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Probing the CP violation effects via the angular coefficients in Drell-Yan production

T0 review · 3 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read 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.

desk verdict A6/A7 CP probe is a good idea, but the 'only dipoles' claim is unsupported and likely false; the extracted bounds may be biased. read the letter →

arxiv 2608.04437 v1 pith:W464ZWMV submitted 2026-08-05 hep-ph hep-ex

Qingyi Situ , Bin Yan This is my paper · ORCID
classification hep-phhep-ex
keywords Drell-Yanproductionnaive-T-oddangularcoefficientsCPviolationSMEFTquarkdipoleoperatorsWilsonHL-LHCsensitivityCollins-Soperframe
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

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.

What carries the argument

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 $\mathrm{Im}(C_{qG} C_{qZ}^*)$.

What would settle it

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.

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Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

  • 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.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • 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.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

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).

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 (3)
  1. [Sec. II, discussion following Eq. (8)] 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.
  2. [Sec. III, Eq. (10) and Figs. 2–5] 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.
  3. [Sec. III, Case-II pseudo-data projection] 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.
minor comments (5)
  1. [Sec. III, Eq. (9) and Fig. 2] 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.
  2. [Sec. III, scenario list] The phrase 'regularized data' in the first scenario is vague; specify what regularization is applied to the ATLAS measurements and why.
  3. [Sec. III, Fig. 5] 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.
  4. [References] 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.
  5. [Throughout] 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.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the dipole calculation is independent and the constraints are fits to external LHC data.

full rationale

The derivation chain is self-contained. The angular coefficients A5-A7 are defined by orthogonal projections (Eqs. 1-3) and expressed in terms of spin-density-matrix components (Eqs. 4-5); the dipole operators of Eq. (6) are inserted into the matrix-element calculation, and the O(1/Lambda^4) interference contribution is computed rather than read off from the data. The constraints in Eq. (10) are fits to external ATLAS/CMS measurements with A_SM supplied from an independent QCD calculation; the HL-LHC estimate is explicitly described as pseudo-data generated from SM predictions, so it is a projected sensitivity, not a claim of discovery. Self-citations [9,11,29-34] are motivational/contextual and do not supply the numerical input or the operator-counting result. The statement that only quark dipole operators can contribute at dimension six is an asserted physics assumption; even if incomplete (e.g., complex four-fermion operators could contribute at lower order), that would be a correctness/completeness issue, not a reduction of the output to the input. No fitted parameter is relabeled as a prediction: Fig. 5 shows the best-fit model compared with the same CMS data after fitting, which is standard presentation. Hence no circular step.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

No new particles, mediators, dimensions, or conserved quantities are introduced; the analysis is within the existing SMEFT operator basis. The central claim rests on standard EFT assumptions, the dipole-only classification, and the quoted ATLAS and CMS measurements.

free parameters (3)
  • C_u = Im(C_uG C*_uZ) = not quoted; 68% C.L. interval shown in Fig. 4
    Fitted to ATLAS 8 TeV and CMS 13 TeV A5-A7 data in Eq. (10); central object of the constraints.
  • C_d = Im(C_dG C*_dZ) = best-fit value used for red bands in Fig. 5, not numerically quoted
    Fitted to the same data; drives the A6 and A7 improvement shown in Fig. 5.
  • central scale m_Z^T = sqrt(m_ll^2 + (p_T^ll)^2) = m_Z^T per bin
    Chosen by hand as the renormalization and factorization scale in Eq. (9); affects the SMEFT and SM predictions and the theory uncertainty estimate.
assumptions (5)
  • domain assumption SMEFT with dimension-six operators is a valid description below Lambda = 1 TeV.
    Standard EFT assumption used throughout; not derived in this paper.
  • domain assumption At dimension six, only quark dipole operators generate tree-level imaginary parts of the Drell-Yan production amplitudes, so only they contribute to A5-A7.
    Stated in Sec. II alongside 'uniquely singles out' but not proven by an operator survey.
  • domain assumption Photon dipole contributions are negligible in the Z-pole window m_ll in [80,100] GeV.
    Stated in Sec. II and used to keep only the Z-dipole operators.
  • domain assumption The SM predictions for A5-A7 at O(alpha_s^2) from ATLAS [16] and CMS [18] are accurate, including their scale-variation uncertainties.
    Used as the baseline in Eq. (10).
  • domain assumption The K-factor ratio kappa = sigma(alpha_s^3)/sigma(alpha_s) from 13 TeV [37] can be extrapolated to 14 TeV for the HL-LHC projection.
    Used in case-II; supported only by weak energy dependence between 8 and 13 TeV.

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Pith. "Pith review of Probing the CP violation effects via the angular coefficients in Drell-Yan production." pith.science (2026). https://pith.science/paper/W464ZWMV

@misc{pith2026260804437,
  author       = {Pith},
  title        = {Pith review of: Probing the CP violation effects via the angular coefficients in Drell-Yan production},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/W464ZWMV}},
  note         = {Machine review of arXiv:2608.04437}
}
abstract

The naive-$T$-odd angular coefficients $A_5$--$A_7$ in Drell--Yan production are highly suppressed in the Standard Model (SM), making them sensitive probes of CP-violating interactions beyond the SM. We study these observables within the Standard Model Effective Field Theory (SMEFT), focusing on dimension-six electroweak and chromomagnetic quark dipole operators. Due to their chirality-flipping structure, the leading contributions from CP-violating dipole interactions arise at $\mathcal{O}(1/\Lambda^4)$ through the interference between electroweak and chromomagnetic dipole amplitudes. We find that the sensitivity is primarily driven by $A_6$ and $A_7$ in the high dilepton transverse momentum region, where the dipole contributions are enhanced, while $A_5$ remains largely insensitive. Combining the ATLAS and CMS measurements, we constrain the CP-violating dipole combinations of Wilson coefficients at the $\mathcal{O}(0.1)$ level for $\Lambda=1~{\rm TeV}$. Assuming statistically dominated uncertainties at the HL-LHC, the sensitivity can be improved to the $\mathcal{O}(10^{-3})$ level. Our results highlight $A_6$ and $A_7$ as complementary probes of CP-violating dipole interactions at hadron colliders.

Figures

Figures reproduced from arXiv: 2608.04437 by the authors.

Figure 1
Figure 1. FIG. 1. The definition of the Collins-Soper frame in the [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. The contribution of dipole operators to the angular [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4. The individual bounds for the Wilson coefficients of [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. The [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]

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