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Antenna Subtraction at NNLO
High Energy Physics - Phenomenology · Submitted 12 May 2005
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim To illustrate the application of NNLO antenna subtraction for different colour structures, we construct the integrated forms of the subtraction terms needed for the five-parton and four-parton contributions to $e^+e^- \to 3$ jets at NNLO in all colour factors, and show that their infrared poles cancel analytically with the infrared poles of the two-loop virtual correction to this observable.
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The abstract, sentence by sentence
The computation of exclusive QCD jet observables at higher orders requires a method for the subtraction of infrared singular configurations arising from multiple radiation of real partons. We present a subtraction scheme relevant for NNLO perturbative calculations in $e^+e^- \to $ jets. The building blocks of the scheme are antenna functions derived from the matrix elements for tree-level $1\to 3$ and $1 \to 4$ and one-loop $1 \to 3$ processes. By construction, these building blocks have the correct infrared behaviour when one or two particles are unresolved. At the same time, their integral over the antenna phase space is straightforward. As an example of how to use the scheme we compute the NNLO contributions to the subleading colour QED-like contribution to $e^+e^- \to 3$ jets. To illustrate the application of NNLO antenna subtraction for different colour structures, we construct the integrated forms of the subtraction terms needed for the five-parton and four-parton contributions to $e^+e^- \to 3$ jets at NNLO in all colour factors, and show that their infrared poles cancel analytically with the infrared poles of the two-loop virtual correction to this observable.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The computation of exclusive QCD jet observables at higher orders requires a method for the subtraction of infrared singular configurations arising from multiple radiation of real partons. | background 1.00 | 0.06 | 0.04 | asserted 1.00 |
| s1 | We present a subtraction scheme relevant for NNLO perturbative calculations in $e^+e^- \to $ jets. | contribution 0.99 | 0.93 | 0.25 | asserted 1.00 |
| s2 | The building blocks of the scheme are antenna functions derived from the matrix elements for tree-level $1\to 3$ and $1 \to 4$ and one-loop $1 \to 3$ processes. | method 0.93 | 0.80 | 0.07 | asserted 1.00 |
| s3 | By construction, these building blocks have the correct infrared behaviour when one or two particles are unresolved. | method 0.80 | 0.70 | 0.06 | asserted 1.00 |
| s4 | At the same time, their integral over the antenna phase space is straightforward. | method 0.76 | 0.60 | 0.04 | asserted 1.00 |
| s5 | As an example of how to use the scheme we compute the NNLO contributions to the subleading colour QED-like contribution to $e^+e^- \to 3$ jets. | contribution 0.62 | 0.95 | 0.13 | asserted 0.99 |
| s6 | To illustrate the application of NNLO antenna subtraction for different colour structures, we construct the integrated forms of the subtraction terms needed for the five-parton and four-parton contributions to $e^+e^- \to 3$ jets at NNLO in all colour factors, and show that their infrared poles cancel analytically with the infrared poles of the two-loop virtual correction to this observable. | contribution 0.53 | 0.96 | 0.39 | asserted 1.00 |
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The paper
Original abstract
The computation of exclusive QCD jet observables at higher orders requires a method for the subtraction of infrared singular configurations arising from multiple radiation of real partons. We present a subtraction scheme relevant for NNLO perturbative calculations in $e^+e^- \to $ jets. The building blocks of the scheme are antenna functions derived from the matrix elements for tree-level $1\to 3$ and $1 \to 4$ and one-loop $1 \to 3$ processes. By construction, these building blocks have the correct infrared behaviour when one or two particles are unresolved. At the same time, their integral over the antenna phase space is straightforward. As an example of how to use the scheme we compute the NNLO contributions to the subleading colour QED-like contribution to $e^+e^- \to 3$ jets. To illustrate the application of NNLO antenna subtraction for different colour structures, we construct the integrated forms of the subtraction terms needed for the five-parton and four-parton contributions to $e^+e^- \to 3$ jets at NNLO in all colour factors, and show that their infrared poles cancel analytically with the infrared poles of the two-loop virtual correction to this observable.
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References
How the literature uses it
224 arXiv papers cite this in 591 sentences
Papers citing it · 258 sentences without a confident label
Contests it 4 papers
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As mentioned earlier, the original NNLO antenna functions derived in Refs. [ref] do not obey all of these requirements, as they typically violate (some of) these principles.
Idealised Antenna Functions for Higher Order QCD Calculations · Generic Design Principles · contest 0.85
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We wish to emphasise again that the original NNLO antenna functions derived in [ref] do not obey these requirements, as they typically violate (some of) these principles, as alluded to above.
A general algorithm to build real-radiation antenna functions for higher-order calculations · Design principles · contest 0.81
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As mentioned earlier, the original NNLO antenna functions derived in [ref] do not obey all of these requirements, as they typically violate (some of) these principles.
A general algorithm to build mixed real and virtual antenna functions for higher-order calculations · Generic design principles · contest 0.81
Builds on it 2 papers
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In a first step towards the calculation of all integrated four-parton initial-initial antenna functions for the double real radiation case, in this paper, we focus on all the crossings of two partons from the following four-parton final-final antennae: $B_4^0(q,q',q̅',q̅)$, $Ẽ_4^0(q,q',q̅',g)$ and $H_4^0(q,q̅,q',q̅')$ defined in [ref] .
Antenna subtraction at NNLO with hadronic initial states: double real radiation for initial-initial configurations with two quark flavours · Integrated antennae with two quark flavours · 0.86
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In the case of the loop antenna functions $X_4^1$ and $X_3^2$, we remove the singular behavior that can be captured by antenna functions of lower loop order, naturally extending the definition of three-parton one-loop antenna functions at NNLO [ref] .
Jet production at electron-positron colliders at next-to-next-to-next-to-leading order in QCD · Method · 0.98
Uses its method or tool 68 papers
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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
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Our perturbative description of a shape-variable distribution $v$ relies on the perturbative computation of $e^+e^-→3$ jets at NNLO, performed using the public EERAD3 code [ref] , which is based on the antenna subtraction formalism [ref] .
Fits of $\alpha_s$ from event-shapes in the three-jet region: extension to all energies · Calculation of the differential distributions · 1.00
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Our numerical results for the photon production cross section are obtained using the parton-level Monte Carlo event generator , which implements the antenna subtraction formalism [ref] at NNLO.
NNLO Photon Production with Realistic Photon Isolation · Implementation · 1.00
Uses its data or values 2 papers
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That necessarily implies that we need the integrated form of the antenna over the antenna phase space (final state kinematics) which has been calculated and documented in [ref] .
Antenna subtraction for gluon scattering at NNLO · Final-Final emitters · 0.81
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For final-final kinematics the integrated antenna was computed in [ref] and reads, [equation] where the colour-ordered infrared singularity operator $I_gg^(1)$ was defined in Eq. ([ref]).
Real-Virtual corrections for gluon scattering at NNLO · Final-Final emitters · 0.89
Compares with it 6 papers
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The $$ formula is given by [equation] and after integration we find the expression [equation] The combination of $2(+ )$ differs from $$ in Eq. (6.22) of Ref. [ref] , starting from $1/^2$.
A general algorithm to build mixed real and virtual antenna functions for higher-order calculations · Quark-gluon antennae · 1.00
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For the $D$-type and $F$-type antennae, we have utilised the $X_3^0$ sub-antenna given in Eqs. (6.13) and (7.13) of Ref. [ref] respectively and therefore the pole structures of the combinations $2 ( D_3^1+D_3^1 )$, $2 D_3^1$, $3 F_3^1$ and $3 F_3^1$ agrees with the expressions for $$, $$, $$ and $$ respectively, given by Eqs. (6.22), (6.23), (7.22) and (7.23) of Ref. [ref] respectively to $^0$.
Idealised Antenna Functions for Higher Order QCD Calculations · Integrals of $X_3^1$ Antennae derived using the $X_3^0$ of Ref. CITEMARK264Z · 0.98
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In implementation we specify the subtraction formulas for colour-singlet and colour-singlet+jet processes and provide numerical results for $Z$ and $Z$+jet using $N$-jettiness subtractions in combination with the P2B method, comparing our results to [ref] .
NNLO predictions with nonlocal subtractions and fiducial power corrections in GENEVA · Introduction · 0.98
Cites it as background 98 papers
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There have been several approaches to build a general subtraction scheme at NNLO [ref] .
Antenna subtraction for gluon scattering at NNLO · Introduction · 0.96
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It was first proposed for perturbative QCD calculations with massless partons in electron-positron annihilation in Refs. [ref] .
Idealised Antenna Functions for Higher Order QCD Calculations · Introduction to Antenna Subtraction · 0.95
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The antenna subtraction method [ref] was developed for $e^+e^-$ annihilation, where it was successfully applied to the calculation of the three-jet cross section at NNLO [ref] .
NNLO QCD corrections to jet production at hadron colliders from gluon scattering · Introduction · 0.83
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