{"id":"fbef3472-2b4c-4487-8438-151b83a6177b","arxiv_id":"2608.04437","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"The naive-T-odd angular coefficients A6 and A7 in Drell-Yan production can constrain CP-violating combinations of electroweak and chromomagnetic quark dipole operators, at the O(0.1) level today and O(10^-3) at the HL-LHC.","lead":"Drell-Yan lepton pairs at the LHC carry three angular coefficients, A5-A7, that are almost zero in the Standard Model. This paper shows these coefficients can expose new CP-violating dipole interactions, with A6 and A7 at high transverse momentum being the most sensitive.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Omitted complex four-fermion operators could generate A5-A7 at O(1/Lambda^2), undermining the dipole-only claim.","rationale":"The reader identified the incomplete operator survey as the weakest assumption; my pass agrees and sharpens it. The central claim is that only the interference of electroweak and chromomagnetic dipole operators generates tree-level A5-A7 among dimension-six SMEFT operators, leading to O(1/Lambda^4) contributions and constraints on Im(C_qG C*_qZ). That claim is load-bearing because it determines both the physics interpretation and the numerical bounds. The Warsaw basis, however, contains four-fermion operators whose diagonal coefficients are not forced to be real when the operators are not self-conjugate. In particular, tensor and scalar semileptonic operators such as O_lequ^(3) and O_lequ^(1) carry complex coefficients and produce helicity-flipping amplitudes that can interfere with the SM amplitude. A nonzero interference term at O(alpha_s/Lambda^2) would dominate the O(1/Lambda^4) dipole-dipole contribution and make the extracted constraints non-exclusive. The proposed numerical test settles the question directly: if the projected A5-A7 are zero, the concern is dismissed; if nonzero, the paper must either include these operators or justify their absence. The chi-squared-correlation and Fig. 5 issues noted by the reader are real but secondary, since they affect the size and significance of the bounds rather than the existence and interpretation of the effect. I therefore keep the verdict CONDITIONAL pending the operator-survey check.","tokens_in":8376,"tokens_out":22069,"duration_ms":214300,"concrete_test":"Perform a complete tree-level SMEFT survey of q qbar -> l+ l- g in the Warsaw basis: generate the process with SMEFTsim (or an independent helicity-amplitude code) for m_ll in [80,100] GeV and the same p_T and rapidity bins as Figs. 2-3, setting Im(C_lequ^(3)) = 1 and similarly Im(C_lequ^(1)) = 1 with Lambda = 1 TeV and all other NP coefficients zero. If A5-A7 or the corresponding angular moments are nonzero at O(alpha_s/Lambda^2), the Sec. II uniqueness claim fails and the O(0.1) constraints in Fig. 4 are not dipole-specific. A null result would validate the paper's operator selection.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"Section II's assertion that \"At dimension six, this requirement uniquely singles out the quark dipole operators\" is the load-bearing step: the entire O(1/Lambda^4) dipole-interference interpretation and the resulting constraints in Fig. 4 depend on it. The requirement is that complex phases in tree-level production amplitudes feed A5-A7. This does not follow from a complete survey of the Warsaw basis. Semileptonic four-fermion operators with chirality-flipping Lorentz structures, such as O_lequ^(3) = (lbar sigma^{mu nu} e)(qbar sigma_{mu nu} u), are not self-conjugate, so their Wilson coefficients can be complex even for diagonal flavor. These operators contribute at tree level to q qbar -> l+ l- (+g), and the interference with the SM gamma*/Z amplitude contains Im(C_lequ^(3)) and can populate the imaginary off-diagonal elements of the dilepton spin-density matrix. The resulting contribution to A5-A7 is O(alpha_s/Lambda^2), one power of 1/Lambda^2 earlier than the dipole-dipole term, and would dominate for Lambda around 1 TeV. The paper provides no helicity or conjugation argument excluding such operators, and none of the numerical results in Figs. 2-5 include them. If this classification is incomplete, the claimed bounds on Im(C_qG C*_qZ) are biased and the complementarity argument in Sec. I is not established.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies the naive-T-odd angular coefficients A5–A7 in Drell–Yan lepton-pair production as probes of CP-violating new physics in the SMEFT. The authors argue that the leading tree-level SMEFT contribution from dimension-six operators is the O(1/Lambda^4) interference between electroweak Z-dipole and chromomagnetic quark-dipole amplitudes, controlled by Im(C_qG C*_qZ). Using public ATLAS 8 TeV and CMS 13 TeV measurements of A5–A7, they derive individual 68% C.L. constraints on the up- and down-type combinations at the O(0.1) level for Lambda = 1 TeV, and they project an improvement to O(10^-3) at the HL-LHC under statistically dominated uncertainties. The central numerical results are presented in Figs. 2–5, with a chi-square analysis defined in Eq. (10).","tokens_in":8702,"tokens_out":15336,"duration_ms":153726,"significance":"If the calculation and the operator classification are correct, the paper identifies a useful complementary observable for CP-violating dipole interactions: A6 and A7 at high dilepton pT are shown to be considerably more sensitive than A5, and the use of already-existing LHC measurements is a practical advantage. The O(1/Lambda^4) dipole-interference mechanism is a coherent and nontrivial observation that deserves attention. However, the significance is conditional on an operator-completeness claim that is not demonstrated: the paper asserts without a full Warsaw-basis survey that only quark dipole operators contribute at dimension six. Because the semileptonic tensor operator O_lequ^(3) can have a complex coefficient and contributes at O(1/Lambda^2) through interference with the SM amplitude, the dipole-only interpretation of the extracted constraints is not yet established. The numerical results are also not reproducible from the text because the SMEFT expressions and Monte Carlo setup are omitted.","major_comments":[{"comment":"The claim that, among dimension-six operators, 'this requirement uniquely singles out the quark dipole operators' is not supported by a complete operator analysis and appears to be incorrect as stated. In the Warsaw basis, the semileptonic tensor operator O_lequ^(3) = (lbar sigma^{mu nu} e)(qbar sigma_{mu nu} u) is not self-conjugate, so its Wilson coefficient can be complex even for diagonal flavor. This operator contributes at tree level to q qbar -> l+ l- and, together with an extra gluon emission, to the pT^ll > 0 angular distribution. The interference of this amplitude with the SM gamma*/Z amplitude contains the combination Im(C_lequ^(3)) times real matrix elements and has the helicity structure required to populate the imaginary off-diagonal elements of the dilepton spin-density matrix probed by A5–A7. The resulting contribution is O(alpha_s/Lambda^2), parametrically larger than the O(1/Lambda^4) dipole-dipole interference for Lambda ~ 1 TeV. The paper provides no helicity or conjugation argument excluding O_lequ^(3) and related operators. This omission is load-bearing: the constraints in Fig. 4 would be biased if such four-fermion operators are present, and the complementarity argument in Secs. I and IV is not established.","section":"Sec. II, discussion following Eq. (8)"},{"comment":"The central numerical constraints are not reproducible from the manuscript. The analytic expressions for the SMEFT contributions A5^{SMEFT}, A6^{SMEFT}, A7^{SMEFT} are not given, and the Monte Carlo specifications are absent: the generator or framework, the QCD order of the SM background, the PDF set, the lepton and jet selection cuts, the binning in pT^ll and y^ll, and the treatment of electroweak corrections are not stated. The theoretical uncertainty delta_Ath in Eq. (10) is introduced but its numerical values and scale-variation prescription are not provided. For the combination of ATLAS 8 TeV and CMS 13 TeV data, the treatment of experimental systematic uncertainties, bin-to-bin correlations, and correlations among A5–A7 is also unspecified. Without these details, the O(0.1) constraints in Fig. 4 and the post-fit agreement shown in Fig. 5 cannot be verified independently.","section":"Sec. III, Eq. (10) and Figs. 2–5"},{"comment":"The HL-LHC projection to O(10^-3) is fragile for two reasons. First, the assumption that uncertainties are 'purely statistical' is not justified for high-pT angular coefficients, where systematic uncertainties in lepton reconstruction and background estimates typically dominate; the paper does not show that the current systematic components scale with luminosity. Second, the SM prediction at 14 TeV is evaluated at O(alpha_s) and corrected by a k-factor obtained at 13 TeV, whereas the A5–A7 SM background relevant for the pseudo-data is quoted at O(alpha_s^2); the mismatch in perturbative order is not addressed. These issues do not necessarily invalidate the projection, but they make the stated order-of-magnitude improvement less robust than the abstract implies.","section":"Sec. III, Case-II pseudo-data projection"}],"minor_comments":[{"comment":"The variable pT^ll in Eq. (9) is used before it is defined; please define the dilepton transverse momentum and clarify that m_T^Z is the transverse mass of the dilepton system.","section":"Sec. III, Eq. (9) and Fig. 2"},{"comment":"The phrase 'regularized data' in the first scenario is vague; specify what regularization is applied to the ATLAS measurements and why.","section":"Sec. III, scenario list"},{"comment":"The statement that including the dipole contribution 'improves the agreement' is a post-fit consistency check; please provide a quantitative goodness-of-fit or delta-chi^2 value for the SM-only versus SM+dipole hypotheses.","section":"Sec. III, Fig. 5"},{"comment":"Reference [18] is cited as a 2026 CMS preprint without journal information; if it is an unpublished preprint, state this explicitly, and verify the arXiv number format.","section":"References"},{"comment":"There are minor typographical and formatting issues, including the section heading 'DRELL-Y AN' and inconsistent spacing in expressions such as 'O(α2 s)'; these should be corrected in a revision.","section":"Throughout"}],"recommendation":"major_revision","confidential_remarks":"The main risk is the operator-completeness claim: if O_lequ^(3) and similar semileptonic four-fermion operators contribute at O(1/Lambda^2), the dipole-only interpretation and the numerical constraints are not valid as absolute statements. The authors should either perform a complete Warsaw-basis analysis and include the leading four-fermion contributions, or explicitly restrict the scope and reframe the results as constraints on dipole combinations under the assumption that interfering four-fermion operators are absent. The paper's dipole calculation itself appears coherent, so a major revision rather than rejection seems appropriate."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Take a look before trusting the numbers. The paper is the first to connect the measured A5-A7 coefficients to CP violation from the product of weak and chromomagnetic quark dipoles. The mechanism is concrete, the existing data are public, and the HL-LHC projection to O(10^-3) is a useful benchmark. But the paper carries a load-bearing claim that only dipole operators can contribute at dimension six. That is not demonstrated, and it is likely false. Operators like O_lequ^(3) are not self-conjugate; their Wilson coefficients can be complex. They enter q qbar -> l+ l- (+g) at tree level and, on a first pass, the interference with the SM contains Im(C) and feeds the imaginary off-diagonal elements that generate A5-A7. That contribution is O(alpha_s/Lambda^2), one power of Lambda^2 less suppressed than the dipole-dipole term. The paper gives no helicity or conjugation argument excluding them. If they are present at O(1) coefficients, the constraints in Fig. 4 are not on dipole combinations alone, and the complementarity to EDM bounds is overstated. What is genuinely good: the chirality-flip counting that makes a single dipole insertion ineffective is correct, and within the dipole-only sector the direction of the effect (A6/A7 growing at large p_T) is physically sensible. The ATLAS/CMS comparison in Fig. 5 is interesting. But the numerical analysis is under-documented: no analytic expressions for the SMEFT contributions, no Monte Carlo setup, and the chi-squared in Eq. (10) treats all points as independent, ignoring correlations. The 'improves agreement' statement is not quantified. I would send this to a referee, but the referee's first task is to get the authors to confront the four-fermion operator issue. If they can show those contributions vanish (or are negligible under stated assumptions), the paper becomes a solid, worth-restating result. As it stands, the central claim is not established.","headline":"A6/A7 CP probe is a good idea, but the 'only dipoles' claim is unsupported and likely false; the extracted bounds may be biased.","tokens_in":9229,"tokens_out":15735,"would_cite":true,"duration_ms":146834,"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":"Nearly vanishing in the Standard Model, the Drell-Yan angular coefficients A6 and A7 expose CP-violating quark dipole interactions at the O(0.1) level with existing hadron-collider data, and could reach O(10^-3) at the HL-LHC.","keywords":["Drell-Yan production","naive-T-odd angular coefficients","CP violation","SMEFT","quark dipole operators","Wilson coefficients","HL-LHC sensitivity","Collins-Soper frame"],"falsifier":"A tree-level calculation of the interference of a single quark dipole operator with the Standard Model $\\gamma^*/Z$ amplitude for $pp\\to \\ell^+\\ell^-$: a nonzero A6 or A7 appearing already at $O(1/\\Lambda^2)$ would falsify the paper's two-dipole $O(1/\\Lambda^4)$ mechanism. Equivalently, a high-transverse-momentum measurement of A5 significantly above the predicted negligible dipole contribution would signal operators beyond those considered.","tokens_in":8186,"feed_emoji":"⚛️","tokens_out":11296,"duration_ms":94137,"temperature":0.7,"pith_summary":"Only a handful of the angular coefficients describing Drell-Yan lepton pairs are essentially zero in the Standard Model, and this paper argues that three of them—A5 through A7—can be used as clean collider probes of new sources of CP violation. Within the Standard Model Effective Field Theory, the leading effect comes from the interference between electroweak and chromomagnetic quark dipole operators, suppressed by $1/\\Lambda^4$ and controlled by the combination $\\mathrm{Im}(C_{qG} C_{qZ}^*)$. Fitting existing 8 TeV and 13 TeV hadron-collider measurements, the paper derives $O(0.1)$ constraints for a new-physics scale of $\\Lambda=1$ TeV, and projects that the High-Luminosity LHC could reach $O(10^{-3})$. If correct, high-transverse-momentum measurements of A6 and A7 would provide a collider route to CP-violating physics that is complementary to low-energy electric dipole moment searches.","feed_headline":"Drell-Yan angles A6 and A7 expose CP-violating dipoles","feed_subtitle":"Two near-zero angular coefficients expose the dipole interference, promising 0.001-level sensitivity at HL-LHC.","key_machinery":"The machinery is the spin-density matrix of the intermediate $\\gamma^*/Z$ boson in the Collins-Soper frame, projected onto the imaginary components $A_5 \\propto Q_{xy}$, $A_6 \\propto Q_{yz}$, and $A_7 \\propto J_2$; these vanish unless the production amplitude has an imaginary phase. The key mechanism generating such phases is the chirality-flipping structure of dimension-six quark dipole operators: a single dipole insertion flips chirality, so interference with the Standard Model amplitude is suppressed, and a nonzero A5–A7 requires two insertions—one electroweak Z-dipole and one chromomagnetic gluon dipole—on opposite sides of the cut, giving an $O(1/\\Lambda^4)$ term proportional to $\\mathrm{Im}(C_{qG} C_{qZ}^*)$.","core_discovery":"The paper claims that the naive-T-odd angular coefficients A5–A7 in Drell-Yan production, which are extremely small in the Standard Model because they require absorptive phases and first arise at $O(\\alpha_s^2)$, receive their leading tree-level beyond-Standard-Model contributions at $O(1/\\Lambda^4)$ from the interference between electroweak Z-dipole and chromomagnetic gluon-dipole amplitudes. The relevant CP-violating quantities are $C_u = \\mathrm{Im}(C_{uG} C_{uZ}^*)$ and $C_d = \\mathrm{Im}(C_{dG} C_{dZ}^*)$, and the sensitivity is carried by A6 and A7 at high dilepton transverse momentum, while A5 remains largely insensitive. Using the existing experimental measurements of these coefficients, the paper constrains these combinations at the $O(0.1)$ level for $\\Lambda=1$ TeV, and under statistically dominated uncertainties projects $O(10^{-3})$ sensitivity at the HL-LHC.","pith_inferences":["Beyond the paper: because A6 and A7 measure the product $\\mathrm{Im}(C_{qG} C_{qZ}^*)$ rather than the individual phases, a future nonzero signal would not say which dipole carries the phase; combining these coefficients with transverse-spin observables that weight the two dipoles differently could break that degeneracy.","Beyond the paper: the near-insensitivity of A5 to the quark-dipole mechanism means that a high-$p_T$ observation of A5 would point to a different operator class, such as dimension-eight CP-odd operators or four-fermion interactions, rather than the dipoles studied here.","Beyond the paper: the quoted $O(0.1)$ and $O(10^{-3})$ sensitivities are tied to $\\Lambda = 1$ TeV; because the signal scales as $1/\\Lambda^4$, the same fits become much weaker for heavier new physics, so translating the bounds to a concrete ultraviolet model requires specifying the scale at which the Wilson coefficients are generated."],"forward_implications":["Existing 8 and 13 TeV measurements of the angular coefficients already constrain $\\mathrm{Im}(C_{uG} C_{uZ}^*)$ and $\\mathrm{Im}(C_{dG} C_{dZ}^*)$ at the 0.1 level for a new-physics scale of 1 TeV.","At the HL-LHC, with statistically dominated uncertainties, the same observables would reach roughly $10^{-3}$ sensitivity, about two orders of magnitude better than today.","The discriminating power lives almost entirely in A6 and A7 at high dilepton transverse momentum; A5 contributes negligibly for these dipole operators.","Because up- and down-type dipole operators enter with opposite signs, the measured coefficients can in principle distinguish up-quark from down-quark dipole couplings.","The collider constraints are complementary to low-energy electric dipole moment searches, since the two classes of observables probe different combinations of Wilson coefficients."],"supporting_citations":[{"why":"Supplies the 8 TeV Drell-Yan angular-coefficient measurements used in the chi-squared fit for the current-data constraints.","marker":"[16]"},{"why":"Supplies the 13 TeV measurements and the second-order QCD Standard Model predictions used as the baseline for the fit.","marker":"[18]"},{"why":"Defines the Warsaw basis in which the electroweak and chromomagnetic quark dipole operators are classified.","marker":"[25]"},{"why":"Establishes that naive-T-odd observables require absorptive parts of amplitudes, the reason the Standard Model contributions to A5–A7 are suppressed.","marker":"[26]"},{"why":"Provides the related dimension-eight CP-odd analysis and the observation that A5 receives negligible dipole contributions.","marker":"[27]"},{"why":"Defines the Collins-Soper frame used for the polar and azimuthal angles in the angular-coefficient expansion.","marker":"[35]"},{"why":"Gives the luminosity-scaling prescription used to estimate HL-LHC statistical uncertainties for the pseudo-data.","marker":"[36]"},{"why":"Provides the ratio of third-order to first-order QCD cross sections used to estimate higher-order effects in the HL-LHC prediction.","marker":"[37]"},{"why":"Defines the transverse-mass scale used for renormalization and factorization, appropriate for the high-transverse-momentum region studied.","marker":"[19]"}],"fun_headline_variants":["A6 and A7: the quiet probes of CP violation","Drell-Yan angles A6, A7 reveal CP-violating dipoles","High-pT Drell-Yan coefficients expose new CP violation","HL-LHC to probe CP violation via Drell-Yan A6, A7"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The argument assumes that among dimension-six operators only the quark dipole operators produce the tree-level imaginary parts of the production amplitudes that A5–A7 probe, leaving other complex operators such as four-fermion interactions out of the analysis; if that operator selection is incomplete, the extracted constraints on $\\mathrm{Im}(C_{qG} C_{qZ}^*)$ would be biased.","fun_headline_variants_meta":{"raw":{"variants":["A6 and A7: the quiet probes of CP violation","Drell-Yan angles A6, A7 reveal CP-violating dipoles","High-pT Drell-Yan coefficients expose new CP violation","HL-LHC to probe CP violation via Drell-Yan A6, A7"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000664,"raw_usage":{"total_tokens":3062,"prompt_tokens":1004,"completion_tokens":2058,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":620,"completion_tokens_details":{"reasoning_tokens":1978}},"tokens_in":620,"tokens_out":2058,"duration_ms":12916,"temperature":1.0,"reasoning_tokens":1978,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T14:40:30.480091+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A tree-level calculation of the interference of a single quark dipole operator with the Standard Model $\\gamma^*/Z$ amplitude for $pp\\to \\ell^+\\ell^-$: a nonzero A6 or A7 appearing already at $O(1/\\Lambda^2)$ would falsify the paper's two-dipole $O(1/\\Lambda^4)$ mechanism. Equivalently, a high-transverse-momentum measurement of A5 significantly above the predicted negligible dipole contribution would signal operators beyond those considered.","supporting_citations":[{"cited_title":"Measurement of the Z $\\to$ $\\mu^+\\mu^-$ angular coefficients in pp collisions at $\\sqrt{s}$ = 13 TeV as functions of transverse momentum and rapidity","cited_arxiv_id":"2604.25678","evidence_quote":"Supplies the 13 TeV measurements and the second-order QCD Standard Model predictions used as the baseline for the fit."},{"cited_title":"Hagiwara, K","cited_arxiv_id":null,"evidence_quote":"Establishes that naive-T-odd observables require absorptive parts of amplitudes, the reason the Standard Model contributions to A5–A7 are suppressed."},{"cited_title":"Petriello and K","cited_arxiv_id":null,"evidence_quote":"Provides the related dimension-eight CP-odd analysis and the observation that A5 receives negligible dipole contributions."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines the Collins-Soper frame used for the polar and azimuthal angles in the angular-coefficient expansion."}],"review_version":2}