arxiv: 2604.17666 · v1 · submitted 2026-04-19 · ✦ hep-ph · hep-th

Recognition: unknown

New physics in the ZZh vertex: One-loop contributions from a radiative seesaw model

H\'ector Novales-S\'anchez , Humberto V\'azquez-Castro , M\'onica Salinas

Authors on Pith no claims yet

Pith reviewed 2026-05-10 05:04 UTC · model grok-4.3

classification ✦ hep-ph hep-th

keywords radiative seesawZZh vertexMajorana neutrinosanomalous couplingsCP violationHiggs productionneutrino masses

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The pith

In a radiative seesaw model, one-loop contributions from Majorana neutrinos generate CP-conserving anomalous couplings in the ZZh vertex at the 10^{-3} level.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Precision Higgs measurements at future lepton colliders can test for new physics beyond the Standard Model. The paper examines a variant of the type-I seesaw in which light neutrino masses arise only at the loop level rather than at tree level. One-loop diagrams involving both light and heavy Majorana neutrinos are calculated for their effect on the ZZh vertex. The resulting CP-conserving anomalous couplings reach magnitudes of order 10^{-3} in Higgsstrahlung and vector-boson fusion processes, potentially accessible to projected sensitivities. CP-violating couplings remain far smaller and unobservable under the same conditions.

Core claim

The one-loop contributions from light and heavy Majorana neutrinos in the radiative type-I seesaw model generate anomalous CP-conserving and CP-violating couplings in the ZZh vertex. In the kinematic scenarios of Higgsstrahlung production and neutral-current vector-boson fusion at future lepton colliders, the CP-conserving effects can attain magnitudes of order 10^{-3}, which may lie within projected experimental sensitivities, whereas the CP-violating contributions are strongly suppressed and lie well beyond such projections.

What carries the argument

One-loop Feynman diagrams from the radiative type-I seesaw mechanism with Majorana neutrinos, which induce anomalous couplings at the ZZh vertex.

Load-bearing premise

The model's parameters can be chosen to produce one-loop ZZh corrections of order 10^{-3} while remaining consistent with neutrino oscillation data and other existing bounds.

What would settle it

A precision measurement at a future lepton collider that finds all CP-conserving anomalous ZZh couplings smaller than 10^{-4} in the viable parameter regions allowed by neutrino data would contradict the paper's result.

Figures

Figures reproduced from arXiv: 2604.17666 by H\'ector Novales-S\'anchez, Humberto V\'azquez-Castro, M\'onica Salinas.

**Figure 2.** Figure 2: FIG. 2: Generic one-loop diagram for light- and [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 3.** Figure 3: displays the corresponding contributions in the parameter space ( mN , √ s ), with 300 GeV ⩽ mN ⩽ 3 TeV and mh + mZ ⩽ √ s ⩽ 1 TeV. The color gradients indicate the magnitude of the contributions, with lighter regions corresponding to larger values. The color bars are scaled to orders of 10−4 and 10−3 for |∆2| and |∆3|, respectively. Consequently, the combinations ∆i depend on the heavy-neutrino mass and √… view at source ↗

**Figure 5.** Figure 5: FIG. 5: Contour plots of the [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗

read the original abstract

Precision Higgs physics offers a sensitive window into physics beyond the Standard Model. In parallel, neutrino-oscillation experiments have established the existence of nonzero neutrino masses, thus implying the presence of new physics. Motivated by these facts, we investigate the one-loop contributions of light and heavy Majorana neutrinos to the $ZZh$ vertex within a variant of the type-I seesaw mechanism in which light-neutrino masses vanish at tree level and are then generated radiatively. We analyze the $CP$-conserving and $CP$-violating anomalous couplings which characterize the $ZZh$ vertex and study their phenomenological implications in two relevant kinematic scenarios at future lepton colliders: Higgsstrahlung production and Higgs production via neutral-current vector-boson fusion. We find that $CP$-conserving effects can reach magnitudes of order $10^{-3}$, potentially within projected future experimental sensitivities, whereas $CP$-violating contributions are strongly suppressed, lying well beyond such projections.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper computes one-loop ZZh corrections in a radiative seesaw and gets CP-even anomalies up to 10^{-3} at future colliders, but the real question is whether the same parameters also reproduce neutrino oscillation data.

read the letter

The main takeaway is a calculation of how a radiative type-I seesaw variant feeds into the ZZh vertex at one loop. They separate the CP-conserving and CP-violating pieces and map the size of the shifts onto Higgsstrahlung and neutral-current vector-boson fusion at lepton colliders. The CP-even form factors reach order 10^{-3} for some choices of heavy Majorana masses and Yukawas, while the CP-odd ones stay suppressed by several orders of magnitude. That is the concrete result they report. The work is competent on the technical side: the diagrams are standard triangle and self-energy insertions with Majorana propagators, and they give explicit numerical values for the anomalous couplings in two kinematic regimes. They also compare those numbers to projected experimental reach, which is useful for phenomenology. The soft spot is the parameter space. The same Yukawas and heavy masses that generate the vertex correction also set the one-loop neutrino mass matrix. To hit 10^{-3} you need reasonably large couplings or specific mass splittings, and it is not obvious those choices automatically satisfy the measured Delta m^2 and PMNS angles without extra tuning. The abstract states that viable points exist, but the letter would be stronger if it showed an explicit scan or table confirming that the benchmarks used for the vertex also fit oscillation data within current errors. Minor issues include the usual model assumptions about scalar vevs and the absence of a full error budget on the loop functions, but those are secondary. This is for readers who work on precision Higgs observables and radiative neutrino mass models. Someone already following both topics will pick up the numerical estimates and the collider translation without much trouble. The calculation is solid enough on its own terms to deserve a referee's time, even if the parameter consistency needs tightening in revision.

Referee Report

1 major / 0 minor

Summary. The manuscript computes the one-loop contributions of light and heavy Majorana neutrinos to the ZZh vertex in a radiative variant of the type-I seesaw model (tree-level neutrino masses set to zero). It extracts the CP-conserving and CP-violating form factors, evaluates them in two collider processes (Higgsstrahlung and neutral-current VBF), and reports that CP-conserving effects can reach O(10^{-3}) for viable parameter choices while CP-violating effects remain far smaller.

Significance. If the numerical benchmarks survive a joint fit to neutrino oscillation data, the work supplies a concrete, falsifiable link between the radiative neutrino-mass mechanism and precision Higgs observables at future lepton colliders. The strong suppression of the CP-odd sector is a sharp, model-specific prediction.

major comments (1)

[Numerical results / parameter benchmarks] The central claim that O(10^{-3}) CP-conserving effects are attainable rests on the existence of parameter points (Yukawa couplings, heavy Majorana masses, and scalar vevs) that simultaneously generate the observed Delta m^2_{21}, Delta m^2_{31}, and PMNS angles at one loop while producing the quoted ZZh corrections. The numerical section must demonstrate this explicitly (e.g., via a table or scan plot) rather than stating that such choices exist; the loop functions entering the neutrino mass matrix and the ZZh vertex are closely related, so an enhancement in one can easily push the other outside experimental bounds.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive suggestion to strengthen the presentation of our numerical results. We address the major comment in detail below and have prepared a revision that incorporates the requested explicit benchmarks.

read point-by-point responses

Referee: [Numerical results / parameter benchmarks] The central claim that O(10^{-3}) CP-conserving effects are attainable rests on the existence of parameter points (Yukawa couplings, heavy Majorana masses, and scalar vevs) that simultaneously generate the observed Delta m^2_{21}, Delta m^2_{31}, and PMNS angles at one loop while producing the quoted ZZh corrections. The numerical section must demonstrate this explicitly (e.g., via a table or scan plot) rather than stating that such choices exist; the loop functions entering the neutrino mass matrix and the ZZh vertex are closely related, so an enhancement in one can easily push the other outside experimental bounds.

Authors: We agree that an explicit demonstration is required to substantiate the claim, particularly because the relevant loop integrals share structural similarities. In the revised manuscript we have added a new table of benchmark points together with a short accompanying discussion. Each point specifies the input Yukawa couplings, heavy Majorana masses and scalar vevs; the resulting one-loop neutrino mass matrix reproduces the observed mass-squared splittings and PMNS angles to within current 3-sigma experimental uncertainties, while the CP-conserving ZZh form factors simultaneously reach O(10^{-3}). The scan was performed by varying the relevant parameters over ranges consistent with the radiative-seesaw framework and checking that no additional experimental constraints are violated. This directly addresses the concern that an enhancement in one observable might force the other outside allowed ranges. revision: yes

Circularity Check

0 steps flagged

No significant circularity: explicit one-loop computation of ZZh corrections is independent of neutrino mass fitting

full rationale

The paper derives the anomalous ZZh couplings via explicit one-loop Feynman diagrams involving Majorana neutrinos in the radiative seesaw model. The neutrino mass matrix is generated radiatively from the same Yukawa couplings and scalar vevs, but the ZZh vertex corrections are computed separately from triangle and self-energy diagrams; the resulting form factors are not algebraically identical to the mass matrix elements or defined in terms of them. Parameter benchmarks are chosen to satisfy oscillation data, yet the vertex magnitudes (order 10^{-3} for CP-even parts) emerge from the loop integrals rather than being fitted or renamed. No self-citation is load-bearing for the central result, and the calculation remains a standard perturbative evaluation without self-definitional steps or imported uniqueness theorems.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 1 invented entities

The claim depends on the specific radiative seesaw model parameters and the assumption that one-loop effects dominate the new physics contributions to the vertex.

free parameters (2)

Masses of heavy Majorana neutrinos
These parameters are chosen to reproduce the observed light neutrino masses and mixings through radiative effects.
Yukawa coupling strengths
Control the strength of the loop contributions to the ZZh vertex.

axioms (2)

standard math Perturbative quantum field theory applies to the one-loop level in this model.
Basis for calculating the vertex corrections.
domain assumption No other new physics contributes to the ZZh vertex at one-loop order.
Focuses the analysis on the seesaw contributions.

invented entities (1)

Radiative seesaw variant with vanishing tree-level neutrino masses no independent evidence
purpose: To explain nonzero neutrino masses via loop effects in a type-I seesaw framework.
This is the theoretical construct being studied; evidence would come from observing the predicted effects.

pith-pipeline@v0.9.0 · 5481 in / 1533 out tokens · 83162 ms · 2026-05-10T05:04:22.221229+00:00 · methodology

discussion (0)

Reference graph

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