Improved BSM Sensitivity in Diboson Processes

Brian Henning; Davide Maria Lombardo; Francesco Riva

REVIEW 3 major objections 5 minor 50 references

Improved BSM Sensitivity in Diboson Processes

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Polarization-tuned W-pair and Zh analyses at 3 TeV CLIC can reach new-physics effects roughly ten times smaller than HL-LHC or ILC projections, and about a hundred times smaller than LEP limits.

desk verdict Solid, honest EFT projection for future e+e- colliders; the c3W and Zh reaches are credible, but the 2D cW-cB plot rests on an unquantified polarization approximation that a referee should push on. read the letter →

arxiv 1909.01937 v1 pith:KCT7B2MH submitted 2019-09-04 hep-ph

Brian Henning , Davide Maria Lombardo , Francesco Riva This is my paper · ORCID

classification hep-ph

keywords dibosonproductiondimension-6operatorsstandardmodeleffectivefieldtheorybeampolarizationCLICILCanomaloustriplegaugecouplingsDrell-Yanprocesses

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

The paper argues that future electron-positron linear colliders can turn diboson production into a precision probe of beyond-Standard-Model physics by tailoring the analysis to the polarization of the produced W's. Its central projection is that a 3 TeV CLIC run would be sensitive to dimension-6 operator effects roughly an order of magnitude smaller than the HL-LHC or ILC, and two orders of magnitude smaller than LEP. The key trick for transverse W pairs is to bin events in the azimuthal angle of the W decay planes, which resurrects an interference between Standard Model and BSM helicity amplitudes that cancels in inclusive measurements. For longitudinal W pairs and the associated Higgs process Zh, the trick is beam polarization, which suppresses the large transverse Standard Model background. The paper further shows that the ratio of the two induced Wilson coefficients depends only on the spin of the heavy particle generating them, offering a way to identify the spin of new states.

What carries the argument

Two mechanisms carry the argument. The first is azimuthal interference resurrection: for $e^+e^- \to W^+W^-$ with both W's transverse, BSM same-helicity amplitudes and SM opposite-helicity amplitudes do not interfere inclusively, but the decay-plane azimuthal angle $\phi$ modulates their interference as $\cos 2\phi$; binning $\phi$ (ten bins) and $\cos\Theta$ (five bins) exposes the interference. The second is the high-energy helicity-amplitude decomposition of longitudinal $W^+W^-$ and $Zh$, which shows that in the massless limit each initial-state helicity selects a unique combination of the operators $\mathcal{O}_W$ and $\mathcal{O}_B$; combined with polarized beams that suppress the transverse t-channel background, this converts $Zh$ associated production into a near-background-free counting measurement. A third object, the spin-dependent ratio $C_{2W}^i/C_{3W}^i = 1 - 20k_i(j_1,j_2)/N_{\mathrm{dof}}^i$, encodes the spin of the heavy particle integrated out: $+1$ for scalars, $-4$ for Dirac fermions, and $-37/3$ for massive vectors, where $k$ is a representation-theoretic index and $N_{\mathrm{dof}}$ counts physical degrees of freedom.

What would settle it

Re-run the 3 TeV longitudinal WW and Zh analyses with the full set of relevant dimension-6 operators (including OHW and OHB), exact finite W/Z masses, and the real 80-90 percent polarization; if the resulting 68% CL bounds on cB move outside the bands shown in the paper's Fig. 4, the central complementarity claim fails.

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Extended reading notes

Core claim

In the effective-field-theory picture used here, the leading new-physics effects in diboson production are captured by dimension-6 operators whose contributions grow as $s/\Lambda^2$. For transverse $W^+W^-$, the BSM operator $\mathcal{O}_{3W}$ produces same-helicity $++$ and $--$ amplitudes that do not interfere with the dominant $+-$ and $-+$ Standard Model amplitudes in the inclusive cross section; the paper's single-differential analysis bins the azimuthal angle $\phi$ of one W decay plane and the polar angle $\cos\Theta$, recovering a $\cos 2\phi$ interference term that approximately doubles the sensitivity relative to an inclusive analysis. For longitudinal $W^+W^-$ and $Zh$, where the Standard Model signal is small and transverse pairs act as background, right-handed electron polarization suppresses the t-channel neutrino background; the resulting 68% CL projections at 3 TeV CLIC are $c_{3W}$ in the range of about $\pm 1.1\times 10^{-2}$ (semileptonic, $\phi$-binned, 3% systematics) and $c_W$ around $\pm 2.8\times 10^{-3}$ from $Zh$, with the combined $WW$ and $Zh$ information separating $c_W$ and $c_B$ in a way complementary to Z-pole S-parameter measurements. The paper interprets these bounds in weakly and strongly coupled ultraviolet scenarios, concluding that Drell-Yan processes generally offer better discovery potential, while diboson channels add spin-discriminating power.

Load-bearing premise

The quoted reach on the Higgs-sector operators assumes that high-energy longitudinal W-pair and Zh production is governed entirely by the two specific dimension-6 operators OW and OB, with finite-mass corrections and the difference between 90-percent and 100-percent beam polarization negligible.

Editorial extensions

If this is right

The 3 TeV CLIC projections on $c_{3W}$ and $c_W$ are roughly an order of magnitude more sensitive than HL-LHC or ILC and two orders more sensitive than LEP.
Polarized beams improve the longitudinal $WW$ bound by roughly a factor of two: at 3 TeV, fully hadronic $c_W$ goes from about $[-2.0,1.6]\times 10^{-2}$ unpolarized to $[-0.96,0.94]\times 10^{-2}$ polarized at 3% systematics.
A simple counting analysis of $Zh$ associated production yields the strongest single-operator bound, $c_W$ around $\pm 2.8\times 10^{-3}$ at 3 TeV at 3% systematics, corresponding to new-physics scales near 25 TeV in the weakly coupled triplet-vector scenario.
In weakly coupled UV completions, Drell-Yan processes generally beat dibosons for discovery, but if both $C_{2W}$ and $C_{3W}$ are measured, their ratio distinguishes scalar, fermion, and vector ultraviolet states ($+1$, $-4$, and $-37/3$ respectively).
The combined CLIC $WW$ plus $Zh$ measurement is complementary to a future Z-pole run: the Z-pole S-parameter would need precision of order $10^{-5}$ ($c_W+c_B \sim 2\times 10^{-3}$) to match the CLIC information.

Reading between the lines

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

A direct extension the paper leaves implicit: the same azimuthal-binning method, applied to fully hadronic boosted dibosons at a higher-energy lepton or muon collider, should push $c_{3W}$ sensitivity below $10^{-3}$ because the BSM term grows as $s/\Lambda^2$; this is our extrapolation, not a paper claim.
The spin-ratio identity could be generalized into a multi-coefficient 'spin fingerprint' using $C_{2B}$ and $C_{3B}$ as well as $C_{2W}$ and $C_{3W}$; the paper sketches the $C_{2W}/C_{3W}$ case only, so the broader version is an editorial inference.
If jet energy resolution improves beyond the assumed 4% smearing, the fully hadronic channel, with its larger luminosity, should overtake the semileptonic channel; the paper's central-region ambiguity currently makes the two nearly degenerate.
In strongly coupled scenarios, the paper's comparison suggests that a future null result in dibosons but a positive Drell-Yan signal would favor strongly coupled multipolar new physics over weak-coupling spin-0 models.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

I read the Henning-Lombardo-Riva diboson paper. Bottom line: it's a solid, honestly written projection paper, more useful as a systematic comparison than as a source of any single new trick. The main new elements—phi-binned interference resurrection applied to WW at CLIC/ILC, the polarization strategy for longitudinal WW, and the spin-determination ratio C2W/C3W—are all built from existing ingredients (Refs. [19], [43], [14]), but the paper's specific combination, and especially the transparent comparison of channels and energy stages, is a genuine addition.

What it does well: The amplitude-level logic in Eqs. (10)-(12) and (17)-(18) is standard and correctly handled. The E^2/Lambda^2 growth is respected, and the interpretation sections are careful to distinguish direct simulation from analytic extrapolation. The paper is commendably explicit about its overlaps with the CLIC report and Ref. [27], and the spin ratio from the one-loop calculation (Eq. 5, Table 1) is a clean and interesting observation, even if not the central numerical result. I found no circular reasoning or fitting-dressed-as-prediction.

Soft spots, in proportion: The numerical reaches depend on simplified assumptions—flat 1% or 3% per-bin systematics, a uniform 50% acceptance, 4% jet smearing. Those are crude but not disqualifying for a first projection; the qualitative ordering of channels and colliders is unlikely to change with better detector models. The bigger concern is the two-dimensional cW-cB constraint in Fig. 4. The paper simulates only OW and recovers OB analytically, and it replaces a 90% polarized beam with a 100% polarized one (footnote 11). For the right-handed run this matters: the SM transverse WW amplitude vanishes in the massless limit, so the cB signal sits on top of a background that, with 5% left-handed contamination, is dominated by the t-channel left-handed amplitude. The paper asserts that the central bins make the approximation work 'particularly well,' but it never quantifies the residual contamination. That is a real gap, because the claimed complementarity with Z-pole measurements is a central interpretive point. The single-operator reaches (c3W in Table 3, cW from Zh in Table 5) are based on direct simulation and are not affected, so the headline sensitivity story survives; it's specifically the 2D plot that needs a quantitative check or a caveat.

Who should read it: anyone planning the e+e- collider physics program, and EFT practitioners interested in spin discrimination. It deserves a serious referee. I'd recommend publishing after the authors either add a simulation with O_B and a realistic polarization mixture, or at least give a numerical estimate of the wrong-helicity contamination in the right-handed bins.

Referee Report

3 major / 5 minor

Summary. The manuscript studies W+W− and Zh production at future linear e+e− colliders (ILC and CLIC) within the Standard Model Effective Field Theory (SMEFT). The transverse W+W− final state is analyzed using the azimuthal distribution of decay products to recover SM-BSM interference for the operator O3W, and the longitudinal W+W− and Zh channels are used to probe the operators OW and OB with the aid of beam polarization and polar-angle distributions. The authors provide projected 68% C.L. bounds on c3W and cW for a range of collider energies and systematic assumptions, and then combine the WW and Zh information to constrain the two-dimensional (cW,cB) parameter plane. The results are interpreted in weakly and strongly coupled BSM scenarios, where the ratio C2W/C3W is argued to act as a spin discriminator, and the abstract claims that CLIC can probe effects roughly an order of magnitude smaller than HL-LHC or ILC and two orders of magnitude smaller than LEP.

Significance. If the projections hold, this paper makes a strong quantitative case for the physics reach of a multi-TeV e+e− collider, particularly CLIC, in the electroweak sector. The methodological contribution is genuinely useful: the azimuthal-angle analysis for resurrecting the interference in transverse WW production, the exploitation of beam polarization to isolate longitudinal final states, and the spin-ratio interpretation based on published one-loop results are all clearly presented. The paper is well organized and provides explicit amplitude-level expressions and detailed tables of cuts, luminosities, and results, which facilitates scrutiny. However, the headline reach numbers and especially the two-dimensional (cW,cB) constraints rest on several assumptions that are either optimistic or not fully validated, so the central claims should be treated as conditional on further checks.

major comments (3)

[Sec. 4.2, footnote 11 and Fig. 4] The two-dimensional (cW,cB) constraints of Fig. 4 are obtained by approximating the 90% polarized beam as 100% polarized. For the right-handed run, the SM transverse WW amplitude vanishes in the massless limit, so the sensitivity to cB relies on the suppression of the transverse background. The 10% wrong-helicity (left-handed) contamination, however, produces the full t-channel transverse WW cross section, which is unsuppressed. Since the e_R^- longitudinal WW and Zh signals are suppressed by additional powers of g'^4 relative to the e_L^- processes, this contamination could be comparable to or larger than the cB signal in the central bins that the authors select, where footnote 11 claims the approximation works 'particularly well.' The size of this effect is not quantified anywhere in the paper. I request that the authors repeat the analysis with the actual beam admixture (or at least a 90/10 mixture) and demonstrate that the Fig. 4 bounds are stable, or at minimum report the background contamination in the right-handed central bins. This is load-bearing because the claimed complementarity with Z-pole measurements and the cB reach are central conclusions of the longitudinal-sector analysis.
[Sec. 3.2 and Sec. 4.2] The cW-cB plane is constructed from Whizard simulations that include only the operator OW (as stated in Sec. 3.2) and then rescaled using the massless-limit amplitudes of Eqs. (17)-(18). This mapping implicitly assumes that the OB contribution, and the interference combination, passes the same selection cuts and has the same acceptance as OW. The paper does not validate this assumption against a direct simulation of OB or of a general linear combination of OW and OB. Given that the high-energy cuts, angular selection, and beam-polarization admixture can affect different helicity amplitudes differently, I request a validation on at least one benchmark point where the full simulation (or a reliable approximate simulation) is compared with the analytic rescaling after all cuts. Without this check, the combined (cW,cB) reach and the complementarity claim rest on an unverified extrapolation.
[Sec. 3.1, Tables 3-5] The numerical reach tables rely on a flat 1% or 3% systematic uncertainty in every bin, a uniform 50% signal acceptance, and for the Zh channel complete final-state reconstruction with an effective 50% luminosity reduction. These assumptions are quite optimistic; in particular, a 1% bin-to-bin systematic in a 10-bin azimuthal distribution is difficult to achieve in practice, and a flat 50% acceptance for all signals and backgrounds is a strong simplification. The paper shows the 1% vs 3% variation, but does not study the dependence on acceptance or on the completeness of reconstruction. I recommend adding a small robustness scan (e.g., varying acceptance between 30% and 70%, or systematics to 5% in a subset of bins) to substantiate the claim that CLIC reaches 'an order of magnitude smaller' effects than HL-LHC or ILC, which is the headline result of the abstract.

minor comments (5)

[Table 3] In the CLIC(1%) 380 GeV row, the semileptonic exclusive entry is given as [20.1, 21.0]; since a 68% C.L. interval around the SM value should contain zero, this appears to be a typographical error (likely the lower bound should be negative). Please check and correct.
[Sec. 4.2] The text refers to 'Eq. (3.2)' in two places (e.g., 'as shown in Eq. (3.2)' and 'using Eq. (17) and Eq. (3.2)'), but the displaying of equations in the manuscript suggests the intended reference is Eq. (18). The equation numbering should be fixed throughout.
[Throughout] There are several typographical errors: 'Drell-Yann' appears in the abstract and text and should be 'Drell-Yan'; 'brehmstrahlung' should be 'bremsstrahlung'; 'incertitude' should be 'uncertainty'; 'verriﬁed' should be 'verified'.
[Sec. 3.1] In the description of the fully hadronic analysis, the authors state that they define φ and Θ by randomly selecting one of the two fermions or W bosons. It would be clearer to state explicitly that this is a procedure to emulate the inherent ambiguity (Eq. (14)) in a real detector, rather than an actual random choice in the Monte Carlo that could introduce statistical noise.
[Footnote 11] The footnote relates the 90% left/right-handed fraction to an 80% polarization in Table 2; this connection is not obvious and could be stated explicitly (e.g., for P=0.8, the left-handed fraction is (1+P)/2=0.9). This would prevent confusion about the exact polarization assumed.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the reach projections are obtained from independent SM-plus-dimension-6 simulations, and the self-cited results used for interpretation are external published calculations, not fitted inputs.

full rationale

The derivation chain is self-contained. The collider sensitivities in Tables 3-5 are obtained by Whizard/MadGraph generation of SM amplitudes plus dimension-6 operator insertions (c3W, cW), with detector smearing, selection cuts and systematic uncertainties; no Wilson coefficient is fitted from the same observable it is then used to predict. The transverse-interference analysis uses Eq. (12) from Ref. [19] and the helicity decomposition from Ref. [10]; these are prior published results, not definitions of the present observables, and the paper's own simulation verifies the expected azimuthal behavior. The spin-discriminating ratio C2W/C3W in Eq. (5) is taken from the independent one-loop calculation of Ref. [14] (one overlapping author); because that result is parameter-free and does not depend on the present projections, invoking it is external support, not circularity. The two-dimensional (cW, cB) constraints of Sec. 4.2 are a linear recombination of the simulated OW sensitivity through Eqs. (17)-(18); this is an algebraic mapping, not a fitted parameter renamed as a prediction. The stated limitations (OW-only Whizard simulation and the 100% vs 90% polarization approximation in footnote 11) are accuracy or validity caveats, not definitional circularity.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central reach numbers rest on the EFT validity assumption, the helicity and non-interference results, and the simplified detector and systematics model. The paper introduces no new particles or forces. The spin-discrimination interpretation adds the external one-loop coefficient computation of Ref. [14] and the strong-coupling estimates of Ref. [13], both prior works by overlapping authors.

free parameters (4)

systematic uncertainty per bin = 1% (optimistic) and 3% (pessimistic)
Chosen by hand; directly sets the 68% C.L. intervals in Tables 3-5; no detector-level model is used.
signal acceptance = 50%
Applied uniformly to all channels; effectively halves the luminosity; chosen as an estimate, not from full simulation.
jet energy resolution = 4% Gaussian smearing
Used for jet smearing in the Whizard analysis; a simplified detector assumption.
high-energy selection cuts = sqrt(s) > 2600, 1300, 330, 400, 200 GeV
Chosen to select genuinely high-energy events and reduce ISR and beamstrahlung effects; the sensitivity results depend on these thresholds.

assumptions (5)

domain assumption Dimension-6 operator EFT with omitted higher-dimension terms is valid at the energies probed.
Used throughout via Eq. (1); the paper cites Ref. [36] for validity limits but does not check each collider energy point in detail.
domain assumption Helicity selection rules suppress SM-BSM interference at the inclusive level, so the cos(2phi) azimuthal distribution is the main carrier of transverse sensitivity.
Taken from Refs. [18,19]; the transverse analysis and its phi-binned design rely on this background result.
domain assumption The high-energy massless-limit amplitudes for WLWL and Zh (Eqs. 17-18) are accurate at the collider energies used.
Used to translate the OW simulation into cW-cB constraints; finite-mass corrections are neglected.
ad hoc to paper Only OW and OB contribute in the longitudinal and Higgs sectors.
Stated in Section 4.2; not derived from a UV model, and other operators such as OHW and OHB are dropped on loop-level arguments.
domain assumption The one-loop coefficient formulas for C2W and C3W, and the spin-dependent ratio in Table 1, are correct.
Taken from Ref. [14]; the spin-discrimination interpretation rests entirely on this prior computation.

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Pith. "Pith review of Improved BSM Sensitivity in Diboson Processes." pith.science (2026). https://pith.science/paper/KCT7B2MH

@misc{pith2026190901937,
  author       = {Pith},
  title        = {Pith review of: Improved BSM Sensitivity in Diboson Processes},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KCT7B2MH}},
  note         = {Machine review of arXiv:1909.01937}
}

abstract

We study $W^+W^-$ and $Zh$ final states at future linear $e^+e^-$ colliders; designing analyses specific to the various final state polarizations allows us to target specific beyond the Standard Model (BSM) effects, parametrized in the form of dimension-6 operators. We find that CLIC can access effects roughly an order of magnitude smaller than HL-LHC or ILC, and two orders of magnitude smaller than LEP. These results are interpreted in the context of well-motivated BSM scenarios---at weak and strong coupling---where we expect correlated effects in Drell-Yann processes. The latter turn out to have better discovery potential, although the diboson processes provide additional discriminating power, potentially furnishing a way to measure the spin and coupling of BSM states.

Figures

Figures reproduced from arXiv: 1909.01937 by the authors.

**Figure 1.** Bounds on the Wilson coefficient c3W (left) cW (right) or equivalently in the BSM parameter λγ and δgZ 1 . The systematics is set to 1%; the LEP and LHC results are taken from the references in the text. 3.2 Longitudinal W+W− and Zh Final States New physics in the Higgs sector manifests itself both in processes with longitudinal polarizations W+ L W− L and ZLh associated production. At high-energy only one dimensio… view at source ↗

**Figure 2.** Ultimate reach of HL-LHC and CLIC on the BSM-coefficients C2W/3W for dibosons and Drell-Yan processes. The dashed lines indicate the theoretical prediction in weakly coupled models for different spins of the heavy BSM states (spin-0 denotes complex scalars), while the solid dots on them highlight the value for a particle with mass just beyond the CLIC 3 TeV reach, and in a gauge representation with µ(R) = 2. 4 Inter… view at source ↗

**Figure 3.** Comparison of the reach of Drell-Yan and Dibosons at HL-LHC and CLIC, on the strongly-coupled BSM scenarios of Ref. [13]. Here g∗ denotes the coupling and M the mass scale associated with the new BSM sector. Nevertheless, as shown in Eq. (3.2), Zh and WW are sensitive to different combinations of cW and cB, and their combined information allows us to reach this 2-dimensional parameter space. Notice that the combina… view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: Probed BSM-directions and their constraints. The shaded areas are derived singling out one process at time, while the solid one is the bound from the summed distribution. The purple line indicates the direction (cW + cB) = 0, studied at LEP. 5 Conclusion In this work,…

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