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REVIEW 4 major objections 6 minor 105 references

CP violation in top-pair production is stored in two definite spin-density structures that current LHC data already constrain.

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2026-07-31 03:02 UTC pith:3WT2IRHY

load-bearing objection Solid production-level framework: CP-odd effects live cleanly in ΔB and C_A; the a_k “beats existing bounds” claim is the soft quantitative spot, not the structure. the 4 major comments →

arxiv 2607.25029 v1 pith:3WT2IRHY submitted 2026-07-27 hep-ph hep-exhep-thquant-ph

Quantum detection of CP violation in the tbar{t} system: production

Priyanka Lamba , Fabio Maltoni , Olimpia Miniati , Eleni Vryonidou This is my paper
classification hep-ph hep-exhep-thquant-ph
keywords top-quark pair productionCP violationSMEFTspin density matrixFano-Bloch decompositionquantum information observableschromoelectric dipole momentcollider phenomenology
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper shows that new sources of CP violation in top-quark interactions leave a clear fingerprint on the quantum spin state of a produced top-antitop pair. Working in a common spin basis, CP invariance forces the top and antitop polarisation vectors to be equal and the spin-correlation matrix to be symmetric. Any violation therefore appears as a polarisation difference ΔB and an antisymmetric correlation piece C_A. The authors derive the full production density matrix analytically for scalar decay, electron-positron annihilation, photon fusion, and the quark- and gluon-initiated channels at hadron colliders, mapping SMEFT operators onto these CP-odd structures. They then build direct probes (the norms of ΔB and of the antisymmetric vector a, plus the trace distance to the CP-transformed state) and compare them with quantum-information measures such as discord, concurrence and magic. Using existing CMS spin-correlation measurements and projections for the LHC and a future lepton collider, they find that the antisymmetric component a_k already supplies the strongest individual bound on the imaginary part of the chromoelectric dipole coefficient, while concurrence offers promising projected reach. The work supplies the production-level target whose experimental reconstruction is treated in a companion paper.

Core claim

For the unpolarised production processes considered, after expressing the top and antitop spins in a common basis, CP violation in production is encoded exactly in two independent Fano–Bloch structures: the polarisation difference ΔB = (B − B̄)/2 and the antisymmetric part of the spin-correlation matrix C_A = (C − C^T)/2. Direct observables built from these structures, especially the component a_k, currently give the strongest individual constraint on Im(C_tG) from CMS data.

What carries the argument

The Fano–Bloch decomposition of the two-qubit production density matrix in a common spin basis, which converts CP invariance into the elementary conditions B = B̄ and C = C^T and thereby isolates the two CP-odd markers ΔB and C_A.

Load-bearing premise

The sensitivity claims rest on leading-order production matrices, one-operator scenarios, uncorrelated experimental errors, and a fixed 5 percent uncertainty assigned to projected quantum observables, while quadratic dimension-six terms are kept without the matching dimension-eight operators.

What would settle it

A statistically consistent combination of the full set of measured Fano–Bloch coefficients (including a_k) that either tightens or fails to improve the present interval on Im(C_tG), or a future measurement of concurrence at the few-percent level that does not follow the projected exclusion contours.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Direct CP markers built from ΔB and C_A become standard null tests for new top CP violation at the LHC and future colliders.
  • The component a_k of the antisymmetric correlation vector can already improve existing bounds on the imaginary chromoelectric dipole coefficient.
  • Projected concurrence measurements with few-percent precision would add competitive sensitivity to both CP-even and CP-odd dipole operators.
  • Electron-positron colliders gain an extra CP-odd handle (the polarisation difference ΔB) that is absent in leading-order hadronic production.
  • The same production-density-matrix framework extends immediately to tau-pair channels once the corresponding dipole operators are inserted.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Once the companion tomography paper is available, production-side and decay-side CP-odd effects can be separated experimentally, turning the two-paper programme into a complete CP diagnostic for top pairs.
  • Because magic and concurrence respond differently to real versus imaginary dipole coefficients, a joint measurement of both could help discriminate CP-even from CP-odd new physics even when the direct markers are statistically limited.
  • The clean separation of CP-odd entries in the photon-fusion and gluon-fusion correlation matrices suggests that a high-energy photon collider would offer an especially transparent laboratory for top electric-dipole moments.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 6 minor

Summary. The paper develops the production-side framework for diagnosing CP violation in top-quark interactions through the two-qubit spin density matrix of the tt̄ pair. Working in a common spin basis, the authors show (Sec. 4.1, App. B) that for unpolarised, CP-self-conjugate production configurations, CP invariance is equivalent to B = B̄ and C = C^T, so that CP violation is encoded in exactly two structures: the polarisation difference ΔB and the antisymmetric correlation matrix C_A (equivalently the vector a). They derive analytic production density matrices via the Bouchiat–Michel formalism for five benchmark channels (scalar decay, e⁺e⁻, γγ, qq̄, gg), retaining linear and quadratic dimension-six SMEFT contributions with complex dipole coefficients, and study the response of discord, concurrence, magic, and a CP-sensitive trace distance. A phenomenological section (Sec. 6) compares against CMS spin-correlation measurements and FCC-ee projections, concluding that the component a_k currently provides the strongest individual constraint on Im(C_tG), and that a_k also leads the projected sensitivity to Im(C_tB) at a 365 GeV lepton collider. A companion paper will treat tomographic reconstruction.

Significance. If the results hold, this is a useful and well-organised contribution to the growing quantum-information program in top physics. Particular strengths: (i) the CP classification is derived from the action of CP on the density matrix itself (App. B) with explicit statements of its basis dependence and its restriction to unpolarised initial states and CP-related kinematics — it is not fitted or assumed; (ii) complete analytic Fano–Bloch coefficients are given for five production channels (App. C), including CP-odd structures at quadratic order, cross-checked against Refs. [23, 42, 59, 122] and verified numerically with the code of Ref. [104]; (iii) the scalar-decay example (Sec. 5.1) cleanly demonstrates that maximal entanglement and maximal CP violation are logically independent, a genuinely instructive result; (iv) the EFT-truncation limitations (quadratic dim-6 retained for positivity without dim-8; LO QCD in the LHC fit; uncorrelated uncertainties) are stated openly in Secs. 6–7 rather than hidden. The main quantitative claim — that a_k beats existing Im(C_tG) intervals — is falsifiable and, if it survives a proper covariance treatment, would be of direct interest to the LHC EFT社区

major comments (4)
  1. [§6.1.2, Fig. 21] The headline phenomenological claim (Sec. 6.1.2, Fig. 21; repeated in the conclusions, Sec. 7) that a_k 'improves on the representative existing interval' for Im(C_tG) rests on a χ² over the CMS [15] bins in which all bin-to-bin uncertainties are treated as uncorrelated (stated explicitly at the end of Sec. 6.1). Spin-correlation coefficients in neighbouring m_tt–|cos θ| bins share unfolding, luminosity, and modelling systematics, and the CMS analysis provides covariance information via HEPData [106]. Neglecting these correlations generically overstates the constraining power and can also shift the preferred region. Since the 'strongest individual constraint' sentence is load-bearing for the paper's phenomenological punchline, the fit should be redone (or at least bracketed) with the published covariance matrix, or the claim should be downgraded to an illustration under diagonal uncertai
  2. [§6.1.2, Fig. 21 and Table 3] The comparison underlying the improvement claim mixes normalisations without showing the conversion. Table 3 quotes Im(C_tG)/(y_t g_s) ∈ [−0.33, 0.20] from [12] and Re(C_tG)/g_s from [76], while the fits in Figs. 21–22 bound Im(C_tG) directly in the dim6top_LO convention of [62]. The manuscript never states the explicit mapping used to translate the Table 3 intervals into the (Re C_tG, Im C_tG) plane of Figs. 21–22. A one-line conversion (with the values of y_t, g_s used) is needed in the caption of Fig. 21 or in Sec. 6.1.2; without it, the statement that the a_k contour is 'smaller compared to the experimental bound' is not verifiable from the manuscript.
  3. [§6.2, Figs. 23–24, footnote 6] In the FCC-ee projections, the CP-sensitive observables ΔB_n and a_k lose all sensitivity to Im(C_tB) near Re(C_tB) ≃ −0.35 and ≃ −1.5 respectively. The text correctly traces this to a cancellation between the O(Λ⁻²) and O(Λ⁻⁴) terms in the numerator (footnote 6). However, the O(Λ⁻⁴) terms are retained only as dim-6-squared contributions, without the dim-8 interference terms of the same formal order — a truncation the authors themselves flag as incomplete (Sec. 5.2, Sec. 7). The blind spots are therefore artifacts of an inconsistent-order numerator, yet they visibly deform the allowed contours in Fig. 23 and propagate into the conclusion that a_k is 'the strongest projected sensitivity' in the range Re(C_tB) ∈ [−1,1]. The contours should either be recomputed at consistent O(Λ⁻²) (accepting possible non-positivity of ρ and restricting observables accordingly) or the regions near the zeros
  4. [App. C.3 (Eq. C.22) and App. C.4 (Eq. C.25)] The comparison with Refs. [23] and [59] reports that the spin-correlation coefficient C̃_rk 'differs by an overall sign' — and this same unresolved discrepancy is stated identically in App. C.3 (qq̄) and App. C.4 (gg). No origin is identified (convention vs. genuine disagreement). Since C_rk enters the symmetric correlation structure used in the Sec. 6 fits (via the CMS-basis conversion, Eq. 6.5, and the a_n component (C_rk − C_kr)/2), an unresolved sign discrepancy with two independent published computations is a correctness risk that should be settled before publication — e.g., by tracing it to a specific basis or ε-tensor convention, or by a numerical cross-check at a fixed phase-space point against one of the two references.
minor comments (6)
  1. [App. C.3, Eq. (C.22)] In Eq. (C.22), the Λ⁻² term of C̃^A_kn contains the factor 'βeγgsmt...'; 'eγ' appears to be a typo for ˜γ (cf. the Λ⁻⁴ term of the same coefficient, which correctly carries β˜γ). Please check and correct.
  2. [Figs. 12–13 captions] The caption of Fig. 12 (and similarly Fig. 13) describes the upper panels as showing ∥a∥ and δM₂, but the figure layout places ∥a∥ and δM₂ in the top row and δD, δC in the bottom row; the wording 'upper panels ... and the lower panels' is ambiguous given the 2×2 arrangement. Please rephrase to 'top row / bottom row'.
  3. [Reference [73]] The companion-paper reference [73] is a placeholder ('2607.XXXXX') and the fourth author's name is misspelled ('Vrynidou' for 'Vryonidou'). Please update at revision.
  4. [§4.2.4] Eq. (4.39): the mixed-state SRE₂ formula is used as a 'diagnostic of non-stabilizerness rather than a fully faithful magic monotone' — this caveat is welcome, but it would help the reader to state explicitly whether M₂ can be nonzero for stabilizer mixtures (false positives) or only fail as a monotone, since the phenomenological projections in Sec. 6 treat M₂ as a measurable discriminant.
  5. [Table 3] Table 3: the caption notes that different normalisations are employed, but does not flag that the two C_tG rows from [12] are quoted per (y_t g_s) while the [76] row is per g_s. A footnote giving the numerical conversion factor used elsewhere in the paper would prevent misreading.
  6. [§6.1.1, Eq. (6.5)] Sec. 6.1.1: the basis conversion in Eq. (6.5) introduces sgn(cos θ) factors on n̂ and r̂ to match the CMS convention. Since this redefinition is discontinuous at cos θ = 0 and the binning includes |cos θ| ∈ [0, 0.4], one sentence clarifying that the discontinuity lies inside a single bin and does not mix CP-even and CP-odd components would be useful.

Circularity Check

1 steps flagged

No load-bearing circularity: CP markers follow from symmetry of the density matrix; bounds use external CMS data. Minor self-citations to the authors’ QI/SMEFT programme and companion tomography paper are not inputs to the production-level claims.

specific steps
  1. self citation load bearing [Sec. 1 / Sec. 7; Ref. [73]]
    "This establishes the production-level framework whose experimental reconstruction is developed in a companion paper. ... The reconstruction of the same state from the decay products ... is treated in the companion paper [73]."

    The companion paper is by the same authors and is repeatedly invoked as the place where tomography and decay-side CP effects will be handled. This is ordinary programme self-citation, not load-bearing for the production density matrices or the CMS-based a_k bounds derived here; the production claims stand without [73]. Flagged only as minor overlapping-author citation, not as a circular reduction.

full rationale

The central structural result—that for unpolarised production in a common spin basis CP invariance requires B=B̄ and C=C^T, so CP-odd information sits in ΔB and C_A—is derived in App. B from the unitary action of CP on the two-qubit density matrix (SWAP in the spin basis). It is a symmetry identity, not a fit or a renaming of data. Analytic Fano–Bloch coefficients for S→tt̄, e⁺e⁻, γγ, q q̄ and gg are obtained from tree-level amplitudes plus SMEFT vertices via the Bouchiat–Michel formulae; they are parameter-free once Wilson coefficients are specified. Phenomenological constraints compare those shapes to external CMS spin-correlation measurements [15] and to independent global-fit intervals in Table 3; the χ² and 5% projection assumptions are methodological choices, not circular reductions of outputs to inputs. Self-citations (companion tomography paper [73], prior QI/SMEFT works) supply context or deferred experimental reconstruction and do not underwrite the production-level CP markers or the a_k bound. No step equates a claimed prediction to a fitted input by construction.

Axiom & Free-Parameter Ledger

3 free parameters · 5 axioms · 0 invented entities

The work sits inside standard QFT, SMEFT dimension-six truncations, and two-qubit quantum information. Load-bearing modelling choices are LO amplitudes, neglect of absorptive phases and selected operators, spin-basis CP relations for unpolarised initials, and simplified statistical assumptions in the fits. No new particles are postulated; Wilson coefficients are the EFT parameters being constrained, not free knobs tuned to invent a signal.

free parameters (3)
  • Projected relative uncertainty on concurrence and magic (5%) = 5%
    Hand-chosen precision used for LHC and FCC-ee projections of unmeasured QI observables; directly shapes the claimed prospective bounds.
  • Benchmark Wilson coefficients (e.g. Re/Im C_tB=1.5, Re/Im C_tW=0.1, Re/Im C_tG=−0.2) at Λ=1 TeV = order-one values within Table 3 ranges
    Chosen inside existing experimental ranges to illustrate phase-space maps; not fitted, but they set the visual and qualitative sensitivity claims.
  • Global reconstruction efficiency ε_r and hadronic spin-analysing power α_j at FCC-ee = ε_r=40%, α_j=0.64
    Taken from prior literature (ε_r=40%, α_j=0.64) and enter the statistical uncertainties on Fano coefficients.
axioms (5)
  • domain assumption Dimension-six SMEFT truncation with tree-level SM interference; quadratic dim-6 retained for positive-semidefinite ρ without dim-8 operators
    Stated in §§2, 5.2 and conclusions; required for all EFT density matrices and quantum observables.
  • domain assumption Unpolarised initial states; CP maps to B=B̄ and C=C^T in the common spin basis
    App. B and §4.1; defines the two CP-odd structures that are the paper’s central objects.
  • domain assumption Absorptive phases and selected operators (four-fermion CP-odd at linear order, triple-gluon, Otφ in massless e/q channels) neglected
    §2 and channel sections; simplifies amplitudes and can miss SM-like CP-odd-looking effects from final-state interactions.
  • ad hoc to paper Experimental uncertainties on distinct observables treated as uncorrelated in χ² fits
    Explicit simplifying assumption in §6.1; affects combined bounds on C_tG and C_tB.
  • standard math Standard two-qubit QI definitions (concurrence, geometric discord, stabilizer 2-Rényi entropy, trace distance)
    §4.2; used off-the-shelf to diagnose the same density matrix.

pith-pipeline@v1.2.0-grok45-kimik3 · 66261 in / 3476 out tokens · 68728 ms · 2026-07-31T03:02:31.417002+00:00 · methodology

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read the original abstract

We investigate how possible new CP-violating top-quark interactions are encoded in the quantum state of a produced $t\bar t$ pair. We derive analytic expressions for the production density matrix in several benchmark channels relevant to hadron, lepton and photon colliders. In a common spin basis, we identify two characteristic CP-odd structures in the Fano--Bloch decomposition: a difference between the top and antitop polarisation vectors and an antisymmetric component of the spin-correlation matrix. We construct observables that directly probe these structures and study how quantum information measures, including discord, concurrence, magic and trace distance, respond to CP-even and CP-odd SMEFT contributions. Finally, using current measurements and future collider projections, we assess the sensitivity of these observables to possible new sources of CP violation in top-quark production. This establishes the production-level framework whose experimental reconstruction is developed in a companion paper.

Figures

Figures reproduced from arXiv: 2607.25029 by Eleni Vryonidou, Fabio Maltoni, Olimpia Miniati, Priyanka Lamba.

Figure 1
Figure 1. Figure 1: Helicity basis {n, ˆ r, ˆ ˆk} in tt¯ ZMF. by these coefficients. We therefore consider two complementary classes of observables. The first class consists of direct CP markers constructed from the Fano–Bloch coefficients themselves, such as polarisation asymmetries and antisymmetric spin-correlation observables. The second class consists of quantum information observables, such as discord, concurrence, magi… view at source ↗
Figure 2
Figure 2. Figure 2: Feynman diagram describing the decay of a scalar particle to a [PITH_FULL_IMAGE:figures/full_fig_p017_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: CP-sensitive observables as functions of the CP-mixing angle [PITH_FULL_IMAGE:figures/full_fig_p019_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Dominant s-channel tree-level diagram for e +e − → tt¯. The intermediate neutral vector boson represents either γ or Z exchange. The black dot denotes the ttγ/t ¯ tZ¯ vertices, where anomalous dipole interactions or other new physics contributions may enter. maps the transition between stabilizer and non-stabilizer regimes. Taken together, they yield a more refined characterisation of the CP structure of t… view at source ↗
Figure 5
Figure 5. Figure 5: SM predictions for the quantum information observables as functions of the scattering [PITH_FULL_IMAGE:figures/full_fig_p023_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Changes in the quantum information observables induced by the CP-even dipole coef [PITH_FULL_IMAGE:figures/full_fig_p024_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: The observables for the benchmark Im(CtB) = 1.5, with all other SMEFT coefficients set to zero. The upper panels show, from left to right, the norm of the top-antitop polarisation difference, the norm of the antisymmetric spin-correlation matrix, and the CP trace distance. The lower panels show the corresponding changes δDL G, δC, and δM2 relative to the SM predictions. coefficient produces a shift of appr… view at source ↗
Figure 8
Figure 8. Figure 8: The observables for the benchmark Im(CtW ) = 0.1, with all other SMEFT coefficients set to zero. The upper panels show, from left to right, the norm of the top-antitop polarisation difference, the norm of the antisymmetric spin-correlation matrix, and the CP trace distance. The lower panels show the corresponding changes δDL G, δC, and δM2 relative to the SM predictions. and phase-space dependence of ∥∆B∥ … view at source ↗
Figure 9
Figure 9. Figure 9: Representative Feynman diagrams for γγ → tt¯. Diagrams with the photons exchanged are not shown. Double insertions are not included. Quantum entanglement and Bell nonlocality in γγ → tt¯ have recently been investigated at photon colliders, including the effects of initial-state photon polarisation and QCD corrections [43, 102]. The present analysis instead focuses on the modifications induced by a complex … view at source ↗
Figure 10
Figure 10. Figure 10: SM predictions for the quantum information observables as functions of the scattering [PITH_FULL_IMAGE:figures/full_fig_p028_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Changes in the quantum information observables induced by the CP-even dipole [PITH_FULL_IMAGE:figures/full_fig_p029_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: The observables for the benchmark Im(CtB) = 1.5, with all other SMEFT coefficients set to zero. The upper panels show, from left to right, the norm of the antisymmetric spin￾correlation matrix, and the corresponding changes δM2 relative to the SM predictions. The lower panels show the corresponding changes δD, and δC relative to the SM predictions. pendence on (θ, β) to that obtained for Re(CtB) = 1.5. Th… view at source ↗
Figure 13
Figure 13. Figure 13: The observables for the benchmark Im(CtW ) = 0.1, with all other SMEFT coefficients set to zero. The upper panels show, from left to right, the norm of the antisymmetric spin￾correlation matrix, and the corresponding changes δM2 relative to the SM predictions. The lower panels show the corresponding changes δD, and δC relative to the SM predictions. particular, the discord and concurrence receive predomin… view at source ↗
Figure 14
Figure 14. Figure 14: Representative tree-level Feynman diagram for the quark-annihilation subprocess [PITH_FULL_IMAGE:figures/full_fig_p033_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: SM predictions for the quantum information observables as functions of the scattering [PITH_FULL_IMAGE:figures/full_fig_p034_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Changes in the quantum information observables induced by the CP-even dipole [PITH_FULL_IMAGE:figures/full_fig_p034_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: The observables for the benchmark Im(CtG) = −0.2, with all other SMEFT coefficients set to zero. The upper panels show, from left to right, the norm of the antisymmetric spin￾correlation matrix and the change δM2 relative to the SM prediction. The lower panels show the corresponding changes in the discord, δD, and concurrence, δC. returns to zero at β = 1. This behaviour is qualitatively similar to that f… view at source ↗
Figure 18
Figure 18. Figure 18: Representative tree-level Feynman diagrams for the gluon-fusion subprocess [PITH_FULL_IMAGE:figures/full_fig_p036_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: SM predictions and SMEFT-induced changes in the quantum-information observables [PITH_FULL_IMAGE:figures/full_fig_p037_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: The observables for the benchmark Im(CtG) = −0.2, with all other SMEFT coefficients set to zero. The upper panels show, from left to right, the norm of the antisymmetric spin￾correlation matrix, ∥a∥, and the change δM2 relative to the SM prediction. The lower panels show the corresponding changes in the discord, δD, and concurrence, δC. endpoint β = 1. This central suppression is accompanied by two narrow… view at source ↗
Figure 21
Figure 21. Figure 21: 2σ bounds in the plane of the real and imaginary components of CtG, derived by the observables defined as “current measurements”, namely the symmetry-defined components of the spin-correlation matrix. The coloured domains represent the regions of the parameter space allowed by the χ 2 fit performed for the corresponding observables. Each fit was realised comparing our reconstructed prediction with the mea… view at source ↗
Figure 22
Figure 22. Figure 22: 2σ bounds in the plane of the real and imaginary components of CtG, derived by the observables defined as “combined measurements” and “projections”. The coloured domains represent the regions of the parameter space allowed by the χ 2 fit performed for the corresponding observables. For ∥a∥, our predictions have been compared with the experimental values that can be derived from Ref. [15]. For M2, we show … view at source ↗
Figure 23
Figure 23. Figure 23: 2σ bounds in the plane of the real and imaginary components of CtB, derived by the CP-sensitive combinations of Fano–Bloch coefficients and by the number of events N. The coloured domains represent the regions of the parameter space allowed by the χ 2 fit for the corre￾sponding observables. Each fit was realised using our theoretical prediction for each observable, assuming that the measured value would a… view at source ↗
Figure 24
Figure 24. Figure 24: 2σ bounds in the plane of the real and imaginary components of CtB, derived by the CP-sensitive lengths ∥∆B∥, ∥a∥ and the quantum observables M2, C. The coloured domains represent the regions of the parameter space allowed by the χ 2 fit for the corresponding observ￾ables. Each fit was realised using our theoretical prediction for each observable, assuming that the measured value would align with the SM p… view at source ↗

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Reference graph

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