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REVIEW 3 major objections 5 minor 32 references

Future colliders could tighten Higgs CP-violation limits 20-fold.

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2026-08-03 22:51 UTC pith:DDDWCYQC

load-bearing objection Solid, ATLAS-validated projection that future colliders give order-of-magnitude Higgs CP improvements; exact FCC-hh factors are statistical-only and will soften with systematics, but the qualitative case holds. the 3 major comments →

arxiv 2511.08359 v2 pith:DDDWCYQC submitted 2025-11-11 hep-ph hep-ex

Future Collider Perspectives on Higgs CP Violation

Arun Atwal , Jessica Burridge , Ant\'onio Jacques Costa , Christoph Englert , Sinead Farrington , Jay Nesbitt , Leonor Santos Pereira Trigo , Andrew Pilkington
show 4 more authors
Aidan Robson J\'ulia Cardoso Silva Sarah Williams Yuyang Zhang
This is my paper
classification hep-ph hep-ex
keywords Higgs CP violationdimension-six operatorseffective field theoryfuture collidersCP-odd observablesmachine learningweak boson fusionH to four leptons
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.

The paper argues that future electron-positron and proton-proton colliders would improve sensitivity to CP-violating Higgs couplings by roughly an order of magnitude or more compared with the high-luminosity LHC program. It studies three dimension-six operators that mix the Higgs field with weak gauge fields and uses CP-odd angular asymmetries, some machine-learned, to project 95% confidence intervals on the associated Wilson coefficients. Clean electron-positron machines give the best control for two of the three operators, while the 100 TeV proton-proton option is strongest overall, especially in the H to four-lepton and weak-boson-fusion channels. This matters because these couplings are direct probes of new sources of CP violation, which the baryon asymmetry of the universe likely requires.

Core claim

The paper's central claim is that planned future colliders can probe anomalous CP-violating Higgs interactions roughly an order of magnitude more deeply than the HL-LHC. Using simulated events and a binned profile likelihood, the authors find that the H to four-lepton channel at a 100 TeV proton-proton collider constrains c_PhiB/Lambda^2 to +/-0.007 TeV^-2 and c_PhiWB/Lambda^2 to +/-0.015 TeV^-2, about twenty and 150 times better than HL-LHC projections; weak-boson-fusion H to tau tau with a machine-learned observable constrains c_PhiW/Lambda^2 to +/-0.007 TeV^-2, over twenty times better. The electron-positron machines provide the best constraints on c_PhiB and c_PhiWB in associated Z-Higgs

What carries the argument

The analysis is carried by the interference term between the Standard Model amplitude and the dimension-six amplitude, Re(M_SM* M_d6), which is CP-odd and integrates to zero over any CP-even observable. To expose it, the paper uses signed angular variables - Delta phi_ll in Z-Higgs production, Phi_4l in H to four leptons, Delta phi_jj in weak boson fusion - and machine-learned observables O_NN = P^+ - P^- built from classifiers trained to separate positively and negatively weighted interference events. These asymmetries map one-to-one onto the three Wilson coefficients c_PhiB/Lambda^2, c_PhiW/Lambda^2, and c_PhiWB/Lambda^2.

Load-bearing premise

The projected improvements assume the simulated CP-odd interference shapes - particularly the sign-flip near the Z pole in the electron channel and the sign separation the classifiers learn - are accurate enough that a normalization-only ISR correction and the omission of systematic uncertainties do not materially change the constraints.

What would settle it

Compute the electron-channel e+e- to l+l- H interference at next-to-leading order in the electroweak theory; if the sign-flip near the Z pole persists with the same magnitude, the ML-amplified 4-5x sensitivity gain is real, while if it is washed out or shifted, the projected e+e- limits on c_PhiB and c_PhiWB must be re-evaluated.

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

If this is right

  • If the projections hold, a 100 TeV proton-proton collider could measure CP-violating Higgs couplings at the level of roughly 0.01 TeV^-2, about twenty times tighter than the HL-LHC.
  • The machine-learned observables outperform traditional angular variables in every channel studied, most decisively in weak-boson-fusion H to tau tau, where they roughly double the sensitivity.
  • Electron-positron and proton-proton facilities are complementary: the e+e- machines dominate for c_PhiB and c_PhiWB in Z-Higgs production, while the pp machine dominates for c_PhiW via weak boson fusion.
  • Beam polarization at a linear collider improves limits by 1.2 to 1.8, partially compensating for its lower integrated luminosity.
  • The H to four-lepton channel benefits strongly from finer binning in Phi_4l and the dilepton mass at high-luminosity pp machines, producing gains larger than luminosity scaling alone would suggest.

Where Pith is reading between the lines

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

  • The electron-channel sensitivity gain at e+e- machines rests on a sign-flip in the interference near the Z pole that the muon channel lacks; a direct measurement comparing electron and muon channels would test whether this feature is physical or a generator artifact.
  • A natural extension is to apply the same interference-sign classification to existing LHC data in similar final states; this paper's framework suggests such gains are possible, but does not itself establish that they survive real systematic uncertainties.
  • The assumed symmetry of systematic uncertainties is the main place the advertised factors could shrink; a follow-up with full detector simulation and correlated systematics would bound the realistic improvement.
  • If the sign-flip near the Z pole is confirmed at higher order in electroweak perturbation theory, the ML-amplified asymmetry could become a standard tool for measuring CP violation at future Higgs factories.

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

3 major / 5 minor

Summary. The paper presents projected sensitivities to CP-violating dimension-six operators in the gauge-Higgs sector at HL-LHC, FCC-ee, LCF, and FCC-hh. It uses CP-odd observables (Delta phi_ll, Phi_4l, Delta phi_jj) and ML-based observables trained on constructive/destructive interference samples, with the binned Poisson likelihood of Eq. (4.1). The central claim is that future colliders, especially FCC-hh, will improve sensitivity by roughly an order of magnitude over the HL-LHC: Tab. 5 gives c_PhiB/Lambda^2 = +/-0.007 TeV^-2 and c_PhiWB/Lambda^2 = +/-0.015 TeV^-2 for H->4l at FCC-hh (~20x better than HL-LHC), and Tab. 6 gives c_PhiW/Lambda^2 = +/-0.007 TeV^-2 for WBF H->tautau (~23x better). For e+e- colliders, ML observables are reported to improve limits by a factor of 4-5, driven by a sign-flip of the interference near the Z pole in the electron channel (Fig. 1(d)).

Significance. If the quantitative projections are reliable, the paper provides a valuable input to the upcoming European Strategy update: it makes a concrete case that FCC-hh, despite a busier background environment, could be the strongest single facility for Higgs CP studies, and it demonstrates the practical benefit of ML-optimised observables. The simulation pipeline is carefully cross-checked against ATLAS yields in Secs. 6-8 (79 H->4l events at Run-II, WBF yields, Z+jets scalings), and the paper is transparent about several limitations (100 TeV baseline, no ISR, factor-of-two interference effects). The methodology is standard and the claimed qualitative ordering of facilities is robust; the main weakness is that the advertised numerical factors are statistical-only projections with no systematic uncertainty budget.

major comments (3)
  1. [Sec. 4, Eq. (4.1), Tables 5-6] The central 'order of magnitude improvement' claim is produced by a likelihood that contains no systematic uncertainties. At FCC-hh the yields are enormous (Sec. 7: 364k signal / 89k background; Sec. 8: 862k signal / 16M background), so the quoted 95% intervals are set by detailed bin-by-bin shapes of Phi_4l vs m_12 and O_NN, not by counting statistics. The statement that systematics 'are expected to be small [28]' cites the same group's earlier paper and is not an independent detector-level estimate. The authors should either introduce nuisance parameters/binned shape distortions to quantify the effect, or explicitly soften the quantitative factors in the abstract and conclusions.
  2. [Sec. 5, first paragraph, and Fig. 1(d)] The e+e- samples are generated without initial-state radiation and corrected only by a flat k_isr factor. However, the main ML gain (factor 4-5 in Tab. 1) is driven by the sign-flip of the interference as a function of m_ee near the Z pole (Fig. 1(d)). A normalization-only k-factor cannot correct a shape distortion of this kind. In addition, the Sec. 5.2 footnote reports an unquantified factor-of-two change in the interference amplitude when using a dedicated llbb sample. These shape-level uncertainties need to be propagated (e.g., by varying the ISR spectrum or by quoting limits with and without the sign-flip feature) before the FCC-ee/LCF numbers in Tables 1-3 can be taken at face value.
  3. [Sec. 2, footnote p. 3] The FCC-hh projections are computed at sqrt(s)=100 TeV, while the current FCC feasibility-study baseline is 84 TeV. The footnote acknowledges a 'slight reduction in sensitivity' but does not quantify it. Since the headline factors in Tables 5-6 (20x and 23x) are the evidence for the abstract's central claim, the paper should either estimate the 84 TeV cross sections and rerun the key projections, or quote a conservative range for the improvement factors.
minor comments (5)
  1. [Eq. (4.1)] n_k is defined as the expected number of events under the SM-only hypothesis, but in a likelihood it should denote the observed (or Asimov) data; please clarify the notation for expected limits.
  2. [Sec. 6, Table 4 caption] The caption says 'multiclass NN', but the text in Sec. 6 describes a binary classifier and states that a multiclass network gave no real improvement. The caption should be corrected to match the body.
  3. [Sec. 5.2, footnote] 'electron-proton collider studies' appears to be a typo; the context indicates electron-positron colliders.
  4. [Sec. 4 / Eq. (1.3)] The |M_d6|^2 term in Eq. (1.3) is not discussed in the limit-setting procedure. It is presumably negligible for the small Wilson coefficients quoted, but this assumption should be stated explicitly.
  5. [Sec. 4, ref. [28]] Reference [28] is used to justify the absence of systematic uncertainties, but it is the same group's previous paper. An independent experimental or detector-level estimate would strengthen the argument.

Circularity Check

0 steps flagged

No significant circularity: projected sensitivities are simulation outputs; a same-group citation for systematics is a caveat, not a circular step.

full rationale

The central claim is a set of projected 95% C.L. intervals (Tabs. 1–6) obtained by feeding SM and EFT-interference Monte Carlo samples through the binned Poisson likelihood, Eq. (4.1). The intervals are computed, not fitted: no Wilson coefficient is adjusted to match projected data, and the ML observables O_NN are trained on simulated interference samples and then evaluated on SM-like pseudo-data. This is the standard optimal-observable construction, not circular, because the projected data are SM-like and the classifier is not a physical parameter in the likelihood. I find no step in which a predicted quantity is equal to an input by construction. The main caveat is in Sec. 4: “Systematic uncertainties are not explicitly included in the likelihood function… their impact is expected to be small [28].” Reference [28] has overlapping authorship with the present paper, and the quantitative FCC-hh factors would indeed be threatened by unmodeled shape systematics. However, this is an assumption about the size of systematic effects, not a definitional reduction, and the paper explicitly surfaces the limitation. Similarly, the Sec. 5.2 footnote acknowledges an unquantified factor-of-two interference effect and states that the Sec. 5.1 constraints are “likely conservative,” and the Sec. 2 footnote acknowledges the 100 TeV vs 84 TeV FCC-hh baseline. These are limitations, not circularity. The simulation pipeline is anchored to external ATLAS event-yield validations in Secs. 6–8 and to LHC constraints [47], providing independent support for the setup. The derivation is therefore self-contained; the score reflects the one notable self-citation in the systematics justification.

Axiom & Free-Parameter Ledger

3 free parameters · 6 axioms · 0 invented entities

The central claim rests on: (i) SMEFT truncation at dimension six with the interference term as the dominant CP-odd signal; (ii) a stated assumption that systematics are symmetric and negligible; (iii) LO matrix elements with k-factor normalizations; (iv) two data-calibrated background rescaling factors; and (v) interpretive claims about the electron-channel sign-flip. No new physical entities are postulated; the O_NN observables are computational constructs trained on the signal they later constrain, which is standard practice, not an invented entity.

free parameters (3)
  • Z+jets background rescaling factor = 1.3
    Applied to LO Z+jets background at all pp colliders to match ATLAS ZH(H->bb) yields (Sec. 6); this data-derived calibration propagates into the pp sensitivity projections.
  • Per-final-state Zjj background scaling N_total/N_Zjj = channel-dependent
    Fit to ATLAS H->tau tau WBF yields (footnote, Sec. 8); normalizes the dominant Zjj background at LHC/HL-LHC/FCC-hh and therefore shapes the projected c_PhiW limits.
  • k_isr ISR correction factor = not quoted
    Flat normalization factor correcting for ISR neglected in the e+e- generator setup (Sec. 5); applied to signal and backgrounds but cannot correct shape distortions, which matter because the O_NN gain exploits an m_ll-dependent sign-flip.
axioms (6)
  • domain assumption SMEFT truncated at dimension six; the |M_d6|^2 (CP-even) contribution is dropped from the likelihoods (Eq. 1.3)
    Standard in the field and justified for CP-odd observables that project out the interference term, but the CP-even squared term does modulate the total yields entering the Poisson likelihood.
  • domain assumption Systematic uncertainties affect CP-odd observable distributions symmetrically and can be neglected (Sec. 4)
    Load-bearing: the order-of-magnitude claims are statistical-only projections. The cited justification is the authors' own ref. [28].
  • domain assumption Backgrounds are symmetric under the CP-odd observables and do not bias the asymmetry-based limits (Secs. 3-4)
    Underpins the procedure of including backgrounds without dedicated CP-specific modeling.
  • domain assumption Leading-order matrix elements with k-factor normalizations describe the SM and interference shapes (Secs. 2, 5-8)
    Only SM-ratio k-factors are applied; no NLO shapes are used. The H->bb and Hjj selections are copied from ATLAS 13 TeV analyses, giving partial validation of the SM side only.
  • domain assumption The electron-channel m_ll sign-flip is a physical VBF contribution, not a generator artifact (Sec. 5.1, Fig. 1(d))
    Interpretive claim that underlies the 4-5x O_NN gain; no amplitude-level proof or ISR-included cross-check is provided.
  • ad hoc to paper Poisson likelihood with linear-in-c bin means (Eq. 4.1) remains valid when interference drives lambda_k negative in some bins
    No lower bound or regularization for negative expected yields is described; the asymmetric low-yield intervals in Tab. 4 (e.g., [-4.3, 2.2]) suggest the issue is material in the LHC/HL-LHC ZH fits.

pith-pipeline@v1.3.0-alltime-deepseek · 18118 in / 26066 out tokens · 248656 ms · 2026-08-03T22:51:03.898954+00:00 · methodology

0 comments
read the original abstract

The search for new sources of CP violation is a cornerstone of the beyond the Standard Model phenomenology programme at the LHC and beyond. We provide a comprehensive analysis of such searches at a range of future facilities with the aim of informing the currently unfolding future collider roadmap. Focussing on new sources of CP violation specifically in the gauge-Higgs sector, we demonstrate the outstanding potential held by future electron-positron and proton-proton colliders to reveal and identify BSM physics with direct relevance for the observed matter-antimatter asymmetry. In particular, the future colliders will provide an order of magnitude improvement in sensitivity to anomalous CP-violating interactions induced by dimension-six effective field theory operators when compared to the high-luminosity LHC programme.

discussion (0)

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Reference graph

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