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REVIEW 4 major objections 4 minor 17 references

T-odd observables from anomalous $tbW$ couplings in single-top W associated production at the LHC

T0 review · 4 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read In $pp \to tW^-X$ at the LHC, the transverse top polarization, the T-odd asymmetry $A(O)$, and the mean $\langle O\rangle$ are all proportional to the imaginary part of a single anomalous $tbW$ coupling, $\mathrm{Im}\,f_{2R}$, and the…

desk verdict Phenomenologically motivated, but the load-bearing only-Im-f2R claim is asserted, not shown; worth refereeing, with a required revision to supply the missing algebra and fix internal typos. read the letter →

arxiv 2501.14806 v1 pith:NX55K5MF submitted 2025-01-15 hep-ph

Saurabh D. Rindani This is my paper · ORCID
classification hep-ph
keywords T-oddobservablestbWanomalouscouplingstoptransversepolarizationtriple-productasymmetrysingle-topproductioneffectiveLagrangianCPviolationLHC
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

This paper argues that three time-reversal-odd (T-odd) observables in LHC single-top production $pp \to tW^-X$ all share one simple origin: the imaginary part of the anomalous $tbW$ coupling $f_{2R}$. A nonzero value of any of them would isolate $\mathrm{Im}\,f_{2R}$ from the other two anomalous couplings, whose imaginary parts contribute nothing at the order considered. That imaginary part could signal either a CP-violating phase or an absorptive part of a form factor, and the paper gives 1-$\sigma$ sensitivities around $10^{-2}$ for an integrated luminosity of 100 fb$^{-1}$ at center-of-mass energies from 7 to 14 TeV. Because the observables are ratios of cross sections, the author argues that leading-order results may survive higher-order QCD corrections reasonably well.

What carries the argument

The central object is the off-diagonal element of the top-quark production spin density matrix, specifically the combination $-i(\rho_{12}-\rho_{21})$, which is the only piece of the production amplitude that survives in T-odd observables. The key identity is that this combination equals $-\mathrm{Im}\,f_{2R}\, g^2 g_s^2 \, \epsilon(p_g, p_b, p_t, s_t) / (3 m_W \hat{s})$, where $\epsilon$ is the totally antisymmetric contraction of the three momenta with the top spin four-vector. This single term carries all the T-odd effect, and the observables are then built as ratios or expectation values so that the overall normalization drops out; that ratio structure is why the author expects NLO QCD corrections to leave the asymmetries roughly unchanged.

What would settle it

Compare the two independent T-odd measurements in the same 13 TeV sample: the transverse polarization $P_t$ and the asymmetry $A(O)$. The paper's Tables 1 and 2 predict a fixed ratio $A(O)/P_t$ for unit $\mathrm{Im}\,f_{2R}$ (about 0.326/0.0444), so a measured ratio that deviates from this prediction, or a nonzero T-odd signal in a control process where $\mathrm{Im}\,f_{2R}$ is absent, would refute the claim that $\mathrm{Im}\,f_{2R}$ alone drives all three observables.

Watch

Extended reading notes

Core claim

Using an effective $tbW$ Lagrangian with complex couplings $f_{1R}$, $f_{2L}$, and $f_{2R}$, and setting their real parts to zero, the paper derives the production spin density matrix for $gb \to tW^-$ and shows that the T-odd combination $-i(\rho_{12}-\rho_{21})$ is proportional to $-\mathrm{Im}\,f_{2R}$ times a Levi-Civita contraction of the gluon momentum, the $b$-quark momentum, the top momentum, and the top spin four-vector. Consequently the transverse top polarization $P_t$, the asymmetry $A(O)$ in the angular correlation $O = \sin\theta_t \sin\theta_\ell \sin\phi_\ell$, and the mean value $\langle O\rangle$ are all linear in $\mathrm{Im}\,f_{2R}$, while $\mathrm{Im}\,f_{1R}$ and $\mathrm{Im}\,f_{2L}$ give vanishing contributions. The paper estimates 1-$\sigma$ limits at 100 fb$^{-1}$: about $1.4 \times 10^{-2}$ for $P_t$ at 13 TeV, about $6 \times 10^{-3}$ for $A(O)$ at 13 TeV, and around $0.19$ for $\langle O\rangle$, with limits improving at 14 TeV.

Load-bearing premise

The numerical limits assume that leading-order, signal-only cross sections with no kinematic cuts, detector simulation, or background subtraction give reliable estimates because the observables are ratios in which QCD corrections are expected to cancel; if that cancellation fails or backgrounds are not negligible, the real reach could be worse.

Editorial extensions

If this is right

  • A nonzero measurement of any of the three T-odd observables would isolate $\mathrm{Im}\,f_{2R}$ among the three anomalous $tbW$ couplings, since $\mathrm{Im}\,f_{1R}$ and $\mathrm{Im}\,f_{2L}$ contribute zero at linear order.
  • The same imaginary coupling can be generated either by genuine CP violation or by an absorptive part of the effective vertex; separating the two requires comparing the $tW^-$ and $tW^+$ conjugate channels.
  • With 100 fb$^{-1}$ at 13-14 TeV, limits on $\mathrm{Im}\,f_{2R}$ of order $10^{-2}$ appear reachable from the asymmetries, improving with collision energy.
  • Because the observables are ratios of cross sections, the author expects the leading-order estimates to be reasonably accurate even though NLO corrections to the cross sections are known to be sizable.
  • Restricting the calculation to the $t \to b\ell^+\nu$ channel gives a conservative sensitivity estimate; including the other two leptonic decay channels would improve the limits.

Reading between the lines

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

  • If the ratio-insensitivity assumption holds, the same T-odd correlation technique could be applied to the other single-top production channels and to $tW^+$ events, and comparing conjugate channels could separate the absorptive phase from a genuine CP-violating phase - a step the paper only outlines.
  • The vanishing of $\mathrm{Im}\,f_{1R}$ and $\mathrm{Im}\,f_{2L}$ contributions is derived at tree level and to linear order; at NLO or with quadratic anomalous-coupling terms, the clean isolation of $\mathrm{Im}\,f_{2R}$ could be diluted, so the quoted limits should be read as idealized.
  • A full detector-level study with realistic kinematic cuts, backgrounds, and systematic uncertainties would likely shift the numerical limits by factors of a few, and combining all three leptonic channels could recover part of that loss.
  • The paper's mention of machine-learning top taggers suggests that hadronic top decays, though harder for triple-product measurements, might become usable for T-odd observables with modern tagging techniques.
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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

4 major / 4 minor

Summary. The paper studies the process pp -> tW^- X at leading order with anomalous tbW couplings f1R, f2L, f2R. It defines three T-odd observables: the transverse top polarization P_t, the asymmetry A(O) in the angular variable O = sin(theta_t) sin(theta_l) sin(phi_l), and the mean value <O>. The central claim is that all three observables are proportional only to Im f2R, with Im f1R and Im f2L giving exactly zero, and the paper estimates 1-sigma limits on Im f2R of order 10^-2 at 100 fb^-1 for LHC energies of 7, 8, 13 and 14 TeV.

Significance. If the central isolation claim is correct, the three observables offer a theoretically clean way to isolate Im f2R among the anomalous tbW couplings, complementary to CP-violation studies. The paper correctly distinguishes naive T violation from CP violation and reasonably relies on the known linear-order independence of the charged-lepton angular distribution from anomalous decay couplings. The numerical estimates are explicitly leading-order, signal-only, and without detector simulation, so their value is indicative rather than a realistic LHC projection. The paper does not tune parameters to the result; it performs a forward calculation with standard inputs, which is a strength.

major comments (4)
  1. [§4, Eqs. (12)–(13)] The central claim that only Im f2R contributes rests on an unshown derivation. Equation (12) gives only the combination -i(rho12 - rho21) for the Im f2R contribution, while the vanishing of the Im f1R and Im f2L contributions is asserted in the text with the full expressions deferred to 'elsewhere'. In addition, Eq. (13) uses [-i(rho12 - rho22)], whereas Eq. (12) determines rho12 - rho21; this is either a typo or a different quantity, and it must be corrected. The authors should provide the complete off-diagonal density-matrix expressions or a reproducible computation, because the isolation of Im f2R is the load-bearing result of the paper.
  2. [§5, paragraph after Eq. (20)] The sentence 'it turns out the observable <O> is zero in the case of the the anomalous couplings f1R and f2R' directly contradicts the main claim and Tables 2–3, which show that Im f2R is the nonzero coupling. Presumably 'f2L' was intended. This error in a central sentence, together with the Eq. (13) typo, indicates that the asserted selection rules have not been carefully checked in the manuscript text.
  3. [§6, Tables 1–3] The projected 1-sigma limits assume leading-order, signal-only cross sections with no kinematic cuts, no detector simulation, and no background subtraction, as the paper acknowledges. Since the abstract and conclusions state that limits 'could be reached', the authors should either soften these statements or provide a quantitative estimate of the effect of at least the dominant backgrounds and acceptance cuts. The current caveat that the numbers are 'expected to give a reasonable indication' is not sufficient for the quoted 10^-2 sensitivities to be interpreted as LHC reach.
  4. [§1 and §6] The assumption that NLO corrections largely cancel in the observables because they are ratios of cross sections is plausible but unsupported. For P_t and A(O), the numerator and denominator receive different NLO corrections, and no reference is given for spin-dependent NLO calculations in this process. The authors should either provide evidence for the cancellation or present the sensitivities as strictly leading-order parton-level estimates.
minor comments (4)
  1. [§5, definition of A(O)] The sentence defining A(O) says 'for which the A(O) is positive', which is tautological; it should say 'for which O is positive'.
  2. [§3 and §4] The text refers to '7, 8, 13 and 14 GeV' when TeV is meant; this unit error appears in Section 3 and should be corrected throughout.
  3. [§5, after Eq. (20)] There is a repeated-word typo, 'the the anomalous couplings', in the same sentence that contains the f1R/f2R error.
  4. [§6] The statement that combining tW^- and tW^+ results 'would lead to increase in statistics' is not fully justified, since the couplings for the two channels are independent unless specific assumptions are imposed; the sentence should clarify the assumed relations.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: T-odd observables are computed forward from an assumed coupling, with only a non-load-bearing self-citation and a proof gap, not a reduction.

full rationale

The paper performs a forward calculation: it assumes an effective tbW Lagrangian (Eq. 1), computes tree-level helicity amplitudes and production spin-density-matrix elements, and evaluates the transverse polarization, the T-odd asymmetry A(O), and the mean <O> as functions of Im f2R. The projected 1-sigma limits in Tables 1-3 follow from the standard statistical inequalities in Eqs. (14)-(15) and (21)-(22) using computed SM cross sections; no parameter is fitted to data and no fitted value is renamed as a prediction. Inputs such as mt, mW, sin^2 thetaW, and the CTEQ PDFs are external constants, not tuned to the result. The only author-overlap citations that are load-bearing are [12] (used to argue that the charged-lepton angular distribution is unchanged by anomalous decay couplings at linear order) and [8,9,15] as background/formalism. The [12] result is a separate published calculation about top decay, not a restatement of the present production-observable result, so it counts as independent support despite self-citation. The central claim that only Im f2R contributes is not circular: the observables are defined kinematically (e.g., O = sin theta_t sin theta_l sin phi_l in Eq. (16)), not in terms of f2R, and the vanishing of the Im f1R and Im f2L contributions is asserted rather than demonstrated. The paper explicitly defers the full density-matrix expressions ('The full expressions will be given elsewhere') and contains a typo in Eq. (13) (rho22 instead of rho21) and an apparent typo in Section 5 ('f1R and f2R' where f2L seems intended); these are proof/completeness and correctness concerns, not circularity. Score 1 reflects the minor, non-circular self-citation and the missing algebra, not a reduction of the result to its inputs.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

The calculation introduces no fitted free parameters and no new particles or forces. It relies on standard external inputs (mt=172.5 GeV, mW=80.379 GeV, sin^2 thetaW=0.223, GammaW=2.085 GeV, CTEQ L1 PDFs) and on domain assumptions about leading-order accuracy, mb=0, the narrow-W approximation, and the cited linearity of the decay distribution. The central content is a forward model calculation with stated simplifications rather than a parameter fit.

assumptions (4)
  • domain assumption The effective tbW Lagrangian of Eq. (1) with complex f1R, f2L, f2R and Vtb=1 is a valid description of new physics at LHC energies.
    Section 2 assumes Lorentz-invariant effective couplings without specifying a UV completion or cut-off scale; validity at LHC energies is taken for granted.
  • domain assumption Leading-order parton-level cross sections with mb=0 in the five-flavour scheme give reliable asymmetries because NLO corrections cancel in ratios.
    Sections 1 and 3: 'It is likely that since we are dealing with ratios of quantities, the results ... will be reasonably accurate.' No NLO calculation is provided.
  • domain assumption Anomalous tbW couplings in the top decay do not affect the normalized charged-lepton angular distribution to linear order, so the SM decay density matrix can be used.
    Section 5 cites [12] for this; it is required for A(O) and <O> to be attributed only to the production process.
  • domain assumption The narrow-width approximation for the W boson and the top quark widths are valid for the decay integration.
    Section 5: 'The expression for the full cross section is evaluated using the narrow-width approximation for the W.'

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Cite this review

Pith. "Pith review of T-odd observables from anomalous $tbW$ couplings in single-top W associated production at the LHC." pith.science (2026). https://pith.science/paper/NX55K5MF

@misc{pith2026250114806,
  author       = {Pith},
  title        = {Pith review of: T-odd observables from anomalous $tbW$ couplings in single-top W associated production at the LHC},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NX55K5MF}},
  note         = {Machine review of arXiv:2501.14806}
}
abstract

We investigate the possibility that an imaginary anomalous $tbW$ coupling can be measured in the process $pp \to tW^-X$ by means of T-odd observables. One such observable is the polarization of the top quark transverse to the production plane. Another is the asymmetry between the cross sections with a positive and with a negative value of a certain T-odd correlation constructed out of observable momenta when the top quark decays leptonically. The mean value of this correlation, which is also T-odd, is the third observable. These three T-odd observables are shown to be proportional to the imaginary part of only one of the $tbW$ anomalous couplings, the other couplings giving vanishing contributions. This imaginary part could signal either a CP-odd coupling, or an absorptive part in the effective coupling. We estimate the 1-$\sigma$ limits that might be derived in the case of each of these observables for centre-of-mass energies 7, 8, 13 and 14 TeV at the LHC.

Figures

Figures reproduced from arXiv: 2501.14806 by the authors.

Figure 1
Figure 1. Feynman diagrams contributing to gb → tW− production. The effective tbW vertex is shown as a filled circle. tering or loop diagrams, characterized by a nonzero imaginary part for an anomalous effective coupling, the forward and backward amplitudes are not the same, and the subsequent T violation would not be a genuine one. In that case the CPT theorem does not necessarily imply CP violation. We study in the process … view at source ↗

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Reference graph

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