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Polar-angle tomography reconstructs the tt̄ spin state and tests production CP, while b–lepton azimuthal sine modulations isolate CP violation in the decay vertex.

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2026-07-31 02:53 UTC pith:3WECAES6

load-bearing objection Solid decay-side tomography that cleanly separates production vs decay CP under NWA; the reflection-odd diagnostic is tree-level only and the numbers are illustrative, not a sensitivity claim. the 1 major comments →

arxiv 2607.25034 v1 pith:3WECAES6 submitted 2026-07-27 hep-ph hep-exhep-thquant-ph

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

Priyanka Lamba , Fabio Maltoni , Olimpia Miniati , Eleni Vryonidou This is my paper
classification hep-ph hep-exhep-thquant-ph
keywords top quarkCP violationquantum tomographyspin density matrixWtb vertexSMEFTspin correlationsazimuthal asymmetries
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.

When a top–antitop pair is produced and both quarks decay leptonically, an observed CP-odd angular pattern could come from how the pair was made, from how each top decays, or from both. This paper shows that, in the narrow-width approximation, the two sources leave different fingerprints in the final-state angles. Polar-angle distributions of the charged leptons still reconstruct the production density matrix (the polarisations and spin correlations) up to known analysing-power shifts, so one can test the production CP conditions that the polarisation difference and the antisymmetric spin-correlation matrix must vanish. Dedicated azimuthal angles between each b jet and its charged lepton instead develop sine modulations that are linear in CP-odd pieces of the Wtb vertex and are absent in the Standard Model. Combining the two classes of observables therefore separates production CP violation from decay CP violation. The paper works out the full set of angular distributions for a general anomalous Wtb vertex and illustrates the signatures at the LHC and at a future e⁺e⁻ collider.

Core claim

Within the factorised narrow-width framework, polar-angle distributions retain their tomographic form (up to modified analysing powers) and thereby test CP properties of the production density matrix through ΔB = 0 and C_A = 0, while reflection-odd components of the relative b–lepton azimuthal distributions isolate the CP-odd decay coefficient w_CPV_s and diagnose CP violation in the Wtb vertex; the two classes together separate production, decay, or joint origins.

What carries the argument

Spin-density-matrix factorisation of production and decay (narrow-width approximation): the squared amplitude becomes a trace of a production density matrix times top and antitop decay density matrices, so angular distributions of decay products map directly onto Fano–Bloch coefficients and onto decay analyser vectors that carry the CP-odd Levi-Civita structures.

Load-bearing premise

The clean split between production and decay rests on treating the tops as on-shell and the decay vertex at tree level without strong phases, so that imaginary couplings map straight onto genuine CP-odd sine modulations.

What would settle it

Measure the reflection-odd component of a mixed polar–azimuthal distribution (for example W_1 or the subtracted W_8) in a high-spin-correlation LHC bin, and separately extract ΔB and C_A from polar-angle tomography; a non-zero reflection-odd signal with production CP relations still satisfied would confirm decay-side CP violation, while the opposite pattern would confirm production-side CP violation.

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

If this is right

  • Polar-angle tomography of B, B̄ and C remains valid even with anomalous Wtb couplings, provided the analysing powers α_ℓ are floated in the fit.
  • At the LHC, where individual top polarisations nearly vanish, spin correlations alone still give linear O(Λ⁻²) sensitivity to decay CP violation through mixed polar–azimuthal distributions.
  • A future e⁺e⁻ collider, with Born-level single-top polarisation, activates additional one-angle b–lepton azimuthal probes that are flat at the LHC.
  • A non-flat double b–lepton azimuthal distribution is a null test for anomalous decays, though at unpolarised hadron colliders it starts only at quadratic order.
  • HL-LHC entanglement-style analyses can be extended to these azimuthal observables to search for CP-odd phases in the top sector.

Where Pith is reading between the lines

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

  • If detector-level reconstruction of the relative b–lepton plane angle reaches percent-level precision, the same data sets already used for entanglement measurements could set competitive bounds on Im(C_tW) without dedicated single-top samples.
  • Finite-width and absorptive-phase corrections that mix production and decay would be the first theoretical contamination to quantify before claiming a production-versus-decay assignment at the HL-LHC.
  • The same reflection-odd / polar-angle split could be ported to other short-lived fermion pairs (e.g. τ⁺τ⁻ or hypothetical heavy fermions) wherever production and decay density matrices factorise.

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

1 major / 5 minor

Summary. The authors develop a quantum-tomographic framework for ttbar events in the dileptonic channel, aimed at deciding whether an observed CP-odd effect originates in production, in the Wtb decay vertices, or in both. Working in the narrow-width approximation, they factorise the full process into a production density matrix and top/antitop decay density matrices (Sec. 2), compute the decay matrices for a general dimension-six SMEFT Wtb vertex (Sec. 3), and show that polar-angle distributions retain their SM tomographic form up to modified analysing powers alpha_l, alpha_bar_l (Sec. 4.2, Eqs. (4.16)-(4.20) with (4.35)). They then classify two-angle and single-angle distributions involving the b-lepton relative azimuthal angles phi_lb, identifying sine modulations controlled by the CP-odd coefficient w_s^CPV and cosine modulations controlled by the CP-even v_c (Sec. 5). A two-stage separation strategy is proposed: Delta B = 0, C_A = 0 tests production CP, while reflection-odd components of the phi_lb distributions test decay CP (Sec. 5.3). Numerical illustrations are given for pp at 13 TeV in two spin-correlation-optimised bins and for e+e- at 365 GeV.

Significance. If it holds, this is a useful and timely contribution. The recent entanglement measurements by ATLAS and CMS make ttbar tomography an active experimental program, and a systematic, observable-level protocol for separating production from decay CP violation has not been laid out in this completeness before. The manuscript ships several concrete strengths: fully analytic expressions for alpha_l, v_c, w_s^CPV through O(Lambda^-4) in Appendix B (checked against Refs. [54, 73], with one apparent typo in the literature identified); linear-in-1/Lambda^2 sensitivity through spin-correlation terms even for unpolarised pp -> ttbar (Eqs. (5.11), (5.22)); genuinely clean null tests with exactly flat SM baselines (W_3, W_8, W_9); and honest framing of the numerical results as illustrative rather than sensitivity projections. The classification of which distributions retain SM form versus acquire new harmonics is clear and directly usable by experimentalists.

major comments (1)
  1. [Sec. 5.3 / Eq. (5.50) and Eq. (4.34)] The inference 'reflection-odd phi_lb modulation implies decay CPV' rests on w_s^CPV being sourced purely by imaginary parts of Wilson coefficients and on the charge-conjugate relations of Eq. (4.34) (v_bar_c=-v_c, w_bar_s^CPV=-w_s^CPV). The authors acknowledge the limitation ('in the tree-level setup without absorptive phases', Sec. 5.3; 'the Levi-Civita structures are naive-T odd', Sec. 3.2), but only in single sentences. Two additions are needed: (i) a quantitative discussion of absorptive phases in t->bW (one-loop QCD/EW imaginary parts, finite-Gamma_W effects relative to the on-shell treatment used below Eq. (A.12), and non-factorisable production-decay interference beyond the NWA of Sec. 2), including literature estimates of induced T-odd triple products (Ref. [75], already cited, computes precisely such SM final-state-interaction T-odd correlations); and (ii) an explicit statement:
minor comments (5)
  1. [Sec. 3.2] 'naive-Todd' appears to be a typographical corruption of 'naive-T-odd'.
  2. [Ref. [67]] Author name misspelled ('Vrynidou' for 'Vryonidou') and the arXiv number is a placeholder ('2607.XXXXX'); please update at revision.
  3. [Eq. (B.4) and Fig. 2] Retaining O(Lambda^-6) terms from dimension-six operators only is formally incomplete at that order (dimension-eight interference enters at the same power). Since this shapes the non-quadratic behaviour of alpha_l(Re C_tW) highlighted in the text, a one-line caveat on the dimension-eight ambiguity is warranted.
  4. [Table 1] The Im(C_phtb) range is a reinterpretation of a bound derived under the assumption of real positive C_phtb; the assumptions behind the reinterpretation should be stated in the caption, not only in the table body text.
  5. [Fig. 15 / Sec. 5.1] Fig. 15 caption refers to 'dotted' vertical lines while earlier figure captions use 'dashed'; please harmonise. Sec. 5.1.3 also uses 'Sects.' where Secs. 5.1.1/5.1.2 use 'Secs.'.

Circularity Check

0 steps flagged

No significant circularity: decay tomography and production/decay separation are derived from SMEFT Feynman rules and spin algebra, not forced by fits or self-definition.

full rationale

The load-bearing chain is: (i) NWA factorisation of |M|^2 into production and decay density matrices (Sec. 2); (ii) SMEFT Wtb vertex → decay matrices via Bouchiat–Michel projectors, with P^μ containing p_ℓ, p_b and Levi-Civita pieces (Sec. 3.2, Eqs. 3.23–3.27); (iii) angular distributions from Tr[ρ_I (Γ_t)^T ⊗ (Γ_t̄)^T], yielding polar forms that retain tomography up to α_ℓ and azimuthal forms linear in v_c, w_CPV_s (Sec. 4); (iv) analytic α_ℓ, v_c, w_CPV_s from Wilson coefficients (App. B), not fitted to the same distributions. Benchmark C_i points are chosen inside published bounds only to illustrate shapes (Tab. 2, Sec. 5). Companion [67] supplies production Fano–Bloch numbers and the production CP markers ΔB=0, C_A=0—ordinary two-paper split, not a uniqueness theorem or Eq. X ≡ Eq. Y by construction. The skeptic’s absorptive-phase concern is a physics-assumption risk, not circularity. No self-definitional loop, no fitted-input-as-prediction, no load-bearing self-citation chain.

Axiom & Free-Parameter Ledger

2 free parameters · 6 axioms · 0 invented entities

The claim rests on standard QFT/SMEFT and spin-density technology plus a small set of modelling choices (NWA factorisation, tree-level no strong phases, specific operator basis, charge-conjugate decay relations). No new particles are postulated. Benchmark Wilson values and kinematic bins are illustrative free choices, not fitted constants that define the result.

free parameters (2)
  • Benchmark Wilson coefficients (CPV/CPC sets) = CPV: C3_φQ=-0.7, C_φtb=-2.6i, C_bW=-0.7, C_tW=-0.2i; CPC analogous real set; Λ=1 TeV
    Hand-chosen inside experimental bounds to maximise w_CPV_s or v_c for illustration (Eqs. 5.3–5.5, Tab. 2); not fitted to data in this paper.
  • LHC analysis bins and spin-axis pairs = bin1: 300–400 GeV, 0.4<|cosθ|<0.7; bin2: mtt>800 GeV, |cosθ|<0.4
    Phase-space bins and (a,b) axis choices selected to maximise |C_ab| following CMS entanglement binning; illustrative, not a fit.
axioms (6)
  • domain assumption Narrow-width approximation factorises the full amplitude into on-shell production and decay density matrices while retaining spin correlations.
    Sec. 2, Eqs. 2.3–2.10; load-bearing for independent production vs decay tomography.
  • domain assumption Tree-level SMEFT Wtb vertex from O3_φQ, O_φtb, O_bW, O_tW with no absorptive phases; Im parts generate CP-odd Levi-Civita structures.
    Sec. 3.2, Eq. 3.23 and following paragraph; maps w_CPV_s onto CP violation.
  • domain assumption Charge-conjugate relations fix antitop decay coefficients: v̄_c=-v_c, w̄_CPV_s=-w_CPV_s, ᾱ_ℓ=-α_ℓ.
    Eq. 4.34; used throughout the separation strategy.
  • domain assumption Leptonic Wℓν vertex is SM-like; V_tb=1; O(m_b^2) neglected in decay matrices.
    Sec. 2 and Sec. 3.2 computational setup.
  • standard math Bouchiat–Michel spinor identities and Fano–Bloch two-qubit decomposition of ρ_tt̄.
    Secs. 3–4; standard spin formalism.
  • domain assumption CP invariance of the production density matrix in the common spin basis implies ΔB=0 and C_A=0.
    Imported from companion paper [67]; Sec. 1 and Sec. 5.3.

pith-pipeline@v1.2.0-grok45-kimik3 · 51684 in / 3475 out tokens · 62269 ms · 2026-07-31T02:53:46.088037+00:00 · methodology

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read the original abstract

We develop a quantum-tomographic framework for determining whether possible CP-odd effects in $t\bar t$ events originate in production, in decay, or in both. In the narrow-width approximation, the process $I\to t\bar t\to b\ell^+\nu\,\bar b\ell^-\bar\nu$ factorises into a production density matrix and top and antitop decay density matrices. We extend the standard tomography procedure to a general anomalous $Wtb$ vertex and derive the corresponding angular distributions. Polar-angle distributions retain their usual tomographic form, up to modifications of the spin-analysing powers, and can therefore be used to reconstruct the production density matrix and test its CP properties. By contrast, dedicated azimuthal observables involving the $b$--lepton decay planes contain characteristic sine modulations that provide linear probes of possible new CP-violating interactions in the decay vertex. Combining the two classes of observables gives a systematic strategy for separating sources of CP violation in production and in decay. We illustrate the resulting angular signatures for representative $t\bar t$ production scenarios at hadron and lepton colliders.

Figures

Figures reproduced from arXiv: 2607.25034 by Eleni Vryonidou, Fabio Maltoni, Olimpia Miniati, Priyanka Lamba.

Figure 1
Figure 1. Figure 1: Diagrammatic representation of the process [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Dependence of the charged-lepton spin-analysing power [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Example of the angular variables used for the [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Dependence of vc and w CPV s on the Wilson coefficients CtW and Cϕtb, with only one coefficient taken to be non-zero at a time and chosen to be either purely real or purely imaginary. The ranges shown are selected according to the experimental bounds summarised in Tab. 1. The left and right panels correspond to CtW and Cϕtb, respectively. The value of Λ has been set to 1 TeV. For CtW , the dominant depende… view at source ↗
Figure 5
Figure 5. Figure 5: Dependence of w CPV s , vc, and αℓ on Im(CtW ) and Im(Cϕtb), with Re(CtW ) = Re(Cϕtb) = 0, and all remaining Wilson coefficients fixed to the benchmark values indicated above the corre￾sponding panels. The benchmark points are chosen to illustrate the largest CP-violating effects within the reference ranges considered. We next consider benchmark configurations in which all the relevant Wilson coefficients … view at source ↗
Figure 6
Figure 6. Figure 6: Dependence of vc and αℓ on Re(CtW ) and Re(Cϕtb), with Im(CtW ) = Im(Cϕtb) = 0 and all remaining Wilson coefficients fixed to the benchmark values indicated above the corresponding panels. The benchmark points are chosen to illustrate the largest CP-even effects within the reference ranges considered. In this configuration, w CPV s = 0. magnitude can, however, already be generated by switching on CtW alone… view at source ↗
Figure 7
Figure 7. Figure 7: Normalised two-angle distribution Wab 1 (ϕ (a) ℓb , cos ¯θ (b) ℓ ), defined in Eq. (5.10), for pp → tt¯ production at the LHC, using the polarisation and spin-correlation coefficients extracted from the simulations. The top row corresponds to (a, b) = (k, k) in bin 2, while the bottom row corresponds to (a, b) = (n, n) in bin 1. The left and right columns show the CPC and CPV benchmark scenarios, respectiv… view at source ↗
Figure 8
Figure 8. Figure 8: Normalised two-angle distribution Wrr 1 (ϕ (r) ℓb , cos ¯θ (r) ℓ ), defined in Eq. (5.10), for e +e − → tt¯ production at √ s = 365 GeV. The curves correspond to the SM, CPC, and CPV benchmark coefficients defined in Eqs. (5.5), (5.4), and (5.3), respectively. The dashed vertical line marks ϕ (r) ℓb = π, while the solid blue contour indicates Wrr 1 = 1. explicit by defining the symmetric and antisymmetric … view at source ↗
Figure 9
Figure 9. Figure 9: Subtracted distribution Wrr 8 (ϕ (r) ℓb , cos ¯θ (r) ℓ ), defined in Eq. (5.18), for e +e − → tt¯produc￾tion at √ s = 365 GeV. The left and right panels correspond to the CPC and CPV benchmark scenarios, respectively. The dashed vertical line marks ϕ (r) ℓb = π, while the solid blue contour indicates Wrr 8 = 0. ponents under ϕ (a) ℓb → 2π − ϕ (a) ℓb : Wab 8,S(ϕ (a) ℓb , c) = (Ba + ¯αℓCabc) vc 4π cos ϕ (a) … view at source ↗
Figure 10
Figure 10. Figure 10: Normalised two-angle distribution Wab 2 (ϕ (a) ℓb , ϕ¯ (b) ℓ ), defined in Eq. (5.21), for pp → tt¯ production in bin 2, using the polarisation and spin-correlation coefficients extracted from the simulations. The top and bottom rows correspond to (a, b) = (k, n) and (a, b) = (k, k), respectively, while the left and right columns show the CPC and CPV benchmark scenarios. The dashed vertical line marks ϕ (… view at source ↗
Figure 11
Figure 11. Figure 11: Normalised distribution Wrn 2 (ϕ (r) ℓb , ϕ¯ (n) ℓ ), defined in Eq. (5.21), for e +e − → tt¯ produc￾tion at √ s = 365 GeV. The panels show the SM, CPC, and CPV benchmark scenarios, defined in Eqs. (5.5), (5.4), and (5.3), respectively. The dashed vertical line marks ϕ (r) ℓb = π, while the solid blue contour indicates Wrn 2 = 1. which the modulation changes sign. The choice of spin axes has a significant… view at source ↗
Figure 12
Figure 12. Figure 12: Subtracted distribution Wrn 9 (ϕ (r) ℓb , ϕ¯ (n) ℓ ), defined in Eq. (5.27), for e +e − → tt¯ produc￾tion at √ s = 365 GeV. The left and right panels correspond to the CPC and CPV benchmark scenarios, respectively. The dashed vertical line marks ϕ (r) ℓb = π, while the solid blue contour indicates Wrn 9 = 0. SM contribution. The CP-odd contribution can be isolated directly through the antisymmetric combin… view at source ↗
Figure 13
Figure 13. Figure 13: Normalised two-angle distribution Wab 3 (ϕ (a) ℓb , ϕ¯ (b) ℓb ), defined in Eq. (5.28), for pp → tt¯ production, using the polarisation and spin-correlation coefficients extracted from the simulations. The top and bottom rows correspond to (a, b) = (k, k) in bin 2 and (a, b) = (n, n) in bin 1, respectively, while the left and right columns show the CPC and CPV benchmark scenarios. The dashed lines mark ϕ … view at source ↗
Figure 14
Figure 14. Figure 14: Normalised two-angle distribution Wrr 3 (ϕ (r) ℓb , ϕ¯ (r) ℓb ), defined in Eq. (5.28), for e +e − → tt¯ production at √ s = 365 GeV. The left and right panels show the CPC and CPV benchmark scenarios, respectively. The dashed lines mark ϕ (r) ℓb = π and ϕ¯ (r) ℓb = π, while the solid blue contours indicate Wrr 3 = 1. which are linear in the anomalous decay coefficients and therefore start at O(Λ−2 ). Alt… view at source ↗
Figure 15
Figure 15. Figure 15: Single-angle distributions Wr 7 (ϕ (r) ℓb ) and Wr ¯7 (ϕ¯ (r) ℓb ) for e +e − → tt¯ production at √ s = 365 GeV. The panel shows the SM, CPC, and CPV benchmark scenarios. The dotted vertical lines mark ϕ (r) ℓb = π and ϕ¯ (r) ℓb = π, respectively. whereas the CP-odd sine modulations present in the CPV scenario break these symmetries. The maximum absolute deviation from the SM prediction is approximately 0… view at source ↗

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