{"id":"e1be6976-9d54-43fc-9b20-b0cb648ec50b","arxiv_id":"2501.14806","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"T-odd observables in pp to tW- X are predicted to depend only on Im f2R among anomalous tbW couplings, with projected 1-sigma limits near 10^-2 at the LHC.","lead":"This paper proposes three time-reversal-odd measurements in top-plus-W production at the LHC that would pin down the imaginary part of one specific anomalous top-bottom-W coupling. The projected sensitivities are about one percent or better at 13 TeV, though the estimates are leading-order and ignore detector effects and backgrounds.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Only-Im-f2R claim rests on unshown algebra; if Im f1R or Im f2L contributions are nonzero, central isolation fails.","rationale":"The reader's verdict is CONDITIONAL with the weakest assumption identified as the LO, signal-only, no-cut idealization of the sensitivity estimates. The rationale, however, also notes that the central derivation is only partially shown. I agree with that secondary point and elevate it to the single most load-bearing concern because it directly threatens the paper's novel physics claim—that the T-odd observables isolate Im f2R. If the unshown vanishing of Im f1R and Im f2L contributions is wrong, the entire central assertion collapses, whereas the NLO/background concern only modifies the quoted limits without invalidating the structural result. Since the reader already conditioned the verdict on this kind of unverified algebra, the recommended verdict remains CONDITIONAL (unchanged). A concrete, independent helicity-amplitude check would settle the concern: if it reproduces the vanishing, the paper's core claim is supported; if not, the paper would need major revision or rejection. The agreement is partial because the reader's weakest assumption was the NLO/cuts issue rather than the derivation gap, though the reader did mention the missing full expressions.","tokens_in":9796,"tokens_out":9189,"duration_ms":98489,"concrete_test":"Perform an independent tree-level helicity-amplitude calculation of gb→tW− with a complex f1R and f2L (with f1L=1 and all other couplings zero) using, e.g., the FORM-based procedure or a generator such as MadGraph5_aMC@NLO with a UFO model implementing the effective Lagrangian of Eq. (1). Compute P_t, A(O), and <O> with the same z-axis convention (defined by the momentum of the tW− pair and the larger-x parton) and the same phase-space cuts (none) as in the paper, for an integrated sample. If any observable is nonzero at linear order in Im f1R or Im f2L, the central claim is refuted. Conversely, if they are identically zero, the paper's key structural assertion is verified; request the full density-matrix expressions to confirm.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central structural claim of the paper is that all three T-odd observables—transverse top polarization P_t, the asymmetry A(O), and the expectation value <O>—receive contributions only from Im f2R among the anomalous tbW couplings, with Im f1R and Im f2L giving exactly zero (Sections 4–5, abstract). This claim is the basis for the paper's asserted ability to isolate Im f2R. However, the manuscript does not show the calculation that establishes the vanishing: Eq. (12) gives only the combination -i(ρ12-ρ21) for the f2R contribution, and the f1R/f2L results are asserted without explicit density-matrix expressions. The full expressions are deferred to 'elsewhere.' The internal typo in Eq. (13), where ρ22 appears instead of ρ21, further indicates that the unshown algebra has not been carefully checked. If either Im f1R or Im f2L actually contributes at linear order, the central conclusion that these observables isolate Im f2R fails, and the limits in Tables 1–3 would be contaminated. This concern is more fundamental than the acknowledged LO, signal-only, no-cut idealization, which affects only the accuracy of the quoted sensitivities and does not bear on the structural isolation claim.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":9970,"tokens_out":4849,"duration_ms":48351,"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":[{"comment":"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.","section":"§4, Eqs. (12)–(13)"},{"comment":"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.","section":"§5, paragraph after Eq. (20)"},{"comment":"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.","section":"§6, Tables 1–3"},{"comment":"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.","section":"§1 and §6"}],"minor_comments":[{"comment":"The sentence defining A(O) says 'for which the A(O) is positive', which is tautological; it should say 'for which O is positive'.","section":"§5, definition of A(O)"},{"comment":"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.","section":"§3 and §4"},{"comment":"There is a repeated-word typo, 'the the anomalous couplings', in the same sentence that contains the f1R/f2R error.","section":"§5, after Eq. (20)"},{"comment":"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.","section":"§6"}],"recommendation":"major_revision","confidential_remarks":"The manuscript's central claim rests on a derivation that is not shown; an appendix or supplementary material with the full density-matrix elements and the vanishing conditions for Im f1R and Im f2L is essential. The typos in Eq. (13) and in the Section 5 sentence make the present version difficult to verify. I would not require a full NLO calculation, but the idealized nature of the numerical limits should be more carefully stated and, if possible, accompanied by a rough estimate of background and acceptance effects."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: Rindani applies the known T-odd observable technology to pp -> tW-X and finds that three observables all isolate Im f2R among the tbW anomalous couplings, with 1-sigma limits around 1e-2. If the algebra checks out, that is a genuinely useful handle on CP and absorptive phases. The problem is that the paper does not let you check the algebra.\n\nWhat is new: earlier work looked at T-odd/CP observables in top processes, but the specific application to tW associated production, with the claim that Im f1R and Im f2L give exactly zero while Im f2R drives all three observables, is not in the cited literature. That structural claim is the paper's main value, and it is clean. The coupling framework is standard, the distinction between absorptive and CP-violating phases is handled correctly, and the author is upfront that the calculation is LO, signal-only, and without detector simulation. The citations to prior top T-odd and CP studies look appropriate; there is no sign of inflated novelty claims.\n\nSoft spots: the central derivation is not in the manuscript. Eq. (12) gives only the Im f2R off-diagonal density-matrix combination; the vanishing of the Im f1R and Im f2L contributions is asserted and deferred to \"elsewhere.\" That is a load-bearing gap, not cosmetic. Internal typos reinforce the concern: Eq. (13) writes rho12 - rho22 where Eq. (12) defines rho12 - rho21, and the Section 5 sentence about <O> says \"f1R and f2R\" when context argues \"f1R and f2L.\" The numerical tables also show a factor-of-ten difference in sigma_SM between Table 1 and Table 2, presumably from leptonic branching and decay cuts, but this is not spelled out. The sensitivity numbers are LO, signal-only, and no-cut; if the ratio-insensitivity assumption fails, the limits weaken, though the author does flag this as an estimate.\n\nOn the stress-test concern: it holds. Until we see the f1R/f2L calculation, the isolation claim is credible but unverified. That is an argument for refereeing, not rejection.\n\nBottom line: a useful phenomenology note for top EFT and CP studies, provided the missing density-matrix expressions are supplied. Send it to review; require the full calculation or a clearly referenced preprint, and fix the typos.","headline":"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.","tokens_in":10615,"tokens_out":2800,"would_cite":true,"duration_ms":29877,"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":"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…","keywords":["T-odd observables","tbW anomalous couplings","top transverse polarization","triple-product asymmetry","single-top production","effective Lagrangian","CP violation","LHC"],"falsifier":"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.","tokens_in":9519,"feed_emoji":"⚛️","tokens_out":8520,"duration_ms":83446,"temperature":0.7,"pith_summary":"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.","feed_headline":"Three T-odd top signals all trace to one coupling","feed_subtitle":"A single measurement could isolate the anomalous top-W coupling's imaginary part at the percent level.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Supplies the result that anomalous $tbW$ couplings in top decay do not change the normalized charged-lepton angular distribution at linear order, allowing the paper to restrict anomalous couplings to the production vertex.","marker":"[12]"},{"why":"The algebraic manipulation software used to evaluate the helicity amplitudes and spin-density-matrix elements that yield the T-odd combination.","marker":"[13]"},{"why":"The method for constructing the production spin density matrix from helicity amplitudes.","marker":"[14]"},{"why":"Provides the decay density-matrix elements for $t \\to b\\ell^+\\nu$ used to fold production with decay.","marker":"[15]"},{"why":"Earlier analysis of CP violation in $tW^\\pm$ production that supplies the phase-convention framework for separating absorptive and CP-violating phases.","marker":"[9]"}],"fun_headline_variants":["T-odd observables isolate imaginary tbW coupling at LHC","One anomalous coupling drives all T-odd top signals","Imaginary tbW coupling pinned by T-odd asymmetries","LHC single-top W probes complex top coupling"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["T-odd observables isolate imaginary tbW coupling at LHC","One anomalous coupling drives all T-odd top signals","Imaginary tbW coupling pinned by T-odd asymmetries","LHC single-top W probes complex top coupling"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000521,"raw_usage":{"total_tokens":2558,"prompt_tokens":1020,"completion_tokens":1538,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":636,"completion_tokens_details":{"reasoning_tokens":1470}},"tokens_in":636,"tokens_out":1538,"duration_ms":12527,"temperature":1.0,"reasoning_tokens":1470,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T20:20:06.859971+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the result that anomalous $tbW$ couplings in top decay do not change the normalized charged-lepton angular distribution at linear order, allowing the paper to restrict anomalous couplings to the production vertex."},{"cited_title":"Vega and J","cited_arxiv_id":null,"evidence_quote":"The method for constructing the production spin density matrix from helicity amplitudes."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the decay density-matrix elements for $t \\to b\\ell^+\\nu$ used to fold production with decay."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Earlier analysis of CP violation in $tW^\\pm$ production that supplies the phase-convention framework for separating absorptive and CP-violating phases."}],"review_version":1}