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This paper presents the first NNLO QCD event-shape distributions for hadronic Higgs decays, for both H→gg and H→bb̄, and finds moderate corrections in the bulk with an enhanced gluon fraction in three-jet configurations.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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First NNLO QCD predictions for six classical event-shape distributions and soft-drop thrust in hadronic Higgs decays, for both H to b bbar and H to gg channels.

T0 review reviewed 2026-08-05 challenge →

load-bearing objection First NNLO event-shape predictions for H→gg and H→bbar decays, solidly done; the main caveat is that the gluonic channel rests on author-derived ingredients not independently cross-checked in the paper. the 2 major comments →

arxiv 2508.14282 v2 pith:5ORT42J5 submitted 2025-08-19 hep-ph

Precise Predictions for Event Shapes in Hadronic Higgs Decays

Elliot Fox , Aude Gehrmann-De Ridder , Thomas Gehrmann , Nigel Glover , Matteo Marcoli , Christian T. Preuss This is my paper
classification hep-ph
keywords hadronic Higgs decaysevent-shape variablesNNLO QCDthrustheavy jet massC-parameterjet broadeningsoft-drop thrust
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 reading

This paper aims to establish the first next-to-next-to-leading-order (NNLO) QCD predictions for event-shape distributions in hadronic Higgs-boson decays, covering the two dominant decay modes: H→gg in the heavy-top limit and H→bb̄ via the Yukawa coupling with kinematically massless quarks. It computes thrust, heavy jet mass, the C-parameter, total and wide jet broadening, the Durham three-jet resolution, and soft-drop thrust. The central finding is that NNLO corrections are moderate in the bulk of each distribution—typically below 20%—but grow near the Sudakov shoulders, and that the gluon-decay channel contributes roughly 25% of the total in three-jet-like configurations, more than double its inclusive fraction. If correct, these predictions give future electron-positron Higgs factories a benchmark for precision tests of QCD and for separating quark-initiated from gluon-initiated Higgs decays.

Core claim

On its own terms, the paper's discovery is that the six classical event-shape distributions and the soft-drop thrust in hadronic Higgs decays can be computed to NNLO accuracy, with the two dominant channels treated separately in an effective field theory where interference between them vanishes. Working in the Higgs rest frame and normalizing by the inclusive NNLO widths, the calculation finds mild corrections in the bulk—less than roughly 10–20% depending on the observable—with reduced scale uncertainty, good perturbative convergence for heavy jet mass, broadenings, and y23, and poorer convergence for thrust and in the region beyond the Sudakov shoulder. A recurring quantitative result is t

What carries the argument

The calculation is built on an effective field theory in which the Higgs couples to gluons through an effective Hgg vertex in the heavy-top limit and to massless bottom quarks through a non-vanishing Yukawa coupling, so the two decay channels have no interference and can be computed as separate processes. Infrared singularities are handled with generalized antenna subtraction, a systematic scheme that cancels divergences between real-emission and virtual contributions by subtracting antenna functions derived from the relevant infrared limits. The two-loop three-parton amplitudes for H→ggg and H→bb̄g supply the NNLO virtual input, and all distributions are evaluated in the Higgs rest frame wi

Load-bearing premise

The H→gg predictions all ride on the correctness of the two-loop three-gluon helicity amplitudes and the completeness of the antenna subtraction used to combine them with real radiation; the paper verifies its H→bb̄g amplitudes against an independent calculation but reports no such independent cross-check for the gluonic channel.

What would settle it

Recalculate the two-loop H→ggg helicity amplitudes by an independent method and rerun the full NNLO subtraction for the gluonic channel; any mismatch in the residual divergences or finite parts would change every displayed H→gg distribution. A shorter path is to measure normalized thrust and heavy-jet-mass distributions at a future e+e− Higgs factory and check whether the NNLO bands, including their scale variation, contain the data across the bulk and shoulder region.

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

If this is right

  • Future electron-positron Higgs-factory measurements of these distributions can be compared directly with these NNLO predictions, turning event shapes into a precision QCD test in the Higgs sector.
  • The quantified differences between the H→bb̄ and H→gg channels serve as a baseline for quark-gluon discrimination studies using hadronic Higgs decays.
  • The earlier breakdown of fixed-order perturbation theory in the gluonic channel identifies exactly where resummation is needed and which region will most constrain it.
  • Soft-drop thrust is shown to improve perturbative convergence toward the infrared, suggesting groomed observables as the practical choice for precision extraction.
  • The near-constant 75/25 channel split in the bulk offers a simple phenomenological rule for estimating background contributions in Higgs-decay analyses.

Where Pith is reading between the lines

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

  • If the gluonic-mode enhancement beyond the Sudakov shoulder persists after resummation, event-shape tails may act as an experimentally accessible proxy for the elusive H→gg decay at lepton colliders.
  • A testable extension is to apply the same soft-drop grooming to the C-parameter and broadenings; based on the thrust result, the strongest grooming (β=0) should push the fixed-order range further into the infrared.
  • Because the paper reports no independent numerical cross-check of the gluonic two-loop amplitudes or of the full gluonic NNLO subtraction, a dedicated recalculation of those amplitudes would be the fastest way to certify the H→gg distributions.
  • Since all distributions are normalized by inclusive widths, small shifts in the inclusive decay-rate corrections rescale every plot; this couples the event-shape precision to the accuracy of the inclusive width input.
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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. This paper presents fixed-order NNLO QCD predictions for a suite of event-shape distributions in hadronic Higgs decays. The two dominant decay modes, H→bbar (non-vanishing Yukawa coupling, kinematically massless b) and H→gg (heavy-top effective coupling), are treated as independent channels. The calculation uses the NNLOJET antenna-subtraction framework with generalized antenna functions and published two-loop amplitudes. Results are shown for thrust, heavy jet mass, C-parameter, total and wide jet broadening, Durham y23, and soft-drop thrust, normalized to the corresponding total decay width, with central scale μ_R=m_H/2 and factor-two variations. The main findings are moderate NNLO corrections in the bulk, Sudakov shoulders, and an enhanced gluonic fraction for large event-shape values, with the breakdown of fixed-order perturbation theory identified by the onset of negative gluonic distributions at small y.

Significance. If the calculation is correct, this is the first NNLO QCD differential event-shape prediction for hadronic Higgs decays and a substantive input for future Higgs-factory phenomenology and quark–gluon discrimination studies. The paper is not a fit: the central predictions are parameter-free perturbative QCD results, and the authors clearly state the region where fixed-order perturbation theory breaks down. They also provide scale-variation uncertainties and verify the H→bbg amplitude class against ref. [91]. The main weakness is a verification gap: the H→gg predictions rely on author-derived two-loop amplitudes (ref. [95]) and generalized antenna functions (ref. [77]), and no independent numerical cross-check of these ingredients or of the full NNLO subtraction in the gluonic channel is reported. This gap is load-bearing for the quantitative gluonic results and for the headline claim of an enhanced gluonic fraction in three-jet-like configurations.

major comments (2)
  1. [Sec. 2, Table 1 and Figs. 2–5] The central H→gg predictions rest on two ingredients that are not independently verified in this manuscript: the two-loop H→ggg and H→gqqbar helicity amplitudes from ref. [95], derived by some of the same authors, and the generalized antenna functions of ref. [77]. The text states that the calculation agrees with the numerical results of ref. [91], but that check concerns the H→bbg amplitude class; no analogous check is reported for the gluonic amplitudes or for the full NNLO antenna subtraction in the H→gg channel. An error in either ingredient would propagate into every displayed H→gg curve and would alter the qualitative observation that the gluonic fraction is enhanced in three-jet-like configurations. Please add a dedicated validation subsection. Concretely: (i) integrate the unnormalized coefficients A, B, C of Eq. (2.3) over the full phase space and compare with the inclusive NNLO
  2. [Sec. 2, after Eq. (2.1)] The statement that 'all interferences between the H→bbar and H→gg decay channels vanish' is load-bearing for treating the two channels as independent and for the total sum in Eqs. (3.2)–(3.3). This assertion is not proved in the manuscript. A standard justification for massless quarks is that the Yukawa amplitude and the Hgg→bbar g amplitude have opposite chirality/helicity structures and hence do not interfere after spin summation, but this should be stated explicitly. Please add a short derivation or a precise reference; if any interference survives at O(α_s^3) in the total rate, the total predictions would need to be revisited.
minor comments (5)
  1. [Appendix B, Eq. (B.1)] In the expression for C_{bbar}(μ_R), the term [(β1+2γ1)L_R + (β0+γ0)(β0+2γ0)L_R^2] appears to multiply B_{bbar}(μ0). By comparison with the gluonic formula in Eq. (B.3) and with the standard structure of scale-dependent expansion coefficients, the final line should multiply A_{bbar}(μ0). Please check and correct.
  2. [Sec. 2.2] Typo: 'obersables' should be 'observables' in the jet-broadening paragraph.
  3. [Sec. 3.1] The notation 'y 1/Γ(k) dΓ/dy' is ambiguous as typeset; please write it as y (1/Γ(k)) dΓ/dy or an equivalent unambiguous form.
  4. [Figs. 2–5] The truncation values (τ>0.015, ρH>0.01, BT>0.05, etc.) are given in the text but not in the captions. Adding them to the captions would make the plots self-contained and avoid the impression of arbitrary cutoffs.
  5. [General] No numerical tables or supplementary data files are provided. For a precision paper of this type, making the central NNLO distributions available in tabulated form would improve reproducibility and allow direct use by the community.

Circularity Check

0 steps flagged

No significant circularity; the NNLO distributions are parameter-free fixed-order QCD calculations with prior independent inputs.

full rationale

The derivation chain is a standard fixed-order QCD calculation: the differential rate in Eq. (2.3) is defined directly from partonic matrix elements and the antenna-subtraction framework [75–77,99,100]. No event-shape distribution is used as an input to define those ingredients, and no parameter is fitted to the quantities being predicted. The only author-overlapping inputs are the two-loop H→3-parton helicity amplitudes from ref. [95] and the generalised antenna functions of ref. [77]. Both are prior, separate derivations with stated assumptions (heavy-top limit for the amplitudes; QCD infrared limits for the antenna functions) and do not use the present event-shape results as inputs. They therefore constitute independent support in the sense required here, even though they are not machine-checked in this paper. The paper reports an external check of the H→bb̄g amplitudes against ref. [91], and although no analogous numerical cross-check is documented for the gluonic two-loop amplitudes or for the full NNLO subtraction in the gluonic channel, that is a verification gap and a correctness risk, not a circularity: no equation in the paper reduces the predicted distributions to the fitted values, to the asserted conclusions, or to a self-citation chain. No self-definitional reasoning, fitted-input-as-prediction, imported uniqueness, or renaming of known results occurs. The central claim is therefore self-contained against external perturbative inputs, and the circularity score is 0.

Axiom & Free-Parameter Ledger

1 free parameters · 4 axioms · 0 invented entities

The calculation has no fitted free parameters in the statistical sense; alpha_s, quark masses, m_H, and G_F are external inputs from prior measurements. The renormalisation scale is a conventional choice, varied for uncertainty. The central new results are derived from previously published parameter-free amplitudes and antenna functions, so the circularity burden is low.

free parameters (1)
  • Central renormalisation scale mu_R = m_H/2 = 62.545 GeV, varied by a factor 2
    Chosen by hand following the inclusive Higgs production convention; all displayed NNLO curves are evaluated at this scale, and the uncertainty bands come from varying it.
axioms (4)
  • domain assumption Heavy-top effective theory for H to gg and massless b-quarks with a non-zero Yukawa coupling, with all interferences between the two channels vanishing
    Invoked in Section 2 to treat H to bb and H to gg as separate processes; finite quark mass effects or interference corrections would change the distributions.
  • domain assumption The generalized antenna functions of refs. [75-77] form a complete NNLO subtraction scheme for these processes
    Core technical framework of the calculation; correctness is assumed from prior work by overlapping authors.
  • domain assumption The two-loop three-parton amplitudes from refs. [95, 91, 98] are correct
    Amplitudes are taken from the literature; only the H to b bbar g amplitudes are numerically cross-checked against ref. [91] in this paper.
  • standard math Three-loop running of alpha_s and quark masses using the results of ref. [87]
    Used for renormalization scale evolution of the strong coupling, Yukawa couplings, and quark masses.

reviewed 2026-08-05 · how reviews work

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Cite this review

Pith. "Pith review of Precise Predictions for Event Shapes in Hadronic Higgs Decays." pith.science (2026). https://pith.science/paper/5ORT42J5

@misc{pith2026250814282,
  author       = {Pith},
  title        = {Pith review of: Precise Predictions for Event Shapes in Hadronic Higgs Decays},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5ORT42J5}},
  note         = {Machine review of arXiv:2508.14282}
}
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abstract

We present NNLO QCD predictions for a wide range of event-shape observables in hadronic Higgs decays, taking into account the two dominant decay modes $H\to gg$ and $H\to b\bar{b}$. Specifically, we consider the six classical event shapes thrust, heavy jet mass, $C$-parameter, total and wide jet broadening, and the three-jet resolution $y_{23}$ in the Durham algorithm. We also present results for the soft-drop variant of thrust. Decays of the Higgs boson to two gluons are treated in the heavy-top limit, whereas decays to a bottom-quark pair are mediated by a non-vanishing Yukawa coupling, despite considering kinematically massless quarks. Our results highlight the importance of NNLO QCD corrections in the calculation of event-shape observables and provide means to quantify the intrinsic difference between the two Higgs decay modes.

discussion (0)

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This paper was first reviewed by deepseek-v4-flash on August 5, 2026.