"tokens_out":13132,"duration_ms":131048,"concrete_test":"Recompute the Oopt rows of Tables 4 and 6 using Eq. (4.3) instead of Eq. (4.2), setting sigma_SM to the quoted SM-reference uncertainties (0.05 and 0.03 at FCC-ee; 0.04 at the LHC) and adding one nuisance systematic, e.g. a 1% b-jet energy-scale shift profiled over its uncertainty. If the resulting 1/d95 for d_gamma and d_Z at FCC-ee falls by more than about 20% relative to the T row, or if the LHC Oopt reach drops below the sgnO1 reach, then the claimed superiority of tomographic observables over traditional observables is not robust.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 4 defines the correct 95% CL condition as |O_data - O_SM^ref| > 1.96 sqrt(sigma_stat^2 + sigma_SM^2 + sigma_syst^2), Eq. (4.3), and states that it collapses to the statistics-only Eq. (4.2) under conditions (i) O_SM^ref ~ 0 and (ii) sigma_SM, sigma_syst << sigma_stat. The paper verifies (i) but only asserts (ii). The quoted validation numbers in Secs. 5.2 and 6.2 (A_SM,reco_rn = 0.07 +/- 0.05 and DeltaB_SM,reco_n = 0.01 +/- 0.03 at FCC-ee; A_SM,reco_rn = -0.03 +/- 0.04 at the LHC) are consistent with zero, but the reported uncertainties are of the same order as, or larger than, the expected sigma_stat of the physics samples: at FCC-ee, sigma_Arn = 4.2 per event and N ~ 4 x 10^4 give sigma_stat ~ 0.02, below the quoted 0.05. Since the reach numbers in Tables 4 and 6 are computed from Eq. (4.2), any nonzero reconstruction bias or non-negligible sigma_SM/sigma_syst directly degrades 1/d95. The comparison with the triple product T and the quadruple product sgnO1 is particularly fragile at FCC-ee, where Oopt exceeds T by only about 20% (12-15 TeV versus 10 TeV). The theoretical CP-odd selection and the no-go theorem are not affected, but the headline reach numbers are optimistic upper bounds rather than validated experimental targets.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper develops a set of CP-odd observables constructed from the reconstructed spin density matrix of top-quark pairs, and uses them to project sensitivities to the top electric and chromo-electric dipole moments at FCC-ee and the LHC. The observables are the Fano-coefficient combinations Delta B_n, A_rn, A_kn of Eq. (2.5), which are argued to vanish in the CP-conserving SM and to receive contributions only from CP-violating dipole couplings at linear order. The paper also constructs an 'optimal observable' O_opt = f_1/f_0, the score of the SM hypothesis, proves its parton-level optimality in Appendix A, provides closed-form spin density matrices in Appendix B, and carries the analysis from parton level to a Delphes-based fast detector simulation. A no-go theorem is proved showing that the top-antitop discord asymmetry vanishes identically for the dipole operators, contradicting a recent claim. The projected 95% CL reaches are 10-15 TeV for the electroweak dipoles at FCC-ee and 40 (200) TeV for the chromo-EDM at LHC Run 2 (HL-LHC).","tokens_in":31735,"tokens_out":15472,"duration_ms":134975,"significance":"If the projected sensitivities hold, the paper provides a new class of CP-violation searches in top-quark production with competitive reach, and it clarifies the structure of quantum-information observables as CP probes through a clean no-go theorem. The analytic spin density matrices for e+e-, q qbar, and gg channels, cross-checked against MadGraph, are a useful resource. The optimality proof in Appendix A is a correct application of the score-function/CRB argument, and the SM-reconstruction checks show no spurious CP-odd bias. The main caveat is that the detector-level reach projections rely on an unvalidated assumption about the size of SM-reference and systematic uncertainties.","major_comments":[{"comment":"The collapse of the background-subtracted limit Eq. (4.3) to the statistics-only form Eq. (4.2) is not validated. Condition (ii) of that collapse requires sigma_SM and sigma_syst to be much smaller than sigma_stat, but the paper only verifies condition (i) and asserts (ii). The quoted SM-reference uncertainties are not subdominant: at FCC-ee, A_SM,reco_rn = 0.07 +/- 0.05 with sigma_Arn = 4.2 and N ~ 4x10^4 gives sigma_stat ~ 0.02, so the reported +/- 0.05 exceeds sigma_stat by a factor of 2.5. Including sigma_SM in Eq. (4.3) would degrade the A_rn reach by roughly sqrt(1+(0.05/0.02)^2) ~ 2.7, directly affecting the headline reaches in Tables 4 and 6, which are computed from Eq. (4.2). The authors should either generate a sufficiently large SM control sample to demonstrate sigma_SM << sigma_stat, or propagate sigma_SM into the quoted reaches.","section":"Sec. 4, Eq. (4.3); Secs. 5.2, 6.2"},{"comment":"The detector-level analysis uses only t tbar signal samples; no background samples are generated or included in the efficiency, dilution, or sigma_stat. Equation (4.3) mentions residual backgrounds, but the projections do not quantify them. At the LHC, Standard Model backgrounds such as W+W- and single top could dilute the CP-odd observables and increase the effective sigma_stat, potentially reducing the Run 2 and HL-LHC reaches beyond the ~20% effect inferred from the O1 validation in Sec. 6.2. The authors should either include a background estimate in the projections or state and justify the assumption that backgrounds are negligible.","section":"Sec. 4; Secs. 5, 6"}],"minor_comments":[{"comment":"The abstract contains grammatical errors: 'This sensitivities exceed those of the traditional observables currently used by experiments to use for these operators' should read 'These sensitivities exceed those of the traditional observables currently used by experiments for these operators.'","section":"Abstract and Sec. 1"},{"comment":"There are typos: 'teh model' should be 'the model' and 'describeb' should be 'described'.","section":"Sec. 2.2"},{"comment":"The phrase 'a st of realistic CMS-like selection criteria' should read 'a set of realistic CMS-like selection criteria'.","section":"Sec. 6.2"},{"comment":"The table row entries '1342' and '3842' appear as single numbers; based on the text and Table 4, these should be two entries ('13' and '42' for d_gamma; '38' and '42' for d_Z). Please correct the formatting.","section":"Table 1"}],"recommendation":"major_revision","confidential_remarks":"The theoretical core of the paper - the analytic density matrices, the optimality proof, and the discord no-go theorem - appears sound and well cross-checked. The main issue is the unvalidated statistics-only limit, which is load-bearing for the quoted reaches. This is fixable within the scope of the manuscript, so I recommend major revision rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nYou should know two things about this paper. First, the genuinely new result is the no-go theorem in Sec. 2.3: for the CP-violating top dipole operators at tree level, the discord asymmetry ΔD (and steering asymmetry) vanishes identically, because the density matrix is invariant under swap plus local complex conjugation. That is a clean, rigorous kill-shot for the claim in Ref. [38], and it looks right. Second, everything else—the CP-odd Fano combinations, the optimal observable, the use of f1/f0 as the score—is in the earlier literature (Bernreuther & Brandenburg, Atwood & Soni, Durieux et al.). The packaging is good, but the novelty is concentrated in the theorem more than in the tomographic program.\n\nWhat they do well: Appendix B gives closed-form spin density matrices for e+e-, qqbar, gg at SM, interference, and dipole-squared order. That is a useful reference, and they cross-checked it against MadGraph. The optimality proof in Appendix A is a clean Cramér–Rao argument. The detector-level study is honest about reconstruction dilution, and the validation of their O1 projection against the CMS limit is a nice sanity check.\n\nThe soft spot is the reach projections. Eq. (4.3) is the correct background-subtracted limit with SM-reference and systematic uncertainties. They then assert that sigma_SM and sigma_syst are negligible and quote the statistics-only Eq. (4.2). The SM-reference numbers they report, e.g. A_SM,reco_rn = 0.07 ± 0.05 at FCC-ee, have an uncertainty larger than the expected sigma_stat ~ 0.02 on the physics sample. So the collapse to Eq. (4.2) is not demonstrated. This matters: at FCC-ee the optimal observable beats the triple product by only ~20%, and a factor of 2.6 from sigma_SM alone would erase that. The reach tables are upper bounds, not validated experimental targets. They do flag this assumption in the text, so it is not hidden, but they let Eq. (4.2) drive the conclusions anyway.\n\nMinor: no public code or data artifacts, and a few typos in the abstract.\n\nBottom line: worth a serious referee. The no-go theorem alone justifies publication in JHEP. The projections should be revised, either by using a sufficiently large SM MC sample to make sigma_SM negligible or by quoting the reach with sigma_SM included, and the triple-product comparison should be redone on that basis.","headline":"A real no-go theorem for discord-based CP probes buried in an otherwise standard tomography paper whose reach projections rest on an unvalidated statistics-only assumption.","tokens_in":32312,"tokens_out":4787,"would_cite":true,"duration_ms":42759,"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":"The paper claims that CP-violating top-quark dipole moments can be probed cleanly through CP-odd Fano observables and an optimal weight $O_{\\rm opt}=f_1/f_0$, reaching 10–15 TeV at FCC-ee and 40–200 TeV at the LHC.","keywords":["top quark","CP violation","electric dipole moment","chromo-electric dipole moment","spin density matrix","quantum tomography","Fano coefficients","optimal observable"],"falsifier":"Measure the reconstructed CP-odd observables $A_{rn}$ and $O_{\\rm opt}$ on a large pure-Standard-Model dilepton top sample passed through the same kinematic-fit reconstruction and check whether the sample means are consistent with zero within the statistical error; any offset comparable to $\\sigma_{\\rm stat}$, or a systematic uncertainty of that size, would invalidate the projected reaches.","tokens_in":31170,"feed_emoji":"⚛️","tokens_out":9251,"duration_ms":77737,"temperature":0.7,"pith_summary":"The paper argues that the spin density matrix of top–antitop pairs, reconstructed from dilepton angular correlations, contains CP-violation observables that are exactly zero in the Standard Model and cleanly populated by the top-quark electric and chromo-electric dipole moments. Symmetry alone fixes which Fano coefficients are CP-odd: the normal-polarization difference $\\Delta B_n$ and the antisymmetric normal-plane correlations $A_{rn}$ and $A_{kn}$. The paper computes the production density matrix analytically for $e^+e^-$, $q\\bar q$, and $gg$ initial states, builds the statistically optimal per-event weight $O_{\\rm opt}=f_1/f_0$, and takes the whole program through fast detector simulation at the FCC-ee and the LHC. It projects 95% CL reaches on the inverse dipole couplings of $10$–$15$ TeV for the electroweak dipoles at FCC-ee and roughly $40$ TeV (Run 2) to $200$ TeV (HL-LHC) for the top chromo-EDM, exceeding the traditional triple- and quadruple-product observables. It also establishes a no-go result: the recently proposed top–antitop discord asymmetry vanishes identically for these couplings and cannot serve as a CP probe.","feed_headline":"Top-quark spin tomography reaches 200 TeV for CP violation","feed_subtitle":"CP-odd spin correlations read from dilepton decays outdo existing LHC probes of top dipole moments.","key_machinery":"The load-bearing object is the Fano decomposition of the $t\\bar t$ production spin density matrix, $\\rho=\\frac{1}{4}\\left(1\\otimes 1+\\sum_i B^+_i\\,\\sigma_i\\otimes 1+\\sum_j B^-_j\\,1\\otimes\\sigma_j+\\sum_{ij}C_{ij}\\,\\sigma_i\\otimes\\sigma_j\\right)$, evaluated in the helicity basis $\\{\\hat k,\\hat r,\\hat n\\}$ built from the top direction and the production plane. CP symmetry interchanges top and antitop and transposes $C$, so the CP-odd combinations are $\\Delta B_i=B^+_i-B^-_i$ and $A_{ij}=C_{ij}-C_{ji}$; naive time reversal leaves only $\\Delta B_n$, $A_{rn}$, and $A_{kn}$ as tree-level observables for the real dipoles. The paper supplies closed-form analytic expressions for the Fano coefficients in the SM, SM–dipole interference, and dipole-squared orders for all three production channels, and it defines the optimal observable $O_{\\rm opt}=f_1/f_0$ as the per-event ratio of the two density terms, which for a CP-odd dipole becomes the angle-weighted combination of $\\Delta B_n$, $A_{rn}$, and $A_{kn}$ and saturates the Cramér–Rao bound by a Cauchy–Schwarz argument.","core_discovery":"The central claim is that CP violation in the top dipole sector is carried, at tree level, entirely by a small set of Fano coefficients of the two-qubit $t\\bar t$ density matrix: the polarization difference $\\Delta B_n = B^+_n - B^-_n$ and the antisymmetric normal-plane correlations $A_{rn}=C_{rn}-C_{nr}$ and $A_{kn}=C_{kn}-C_{nk}$. These combinations are forced to zero by CP conservation in the Standard Model and in any CP-conserving extension, and the real electric and chromo-electric dipoles are the sole source that populates them at linear order; the paper verifies this pattern both analytically and in Monte Carlo. The paper further proves that the optimal weight $O_{\\rm opt}=f_1/f_0$, defined as the ratio of the linear-dipole to Standard-Model differential cross sections, is the most sensitive per-event observable, saturating the Cramér–Rao bound, and that after detector effects it still outperforms the conventional triple- and quadruple-product observables at both colliders. Finally, it proves a no-go theorem: for these couplings the top–antitop discord asymmetry vanishes identically, so quantum-information measures of the density matrix are blind to this CP violation at tree level.","pith_inferences":["The proof structure suggests a broader blindness theorem: any Hermitian tree-level new-physics operator that leaves the density matrix invariant under combined spin-swap and normal-axis reflection will produce zero discord, steering, and related correlation asymmetries, so CP probes based on those measures may be generically insensitive to tree-level CP violation.","The same Fano-coefficient logic could be transplanted to other two-qubit final states such as $W^+W^-$ or $\\tau^+\\tau^-$ pairs, where analogous CP-odd normal-plane correlations should exist and could be measured from angular distributions.","A data-driven calibration of the statistics-only assumption is testable: measure the CP-odd observables on CP-conserving control samples with the same reconstruction, and if a systematic offset of order $\\sigma_{\\rm stat}$ appears, the relative advantage of $O_{\\rm opt}$ over robust products would shrink; the paper leaves that quantification to experiments."],"forward_implications":["The tomographic observables $A_{rn}$ and $O_{\\rm opt}$ give LHC searches for the top chromo-EDM a detector-level reach beyond the conventional quadruple product: about $41$ TeV at Run 2 and $191$ TeV at HL-LHC.","At FCC-ee, the optimal observable projects sensitivity to electroweak dipole scales of $12$–$15$ TeV, with the parton-level reach growing monotonically if the collision energy is raised toward $1$ TeV.","The no-go theorem means discord, steering, and related correlation asymmetries should not be used as CP-violation probes in $t\\bar t$, since their $t\\leftrightarrow\\bar t$ asymmetries are forced to zero by the same structural conditions that hold for any Hermitian tree-level addition to the SM.","The same reconstructed spin density matrix used for entanglement measurements can be reweighted by $O_{\\rm opt}$ at no extra experimental cost, turning an existing quantum-tomography analysis into a CP search.","Because the CP-odd observable combinations vanish in the SM only up to negligible three-loop corrections, a nonzero measurement of any of them at the projected sensitivities would be an unambiguous discovery of new CP-violating physics."],"supporting_citations":[{"why":"Supplies the symmetry-based CP structure of the top-pair spin density matrix and the T-odd normal-plane observables the paper builds on.","marker":"[10]"},{"why":"Defines the helicity basis and the spin-correlation observables whose conventions the paper adopts at the LHC.","marker":"[12]"},{"why":"Establishes that dilepton angular correlations allow full spin-density-matrix reconstruction, the premise of the tomographic program.","marker":"[17]"},{"why":"Proposes the discord asymmetry whose vanishing for dipole couplings is the paper's no-go result.","marker":"[38]"},{"why":"Supplies the Monte Carlo event samples for the parton- and detector-level projections.","marker":"[41]"},{"why":"Introduces the $f_1/f_0$ ratio as the optimal observable for $e^+e^-\\to t\\bar t$ dipole searches, which the paper generalizes and proves optimal.","marker":"[49]"},{"why":"Develops per-coupling top-dipole optimal observables used as the basis of the optimal weight.","marker":"[53]"},{"why":"The existing LHC search whose quadruple-product reach is the baseline and validation point for the detector-level comparison.","marker":"[32]"}],"fun_headline_variants":["Tomographic spin probe spots top CP violation to 200 TeV","New spin observables expose top dipole CP violation at LHC","Quantum tomography of top pairs beats old CP probes","Top-antitop spin tomography: CP sensitivity to 200 TeV","Spin tomography unveils top CP violation at 200 TeV"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The quoted reaches assume that the detector-level Standard Model expectation of each CP-odd observable is exactly zero with negligible uncertainty and that detector systematics stay below the statistical uncertainty, so the background-subtracted limit reduces to the statistics-only formula.","fun_headline_variants_meta":{"raw":{"variants":["Tomographic spin probe spots top CP violation to 200 TeV","New spin observables expose top dipole CP violation at LHC","Quantum tomography of top pairs beats old CP probes","Top-antitop spin tomography: CP sensitivity to 200 TeV","Spin tomography unveils top CP violation at 200 TeV"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000806,"raw_usage":{"total_tokens":3585,"prompt_tokens":1036,"completion_tokens":2549,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":652,"completion_tokens_details":{"reasoning_tokens":2473}},"tokens_in":652,"tokens_out":2549,"duration_ms":15481,"temperature":1.0,"reasoning_tokens":2473,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T00:08:30.540635+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the reconstructed CP-odd observables $A_{rn}$ and $O_{\\rm opt}$ on a large pure-Standard-Model dilepton top sample passed through the same kinematic-fit reconstruction and check whether the sample means are consistent with zero within the statistical error; any offset comparable to $\\sigma_{\\rm stat}$, or a systematic uncertainty of that size, would invalidate the projected reaches.","supporting_citations":[{"cited_title":"Quantumness of top quark pairs produced at LHC within SMEFT framework","cited_arxiv_id":"2605.12033","evidence_quote":"Proposes the discord asymmetry whose vanishing for dipole couplings is the paper's no-go result."},{"cited_title":"Atwood and A","cited_arxiv_id":null,"evidence_quote":"Introduces the $f_1/f_0$ ratio as the optimal observable for $e^+e^-\\to t\\bar t$ dipole searches, which the paper generalizes and proves optimal."}],"review_version":1}