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Gluon-Gluon Antenna Functions from Higgs Boson Decay

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A. Gehrmann-De Ridder, T. Gehrmann, E.W.N. Glover

High Energy Physics - Phenomenology · Submitted 11 Feb 2005 · 32 references

Pith's verdict: Solid, useful third installment of the antenna-from-matrix-elements program; the actual antenna functions are promised, not delivered, and the authors say so.

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arXiv IDhep-ph/0502110 (version 1)
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CitationA. Gehrmann-De Ridder, E.W.N. Glover, T. Gehrmann. "Gluon-Gluon Antenna Functions from Higgs Boson Decay." arXiv:hep-ph/0502110 (2005). https://pith.science/paper/WQYBCX6N
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The paper

The paper claims

The infrared singularities of Higgs-to-partons matrix elements are shown to reproduce, pole for pole, the structure required of gluon-gluon antenna functions, completing a matched set of three antenna types for NNLO subtraction.

The reading

Antenna functions are the universal building blocks that capture what a QCD matrix element does when an unresolved parton is emitted between two colour-connected hard partons; they are the raw material of subtraction schemes that make next-to-next-to-leading-order (NNLO) collider calculations finite. The paper's goal is to show that the gluon-gluon antenna functions — the last of three types needed, after quark-antiquark and quark-gluon — need not be invented by hand but can be read off a physical process: Higgs boson decay into partons in the effective theory where the Higgs couples to the gluon field strength. To make that case the authors compute the colour-ordered Higgs decay matrix elements with three and four partons in the final state, integrate them over the appropriate dipole and tripole phase spaces, and display the resulting pole coefficients explicitly. Those poles sum to exactly the NNLO infrared operator expression of the standard factorization formula, and they cancel the poles of the two-loop virtual corrections, while the finite remainder reproduces the known NNLO Higgs decay rate. A reader should care because this converts a construction problem into a derivation: if the identification holds, the antenna subtraction terms for processes with adjacent gluons come for free from a process that can be computed.

What carries the argument

The carrier of the argument is the antenna factorization of colour-ordered matrix elements: in the soft or collinear limit, a colour-ordered amplitude factorizes into a hard part, a splitting or eikonal factor, and an antenna function that absorbs all the singular behaviour between two colour-connected hard partons. The authors isolate this by writing the squared $H to ggg$ matrix element (Eq. 4.3) with an explicit factor of $1/3$ for the three ways of choosing which gluon is unresolved, and the leading-order normalization $T^0_{gg}(q^2)$ factored out, so that each individual antenna configuration carries exactly one soft limit and each $g to gg$ collinear splitting is shared between the two antennae of the final-state gluons involved. The second piece of machinery is the effective Lagrangian $L_{int} = - (1/4) (1/4)$-style coupling $H F^{a}_{mu nu} F^{a, mu nu}$ with Feynman rules for the $Hgg$, $Hggg$ and $Hgggg$ vertices (Eqs. 2.2-2.4), together with the all-orders renormalization constant $Z_lambda$ of the effective coupling (Eq. 2.5), which is what makes the comparison with the infrared operator formula well defined. The third piece is the integration over dipole and tripole phase space, which turns the matrix elements into the pole expansions that can be compared term by term against the factorization formula.

Extended reading notes

Core claim

The paper establishes that the colour-ordered matrix elements for $H(q) + n$ partons in the effective Lagrangian $L_{int} = - (1/4) (1/4) ... $ — more precisely $L_{int} = - (1/4) (1/4)$ is not the claim; the claim is structural. It shows that the tree-level processes $H to ggg$ and $H to g q bar q$ at NLO, and $H to gggg$, $H to gg q bar q$, $H to q bar q q' bar q'$ at NNLO, when integrated over dipole and tripole phase space, produce pole coefficients (Eqs. 4.6, 4.11, 5.1, 5.2, 5.9, 5.10, 5.11) whose sum (Eq. 5.12) equals the NNLO infrared singularity operator expression of Eq. 5.13. That expression is exactly the one expected for a process whose leading order contains two gluon-gluon antennae, matching the factor of four multiplying the one-loop operator $I^{(1)}_{gg}$ in the NLO relation of Eq. 3.5. The real-radiation poles cancel the poles of the two-loop virtual corrections of Harlander (Eq. 5.17), and the finite parts of the sum reproduce the NNLO correction to the inclusive Higgs decay rate in the effective theory (Eq. 5.19). From this agreement the authors conclude that gluon-gluon antenna functions can be systematically derived from these Higgs decay matrix elements, in the same way that quark-antiquark antennae come from $gamma^* to q bar q$ and quark-gluon antennae from neutralino decay.

Load-bearing premise

The load-bearing premise is that agreement of the integrated Higgs decay matrix elements with the infrared factorization formula, pole for pole and including the finite remainder, is enough to identify those matrix elements with the gluon-gluon antenna functions themselves; the paper asserts this step and defers the actual extraction, with its normalization and colour-ordering choices, to a follow-up listed as in preparation.

Editorial extensions

If this is right

  • Gluon-gluon antenna functions for NLO and NNLO subtraction become derivable rather than constructed by hand, completing the set of three antenna types alongside the quark-antiquark and quark-gluon cases.
  • The same Higgs decay matrix elements, analytically continued, supply antenna subtraction terms for production and scattering kinematics, where the leading-order process has partons in the initial state.
  • The verified finite remainder (Eq. 5.19) gives an independent cross-check of the NNLO inclusive Higgs decay rate in the heavy-quark effective theory.
  • The pole structure of Eq. 5.13 provides a template that any candidate gluon-gluon antenna function must satisfy before it can be used in an NNLO subtraction scheme.
  • Processes with adjacent gluons in the final state, such as three-jet production at lepton colliders and Higgs-plus-jet at hadron colliders, become accessible to NNLO subtraction once the antenna functions are extracted.

Reading between the lines

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

  • The letter proves pole agreement, not the antenna functions themselves; the actual extraction, including the non-singular remainders and the normalization and colour-ordering prescription, is deferred to a paper listed as in preparation, so the derivation is a programme announced rather than a result delivered here.
  • If the identification holds, the same trick should work for any process whose leading order contains a pair of colour-connected gluons, which suggests a general recipe: pick a physical process with the right colour topology, integrate its real radiation over the appropriate phase space, and read the antenna off the finite remainder.
  • The heavy-quark limit that defines the effective theory is doing quiet work: the antenna functions obtained are those of massless QCD, and any residual dependence on the quark mass in the matching coefficient drops out of the singular structure, which is what makes the derivation process-independent in practice.
  • Because the check is a cancellation between real and virtual poles, a mismatch at order $epsilon^0$ in the finite remainder would be the first place a wrong normalization or colour-ordering convention would show up, and that is where an independent reimplementation would most usefully be aimed.
Original abstract

Antenna functions describe the infrared singular behaviour of colour-ordered QCD matrix elements due to the emission of unresolved partons inside an antenna formed by two hard partons. In this paper, we show that antenna functions for hard gluon-gluon pairs can be systematically derived from the effective Lagrangian describing Higgs boson decay into gluons, and compute the the infrared structure of the colour-ordered Higgs boson decay matrix elements at NLO and NNLO.

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-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,383 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.06 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.06 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

Antenna functions describe the infrared singular behaviour of colour-ordered QCD matrix elements due to the emission of unresolved partons inside an antenna formed by two hard partons. In this paper, we show that antenna functions for hard gluon-gluon pairs can be systematically derived from the effective Lagrangian describing Higgs boson decay into gluons, and compute the the infrared structure of the colour-ordered Higgs boson decay matrix elements at NLO and NNLO.

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 Antenna functions describe the infrared singular behaviour of colour-ordered QCD matrix elements due to the emission of unresolved partons inside an antenna formed by two hard partons. background 1.00 0.05 0.03 asserted 1.00
s1 In this paper, we show that antenna functions for hard gluon-gluon pairs can be systematically derived from the effective Lagrangian describing Higgs boson decay into gluons, and compute the the infrared structure of the colour-ordered Higgs boson decay matrix elements at NLO and NNLO. contribution 1.00 0.97 0.91 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.90 · evidence from proof or derivation 0.99.

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
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  • P abstract
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  • S sections
  • T body sentences
  • C citations
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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. Colour flow contained in tree level decay
Figure 2. Colour flow contained in the colour ordered amplitude
Figure 3. Colour flow contained in the colour ordered amplitude

Figures reproduced from arXiv:hep-ph/0502110 by the authors.

References
How the literature uses it

52 arXiv papers cite this in 88 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 35 sentences without a confident label

Contests it 3 papers
Builds on it 2 papers
Uses its method or tool 16 papers
  • In this work, we employ the calculation of Ref. [ref] based on the antenna subtraction formalism [ref] to provide NNLO-accurate QCD predictions for the distributions of the angular coefficients.

    Precise predictions for the angular coefficients in Z-boson production at the LHC · Numerical predictions · 0.99

  • We will follow the NNLO antenna subtraction method which has been fully developed for the production of massless partons in electron-positron annihilation [ref] , leading to the successful description of the infrared structure of three-jet events at NNLO [ref] and the subsequent numerical calculation of the NNLO corrections to event shape distributions [ref] , the moments of event shapes [ref] and jet rates [ref] .

    Real-Virtual corrections for gluon scattering at NNLO · Introduction · 0.84

  • In order to render each contribution finite and numerically integrable we use the antenna subtraction technique [ref] for the subtraction of real radiation singularities and the reintroduction of its integrated counterparts: [equation] where the integration is performed over the additional phase space of the radiated partons.

    NNLO corrections to VBF Higgs boson production · Section · 1.00

Compares with it 3 papers
Cites it as background 21 papers

Discussion

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