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The paper claims that pp→Vh and pp→VW tails at the LHC are controlled by five flavor-dependent quark-coupling shifts, yielding bounds complementary to electroweak and flavor data, with HL-LHC projections probing the Cabibbo-angle anomaly re

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2026-08-04 20:40 UTC pith:5D6K5ZHB

load-bearing objection A solid, clearly written SMEFT paper: new general-flavor amplitudes for Vh/VW, useful per-flavor LHC bounds, with honest caveats; worth refereeing. the 2 major comments →

arxiv 2509.08437 v1 pith:5D6K5ZHB submitted 2025-09-10 hep-ph

Flavor constraints from ppto Vh and ppto VW at the LHC

O. J. P. \'Eboli , L. P. S. Leal , M. Martines , O. Sumensari This is my paper
classification hep-ph
keywords SMEFTflavor physicsHiggs associated productiondiboson productionCKM unitarityCabibbo angle anomalyhelicity amplitudesLHC
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.

Most previous studies of these LHC channels assumed the new-physics couplings were the same for all quark flavors or followed the Standard Model's flavor pattern. This paper drops that assumption: it derives the high-energy helicity amplitudes for pp→Vh and pp→VW with a general quark-flavor structure, and shows the energy-enhanced parts are controlled by just five effective shifts of the W and Z couplings to quarks, with the quark-mixing (CKM) matrix entering explicitly. Fitting Run-2 differential data from ATLAS and CMS on WW, WZ, Zh and Wh production, it obtains 95% confidence limits on the underlying effective-field-theory operators of dimension six for each flavor pair. The limits from associated Higgs production are about twice as strong as those from diboson production, and they lift flat directions left by electroweak precision data. As an application, the paper shows that HL-LHC projections can probe the right-handed-current scenarios proposed to explain the apparent ~3σ violation of first-row CKM unitarity.

Core claim

The central result is that, at high energies, the helicity amplitudes for pp→Zh, pp→Wh, pp→WW and pp→WZ with longitudinal bosons grow as s-hat/v^2, and each flavor channel is governed by one of five effective coupling shifts (δg_ZuL, δg_ZdL, δg_ZuR, δg_ZdR, δg_WqR) times explicit CKM factors. Gauge invariance ties the left-handed charged-current shift to neutral-current ones, δg_WqL = δg_ZuL·V − V·δg_ZdL, so Vh and WV probe the same operators. From Run-2 differential data the paper derives 95% CL bounds on C_Hq^(1), C_Hq^(3), C_Hu, C_Hd and C_Hud for all flavor pairs, finds Vh roughly twice as sensitive as WV, and shows LHC constraints rival electroweak precision data for light quarks and be

What carries the argument

The load-bearing machinery is five effective coupling shifts — δg_ZuL, δg_ZdL, δg_ZuR, δg_ZdR and δg_WqR — together with the SU(2)_L relation δg_WqL = δg_ZuL·V − V·δg_ZdL. In the high-energy limit, the helicity amplitudes of Eqs. (3.4)–(3.5) scale as s-hat/v^2; the Goldstone equivalence theorem, which identifies longitudinal W/Z amplitudes with those of the would-be Goldstone bosons at high energy, connects the Vh and WV channels, so the same operators produce correlated energy-enhanced tails in both. This five-coupling structure, with explicit CKM factors, is what makes a flavor-general fit possible with existing LHC differential data.

Load-bearing premise

The constraints assume new physics appears only through four-fermion and Higgs-current contact terms that weakly coupled ultraviolet completions generate at tree level, with loop-type dipole operators set to zero even though they would grow with energy just as fast in pp→VW; a model with sizable tree-level dipoles would shift all the quoted bounds.

What would settle it

Refit the same ATLAS/CMS pp→Vh and pp→VW differential data with dipole operators ψ²XH included as free tree-level parameters. If the preferred values of δg_ZuL, δg_ZdL, δg_ZuR, δg_ZdR or δg_WqR move outside the 95% intervals of Fig. 4.1, the paper's five-coupling amplitude basis is not the right description of the tails.

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

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If this is right

  • Associated Higgs production gives the strongest LHC limits on the five Higgs-current operators, about twice as strong as the diboson channels at the same luminosity, because the Vh SM background is dominated by longitudinal modes.
  • LHC Vh+WV data remove flat directions that electroweak precision data leave in the light-quark sector, superseding the constraining power of Drell-Yan forward-backward asymmetry measurements.
  • Right-handed charged currents (operator C_Hud), essentially unconstrained by Z- and W-pole data, are bounded at |C_Hud_11|/Λ² ≲ 0.1 TeV⁻² by the Vh tails.
  • HL-LHC projections reach the C_Hud_11 and C_Hud_12 regions preferred by low-energy fits to the Cabibbo-angle anomaly, so the high-energy LHC can test that anomaly's new-physics explanation.
  • Because no flavor ansatz is imposed, the bounds hold for non-universal models such as TeV-scale vector-like quarks coupled to first- or second-generation quarks.

Where Pith is reading between the lines

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

  • One extension of this approach is to add angular observables of Vh and WV final states, which the paper notes are available and would distinguish the five couplings by their interference patterns with the Standard Model.
  • The same amplitude relations could be applied to other CKM-weighted channels such as vector-boson scattering or final states with charm quarks, extending the method beyond the processes fitted here.
  • A combined future fit of Vh, WV and high-pT Drell-Yan data could simultaneously constrain the full tree-level operator class and test whether the five-coupling description remains sufficient once dipole operators are included.

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

2 major / 5 minor

Summary. The paper studies pp->Vh and pp->VW production at the LHC as probes of SMEFT Higgs-current operators (psi^2 H^2 D) with a general flavor structure. In Sec. 3 the authors derive the high-energy helicity amplitudes and express the leading flavor-dependent contributions in terms of five effective couplings (delta g_ZuL, delta g_ZdL, delta g_ZuR, delta g_ZdR, delta g_WqR) with an explicit CKM-matrix dependence. They then use Run-2 differential data from ATLAS and CMS on WW, WZ, Zh, and Wh to obtain 95% CL bounds on the Wilson coefficients C_Hq^(1), C_Hq^(3), C_Hd, C_Hu, and C_Hud for different quark-flavor indices (Fig. 4.1). The LHC constraints are compared with electroweak precision observables (Sec. 5) and with low-energy flavor data relevant to the first-row CKM unitarity test (Sec. 6), including HL-LHC projections and a vector-like-quark model. The central claim is that these LHC channels provide complementary, and in some cases competitive, constraints on flavor-non-universal Higgs-current operators.

Significance. If the derived bounds are correct, this is a useful step toward a fully flavor-general SMEFT likelihood for high-energy processes. The paper's strengths include the explicit CKM factors in the amplitudes, the use of differential LHC data rather than signal strengths, the demonstration of complementarity with EWPO and low-energy flavor fits, and falsifiable HL-LHC projections. The analysis is not circular: the amplitudes follow from the gauge-invariant SMEFT Lagrangian and are then compared with independent data sets. The main caveats are the tree-level-only operator assumption and the LO treatment of the EFT signal, both of which need quantitative support before the numerical constraints in Fig. 4.1 can be taken at face value.

major comments (2)
  1. [Sec. 2.1 / Table 2.1 / Fig. 4.1] The restriction to operators generated at tree level in weakly coupled UV completions is load-bearing for the identification of the pp->VW observables with the five psi^2 H^2 D couplings. Table 2.1 assigns dipole operators (psi^2 X H) the same E^2/Lambda^2 amplitude growth as psi^2 H^2 D for pp->VW, and the text acknowledges that these are dropped as loop-suppressed without quantifying the loop factor against the sensitivity of the fit. Since Fig. 4.1 combines the WW and WZ data, a loop-induced dipole coefficient of size ~g y_q/(16 pi^2) times a tree-level coefficient could be non-negligible relative to the quoted intervals, which are O(0.01-0.1) TeV^-2. I request a numerical check: either include representative dipole/TGC operators in the fit and show that the five-coupling intervals in Fig. 4.1 shift negligibly, or derive upper bounds on those operators from the same data. The Vh const
  2. [Sec. 4.1 and Sec. 4.2] The EFT contributions (A_NP and B_NP in Eq. (4.1)) are simulated at LO QCD, while the SM predictions are taken from the experimental analyses, and the paper states without demonstration that PDF/scale uncertainties on the EFT terms have a negligible impact. Because the bounds are extracted from the high-pT tails, the scale and PDF dependence of the EFT signal can shift the inferred intervals. Please provide a quantitative estimate of this uncertainty (e.g., a scale/PDF envelope) or cite a validation specific to these final states. This is relevant to all channels and hence to the central bounds in Fig. 4.1.
minor comments (5)
  1. [Sec. 4.1.1, Eqs. (4.3)-(4.4)] The CMS WW recast uses hand-set pull uncertainties sigma_th, sigma_bkg in [0.1,0.2]. The authors state that the implementation was validated against CMS limits, but reporting the dependence of the WW-only bounds on these choices would improve reproducibility and robustness.
  2. [Sec. 1] Typo: 'illlustrate' should be 'illustrate'; 'Particle Distribution Functions' should be 'Parton Distribution Functions'.
  3. [Sec. 6.2.2] Typo: 'short-distand electroweak corrections' should be 'short-distance electroweak corrections'.
  4. [Sec. 6.3] The statement that there are other charged-current transitions for which the LHC constraints derived in this study can already supersede flavor bounds [87] refers to unpublished work. Either show this explicitly or soften the claim.
  5. [Sec. 5] The EWPO bounds are evaluated at mu = 1 TeV, but the LHC bounds in Fig. 4.1 are not accompanied by an explicit statement of the renormalization scale used for the LHC predictions. Please state the scale convention so the comparison in Fig. 5.1 is unambiguous.

Circularity Check

0 steps flagged

No significant circularity: the amplitudes are derived from SMEFT gauge invariance and matched to independent LHC, EWPO and flavor data; the CKM-anomaly benchmark is imported from external fits.

full rationale

The derivation chain is self-contained against external benchmarks. Section 2 defines the SMEFT operator basis and the matching relations (Eq. 2.6), with the gauge-invariance relation Eq. (2.4) taken from an independent reference [32]. Section 3 derives the high-energy helicity amplitudes for pp→Vh and pp→VW directly from those couplings, including explicit CKM factors; no fitted quantity is reused as an input to the same prediction. Section 4 builds a chi-square likelihood from published LHC Run-2 differential measurements and uses it to constrain the Higgs-current Wilson coefficients: these are fits to data, not predictions masquerading as tests. The comparison in Section 5 uses electroweak precision observables that are external to the LHC fit, and Section 6 imports the viable CKM-unitarity-anomaly benchmark from independent global fits [60,61] before applying the LHC constraints. The only assumptions that could affect the interpretation, such as the restriction to tree-level-generated operators and the neglect of loop-suppressed dipole/TGC operators noted in Sec. 2.1 and Table 2.1, are stated model assumptions rather than circular reductions; they concern robustness but do not make the LHC bounds equivalent to any input in the derivation. Self-citations [24,25,79,87] provide Drell-Yan methodology, Kℓ3 expressions, and future-work references, none of which is load-bearing for the central Vh/VW amplitude derivation or for the numerical constraints.

Axiom & Free-Parameter Ledger

4 free parameters · 8 axioms · 0 invented entities

The paper's results rest entirely on the SMEFT framework: the Warsaw basis, the gauge-invariance relation (2.4) linking W and Z coupling shifts, and the Goldstone equivalence theorem used for the high-energy amplitudes. The main modeling assumption is that only tree-level-generated operators matter. The CMS WW recast introduces hand-set nuisance pulls. No new particles or entities are invented; the vector-like quark benchmark is imported from Refs. [60,61].

free parameters (4)
  • CMS WW pull uncertainties (σ_th, σ_bkg, σ_dat) = σ_th, σ_bkg ∈ [0.1, 0.2]; σ_dat = 0.02
    Hand-chosen nuisance parameters for the Poisson chi-square recast of the CMS WW measurement, Sec. 4.1.1; validated only against one limit in Ref. [43].
  • EWPO reference scale μ = 1 TeV = 1 TeV
    The EWPO fit runs Wilson coefficients from μ = 1 TeV to m_Z (Sec. 5); the LHC-side scale is not stated, so the comparison in Fig. 5.1 relies on this implicit choice.
  • Low-energy CKM fit parameters (λ, δg_VR^d, δg_VR^s) = 95% CL region in Fig. 6.1
    Sec. 6.2.4: λ and the right-handed couplings are fitted to pion/kaon/β decay data to identify the viable scenario compared with LHC bounds in Fig. 6.2.
  • Vector-like quark mass m_Q = 2 TeV
    Set to 2 TeV to satisfy direct search bounds (Sec. 6.4); benchmark value for the model constraints in Fig. 6.3, not fitted to the data used in the main analysis.
axioms (8)
  • standard math SMEFT truncated at dimension six in the Warsaw basis
    Sec. 2, Eq. (2.1), Refs. [22,23]; all higher-dimension operators are neglected.
  • standard math Gauge-invariance relation δg_W^L = δg_Zu^L·V − V·δg_Zd^L
    Eq. (2.4) following Ref. [32]; maps the five coupling shifts and connects WW, WZ, Zh and Wh amplitudes.
  • standard math Goldstone Boson Equivalence Theorem
    Sec. 3, Refs. [18,37-40]; used to justify the energy growth and the relations among Vh and WV amplitudes.
  • domain assumption Only tree-level-generated operators are included; dipoles (ψ^2XH) and TGCs (X^3) are neglected
    Sec. 2.1: 'generated at tree level by weakly coupled and renormalizable UV scenarios'; Table 2.1 shows dipoles contribute E^2/Λ^2 to pp→VW, so this assumption is load-bearing for the operator mapping.
  • domain assumption EFT validity Λ ≫ E for the LHC processes
    Sec. 2.1: 'we require that the EFT cutoff Λ is sufficiently larger than the typical energy scale E of the LHC processes'; also underlies the quadratic expansion in Eq. (4.1).
  • domain assumption Wilson coefficients are real
    Sec. 4.2: 'We assume the Wilson coefficients to be real'; complex phases would change interference and the shape of the confidence intervals.
  • domain assumption Down-type quark Yukawas are diagonal with q_i = [(V†u)_Li, d_Li]^T
    Sec. 2 basis convention; determines how the flavor indices of the bounds map to physical quark flavors.
  • standard math External low-energy inputs (lattice decay constants and form factors, S_EW, radiative corrections) are taken as given
    Sec. 6.2: f_K/f_π, f_+(0), S_EW and the β-decay corrections come from the cited FLAG and literature; the paper does not derive them.

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Cite this review

Pith. "Pith review of Flavor constraints from $pp\to Vh$ and $pp\to VW$ at the LHC." pith.science (2026). https://pith.science/paper/5D6K5ZHB

@misc{pith2026250908437,
  author       = {Pith},
  title        = {Pith review of: Flavor constraints from $pp\to Vh$ and $pp\to VW$ at the LHC},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5D6K5ZHB}},
  note         = {Machine review of arXiv:2509.08437}
}
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read the original abstract

We investigate the potential of associated Higgs $pp\to Vh$ and diboson production $pp\to VW$ channels at the LHC (with $V=W,Z$) to constrain flavor-physics operators. Within a general Effective Field Theory (EFT) framework, we derive the helicity amplitudes for these processes at high energies and identify the leading contributions from dimension-six operators involving different quark flavors. Using available LHC data, we show that these processes are sensitive to non-trivial flavor structures and provide complementary constraints to those from low-energy observables. We illustrate this synergy through an explicit comparison between our LHC bounds with electroweak precision data, and with flavor limits derived from charged-current pion and kaon decays. In particular, we show that our HL-LHC projections can probe viable EFT scenarios proposed to accommodate the discrepancies in the extraction of the Cabibbo angle.

Figures

Figures reproduced from arXiv: 2509.08437 by L. P. S. Leal, M. Martines, O. J. P. \'Eboli, O. Sumensari.

Figure 1.1
Figure 1.1. Figure 1.1: Illustration of energy-enhanced EFTcontributions to a) pp → ℓℓ, ℓν b) pp → V h and c) pp → V W, with V = W, Z, from flavor-dependent operators. The insertions of ψ 4 semileptonic operators are denoted in orange, and those from Higgs-current ψ 2H2D operators to quarks in blue and red for neutral- and charged-current interactions, respectively. See [PITH_FULL_IMAGE:figures/full_fig_p004_1_1.png] view at source ↗
Figure 4.1
Figure 4.1. Figure 4.1: Constraints on the dimension-six Higgs-current Wilson coefficients, considering a single non-vanishing coefficient at a time for the V h and W V production channels. Quark flavor-indices ij are specified on the left-hand side of each plot with the 95% confidence interval on the right panels. All coefficients are assumed to be real and contributions to the cross-section include EFT contributions up to the… view at source ↗
Figure 4.2
Figure 4.2. Figure 4.2: The parton-level distributions for the V h (top) and W V (bottom) processes are plotted as functions of the process center-of-mass energy. In the large panels, we present the SM predictions, including all polarizations of the final-state vector bosons (shaded gray area), as well as the separate contributions from the longitudinal (solid orange line) and transverse (solid green line) components. We also s… view at source ↗
Figure 5.1
Figure 5.1. Figure 5.1: Comparison of the limits at 95% CL on the coefficients C (1) Hq, C (3) Hq, CHd, CHu and CHud, for different flavor-diagonal indices, which are extracted from EWPO (blue), and LHC diboson and Higgs associated production data (red). The EFT cutoff is fixed to Λ = 1 TeV in the EWPO analysis. diboson and Higgs associated production on light-flavor quark couplings (i.e., 11 and 22) are competitive with those … view at source ↗
Figure 5.2
Figure 5.2. Figure 5.2: Constraints on Higgs-current operators coupled to first-generation quarks derived from EWPO in Sec. 5 (blue), and pp → V h and pp → V W data in Sec. 4.2 (purple). For comparison, we also display the constraints from Drell-Yan Afb taken from Ref. [55], which are superseded by associated Higgs production. The two-dimensional constraints are provided at 95% CL, setting the other effective coefficients to ze… view at source ↗
Figure 6.1
Figure 6.1. Figure 6.1: Low-energy constraints on the λ ≡ |Vus| and the Wilson coefficients δgq VL ≡ δgqℓ VL and δgq VR ≡ δgqℓ VR (for ℓ = e, µ), which are assumed to be lepton-flavor universal. The 1σ allowed regions are depicted for Kµ2/πµ2 (yellow), Kℓ3 (magenta) and β-decays (blue), with their combination to 1σ and 2σ accuracies depicted by the black lines. For the individual limits, the coefficients not displayed in the pa… view at source ↗
Figure 6.2
Figure 6.2. Figure 6.2: Comparison of current LHC (gray) and flavor (purple) constraints at 95% CL for the right-handed operators entering the d → uℓν and s → uℓν transitions. The projections to HL-LHC are depicted by the dashed lines, which will allow us to test the region currently allowed by low-energy bounds. We stress once again that the improvement with respect to previous studies comes mostly from the differential data t… view at source ↗
Figure 6.3
Figure 6.3. Figure 6.3: Constraints on the couplings of a vector-like quark Q ∼ (3, 2, 1/6) with couplings exclusively to first-generation SM quarks (left panel), and with couplings to first-generation up-type and second-generation down-type quarks (right panel); cf. Eq. (6.22). The vector-like quark mass is set to mQ = 2 TeV and the couplings displayed are set to zero. The constraints from flavor (magenta) and electroweak (gra… view at source ↗

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