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Electroweak corrections to the SM-like Higgs boson decays and the Higgs trilinear coupling in the real Higgs triplet model

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Masashi Aiko, Shinya Kanemura, Mariko Kikuchi, Kodai Sakurai, Sora Taniguchi, Kei Yagyu

High Energy Physics - Phenomenology · Submitted 3 Nov 2026 · 109 references

Pith's verdict: A genuinely useful NLO renormalization calculation for the RHTM with a distinguishability claim that needs statistical support before it can stand.

T0 · AI review

How this review was made: An AI referee (deepseek/deepseek-v4-flash) read the paper on November 4, 2026 and answered a fixed list of questions about it. T0 is the starting level every paper gets. The levels describe how deeply Pith has checked the paper, never the authors.

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arXiv ID2611.04857 (version 1)
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CitationKei Yagyu, Kodai Sakurai, Mariko Kikuchi, Masashi Aiko, Shinya Kanemura, Sora Taniguchi. "Electroweak corrections to the SM-like Higgs boson decays and the Higgs trilinear coupling in the real Higgs triplet model." arXiv:2611.04857 (2026). https://pith.science/paper/BS46ZA3J
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The paper

The paper claims

One-loop corrections to 125 GeV Higgs decays stay sizable in the real Higgs triplet model where tree-level deviations vanish, and the correlation pattern of the shifts can distinguish the model from other extended Higgs sectors.

The reading

The paper sets out to show that in the real Higgs triplet model — the Standard Model extended by an isospin-triplet scalar — one-loop electroweak corrections can make the 125 GeV Higgs boson's decay rates deviate measurably from the Standard Model even where the tree-level deviations are nearly invisible. The tree-level smallness is forced by electroweak precision data, which keep the triplet vacuum expectation value at about 2 GeV or below. The paper constructs a gauge-independent on-shell renormalization scheme for the model, computes the full one-loop corrections, and finds that the dominant effects enter through the SM-like Higgs wave-function (external-leg) renormalization, which suppresses $h\to\tau\tau$ and $h\to ZZ^*$ together, while the charged-Higgs loop drives $h\to\gamma\gamma$ and the trilinear $hhh$ coupling. On this basis it argues that the correlation pattern among those three decay modes can distinguish the RHTM from singlet, doublet, inert-doublet, and complex-triplet extensions, a test that falls within the reach of the HL-LHC and future Higgs factories.

What carries the argument

The load-bearing machinery is a full one-loop on-shell renormalization of the RHTM scalar, gauge, and fermion sectors, with the mixing-angle counterterms fixed in a gauge-independent way by pinch-technique contributions to the $h$–$H$ and $H^\pm$–$G^\mp$ self-energies; the charged-scalar pinch terms are new in that they involve the tree-level $H^\pm W^\mp Z$ vertex, which does not exist in two-doublet models. Two elements then carry the physics. First, the SM-like Higgs wave-function renormalization constant $\delta Z_{hh}$ channels the dominant radiative corrections into all $h\to f\bar f$ and $h\to VV^*$ rates, producing the common negative shift that anchors the correlation pattern. Second, the charged-Higgs coupling $g_{H^+H^-h}\approx-\lambda_3 v$ controls the diphoton rate and, together with the heavy-scalar loops, the effective $hhh$ coupling, so that the whole phenomenology in the small-$v_\Delta$ limit reduces to simple scaling formulas in $\lambda_3$ and $m_{H^\pm}$. The numerical study scans $m_{H^\pm}$ from 200 to 1000 GeV and $v_\Delta$ from 0.1 to 3 GeV, imposing vacuum stability, tree-level unitarity, electroweak precision, and Higgs-signal constraints, and the analytic results are implemented in the H-COUP program so that all five extended models are evaluated under one renormalization scheme.

Extended reading notes

Core claim

The central claim is that a small triplet vacuum expectation value does not mean small new-physics effects. Because the triplet VEV shifts the tree-level rho parameter, precision data force $v_\Delta \lesssim 2$ GeV, and every tree-level coupling of the SM-like Higgs stays close to its Standard Model value; yet the one-loop corrections are not equally suppressed. The dominant loop effect is the wave-function renormalization $\delta Z_{hh}$ of the SM-like Higgs boson, which moves the $h\to f\bar f$ and $h\to VV^*$ rates downward in step, approximately $\kappa_Z^2 - 1 \approx -\lambda_3^2 v^2/(64\pi^2 m_{H^\pm}^2)$, while the charged-Higgs loop, whose coupling is $g_{H^+H^-h} \approx -\lambda_3 v$, controls $h\to\gamma\gamma$ and the $hhh$ vertex, with $\kappa_\lambda \approx 1 + \lambda_3^3 v^4/(32\pi^2 m_h^2 m_{H^\pm}^2)$. Because a single parameter, the doublet–triplet quartic coupling $\lambda_3$, drives all three observables, the resulting pattern — both $\Delta R(h\to\tau\tau)$ and $\Delta R(h\to ZZ^*)$ negative, with the diphoton deviation larger in magnitude — gives a fingerprint that the paper argues separates the RHTM from the HSM, IDM, 2HDMs, and CHTM. The calculation is carried out in an on-shell scheme in which the scalar mixing angles are renormalized gauge-independently via the pinch technique, including new pinch contributions from the tree-level $H^\pm W^\mp Z$ coupling that is absent in doublet extensions.

Load-bearing premise

The distinction from other models depends on the charged Higgs boson being light — a few hundred GeV, where its loop contribution is controlled by the doublet–triplet quartic coupling $\lambda_3$ — while the triplet vacuum expectation value stays below about 2 GeV, because for heavier charged Higgs bosons the one-loop deviations shrink and the RHTM's predictions overlap with those of other extended Higgs models.

Editorial extensions

If this is right

  • Small tree-level deviations do not imply a hidden model: percent-level one-loop shifts in the decay rates put the RHTM within reach of HL-LHC and future Higgs-factory measurements.
  • Vacuum stability excludes the negative $\lambda_3$ values that would lower $\kappa_\lambda$ below one, so the RHTM generically predicts an enhanced trilinear Higgs coupling, with Higgs-pair production providing the strongest $\lambda_3$ bound for $m_{H^\pm}\lesssim600$ GeV and the diphoton rate providing it below about 300 GeV.
  • Branching-ratio correlations carry more discriminating power than rate correlations: because the total Higgs width also shifts, the $\Delta\mu$ plane separates the RHTM from the type-II 2HDM even where the $\Delta R$ plane overlaps.
  • The same renormalization scheme is applied to the HSM, IDM, 2HDMs, and CHTM within the H-COUP program, so the claimed distinction is a direct comparison under identical conventions rather than a model-by-model patchwork.

Reading between the lines

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

  • Scope of the claim: the correlation fingerprint lives in the light-charged-Higgs corner of the model, roughly $m_{H^\pm}\lesssim600$ GeV with $v_\Delta\lesssim2$ GeV; for heavier charged Higgs bosons the loop deviations collapse and the RHTM predictions rejoin those of other models, so the paper's conclusion is best read as a statement about that corner.
  • Transferable machinery: the pinch-term treatment of the tree-level $H^\pm W^\mp Z$ coupling should carry over to any model with such a vertex, such as Georgi–Machacek-style triplet constructions; if the same correlation logic holds there, the $\delta Z_{hh}$-driven pattern may be a general property of triplet rather than doublet extensions, which is an extrapolation beyond what the paper computes.
  • A sharper quantitative discriminator than the paper proposes is the ratio $\Delta R(h\to\gamma\gamma)/\Delta R(h\to ZZ^*)$, which the charged-Higgs loop inflates above the common wave-function shift; a two-loop leading-log check would test whether the $\lambda_3$-scaling pattern survives the next order.
Original abstract

We study new physics effects on the decays of the standard model-like Higgs boson ($h$) and the Higgs trilinear coupling including the full one-loop corrections in the real Higgs triplet model (RHTM). We adopt the on-shell renormalization scheme, in which the scalar mixing angles are renormalized in a gauge-independent way using the pinch technique. We found that sizable one-loop effects can arise in the decay rates through the Higgs wave-function (external-leg) corrections, while the tree-level effects are rather small due to the constraint on the vacuum expectation value of the triplet field from the electroweak precision measurements. In addition, the $h\to\gamma\gamma$ decay rate and the $hhh$ coupling are sensitive to loop contributions. The RHTM may be distinguishable from other extended Higgs models by studying the correlations among the $h\to\tau\tau$, $h\to ZZ^{*}$, and $h\to\gamma\gamma$ decay modes, and such characteristic predictions can be tested at the High-Luminosity LHC or future Higgs factories.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-11-04: 1 request, 4,552 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.37 · human participants 0.01 · controlled comparison 0.12 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.34 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We study new physics effects on the decays of the standard model-like Higgs boson ($h$) and the Higgs trilinear coupling including the full one-loop corrections in the real Higgs triplet model (RHTM). We adopt the on-shell renormalization scheme, in which the scalar mixing angles are renormalized in a gauge-independent way using the pinch technique. We found that sizable one-loop effects can arise in the decay rates through the Higgs wave-function (external-leg) corrections, while the tree-level effects are rather small due to the constraint on the vacuum expectation value of the triplet field from the electroweak precision measurements. In addition, the $h\to\gamma\gamma$ decay rate and the $hhh$ coupling are sensitive to loop contributions. The RHTM may be distinguishable from other extended Higgs models by studying the correlations among the $h\to\tau\tau$, $h\to ZZ^{*}$, and $h\to\gamma\gamma$ decay modes, and such characteristic predictions can be tested at the High-Luminosity LHC or future Higgs factories.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We study new physics effects on the decays of the standard model-like Higgs boson ($h$) and the Higgs trilinear coupling including the full one-loop corrections in the real Higgs triplet model (RHTM). contribution 1.00 0.93 0.08 asserted 0.88
s1 We adopt the on-shell renormalization scheme, in which the scalar mixing angles are renormalized in a gauge-independent way using the pinch technique. method 1.00 0.88 0.03 asserted 0.99
s2 We found that sizable one-loop effects can arise in the decay rates through the Higgs wave-function (external-leg) corrections, while the tree-level effects are rather small due to the constraint on the vacuum expectation value of the triplet field from the electroweak precision measurements. result 1.00 0.94 0.48 asserted 0.99
s3 In addition, the $h\to\gamma\gamma$ decay rate and the $hhh$ coupling are sensitive to loop contributions. result 1.00 0.76 0.14 asserted 0.99
s4 The RHTM may be distinguishable from other extended Higgs models by studying the correlations among the $h\to\tau\tau$, $h\to ZZ^{*}$, and $h\to\gamma\gamma$ decay modes, and such characteristic predictions can be tested at the High-Luminosity LHC or future Higgs factories. interpretation 0.66 0.34 0.51 hedged possibility 1.00

What kind of paper the classifier reports this is: theoretical result 0.97 · evidence from simulation or computation 0.60.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures
Figure 1. (Left) Contours of mH in the λ2–λ3 plane with mH± = 200 GeV and v∆ = 1 GeV. The red (blue) region is excluded by vacuum stability (tree-level unitarity). (Right) Prediction for the W-boson mass with mH± = 200 GeV. The black solid line shows the LO prediction, while the green points are the NLO predictions. The dotted and dashed lines indicate the central value and 2σ uncertainty of the observed W-boson mass, respectively. For the NLO prediction, λ2 and λ3 are scanned under the theoretical bounds. 4.2 Experimental constraints First, we discuss the constraint from the measurement of…
Figure 2. (Left) Prediction for ∆κγ and (Right) κλ with theoretical and experimental constraints. The dashed lines indicate the constraints on κγ and κλ. The colored (gray) points are allowed (excluded) by the Higgs signal measurements. In the right panel, the dot-dashed line indicates the maximal deviation allowed by the theoretical constraints. This definition isolates the effects of new physics from the SM prediction and approaches unity in the decoupling limit. 4.3 Deviation in the SM-like Higgs boson decays We study the deviations in the SM-like Higgs boson decays at NLO. Following the…
Figure 3. Prediction for ∆κZ at LO (left) and NLO (right) subject to theoretical and experimental constraints. The colored (gray) points are allowed (excluded) by the Higgs signal measurements. In the right panel, the dot-dashed line indicates the maximal devia￾tion allowed by the theoretical constraints. the limit v∆ ≪ v and mh ≪ mH± , mH, the leading contribution can be approximated as κλ ≈ 1 + λ 3 3 v 4 32π 2m2 hm2 H± . (4.25) Thus, the loop contribution is positive (negative) for positive (negative) λ3. Since negative λ3 is constrained by vacuum stability, κλ is typically larger than…
Figure 4. Correlations between the deviations in the decay rates (upper panels) and branching ratios (lower panels) of the SM-like Higgs boson at NLO EW. The left and right panels show the predictions on the h → τ τ and h → ZZ∗ and on the h → γγ and h → ZZ∗ channels, respectively. Different colors indicate the different extended Higgs models shown in the upper-left panel. In the 2HDM, predictions with cβ−α < 0 (cβ−α > 0) are shown in darker (lighter) colors. Similarly, in the CHTM, predictions with HS (LS) are shown in darker (lighter) colors. RHTM. In the 2HDMs, ∆R(h → τ τ ) is sensitive to…
Figure 5. Feynman diagrams contributing to the gauge-dependent parts of the charged scalar self-energies. the gauge-dependent parts of the charged scalar self-energies are shown in
Figure 6. Feynman diagrams contributing to the pinch terms extracted from the u ¯d → u ¯d scattering amplitude. – 53 –

Figures reproduced from arXiv:2611.04857 by the authors.

References

Discussion

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