All-Multiplicity Amplitudes with Massive Scalars

Darren Forde; David A. Kosower

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All-Multiplicity Amplitudes with Massive Scalars

Darren Forde, David A. Kosower

High Energy Physics - Theory · Submitted 29 Jul 2005

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The authors' main claim We compute two infinite series of tree-level amplitudes with a massive scalar pair and an arbitrary number of gluons.

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We compute two infinite series of tree-level amplitudes with a massive scalar pair and an arbitrary number of gluons. We provide results for amplitudes where all gluons have identical helicity, and amplitudes with one gluon of opposite helicity. These amplitudes are useful for unitarity-based one-loop calculations in nonsupersymmetric gauge theories generally, and QCD in particular.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We compute two infinite series of tree-level amplitudes with a massive scalar pair and an arbitrary number of gluons.	contribution 0.97	0.96	0.46	asserted 1.00
s1	We provide results for amplitudes where all gluons have identical helicity, and amplitudes with one gluon of opposite helicity.	result 0.68	0.95	0.20	asserted 1.00
s2	These amplitudes are useful for unitarity-based one-loop calculations in nonsupersymmetric gauge theories generally, and QCD in particular.	interpretation 1.00	0.21	0.20	asserted 0.99

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.82.

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The paper

Original abstract

We compute two infinite series of tree-level amplitudes with a massive scalar pair and an arbitrary number of gluons. We provide results for amplitudes where all gluons have identical helicity, and amplitudes with one gluon of opposite helicity. These amplitudes are useful for unitarity-based one-loop calculations in nonsupersymmetric gauge theories generally, and QCD in particular.

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References

Forward citations

Cited by 14 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Massive amplitudes on the Coulomb branch of N=4 SYM
hep-th 2011-04 accept novelty 7.0 of 10

Soft-scalar limits of massless N=4 SYM amplitudes reproduce the leading small-mass Coulomb-branch amplitudes, and the paper derives compact all-n tree formulas and a mixed-degree MHV-band superamplitude.
A direct proof of the CSW rules
hep-th 2005-08 accept novelty 7.0 of 10

A direct inductive proof shows that the CSW MHV-diagram rules for tree-level gluon amplitudes are a consequence of BCFW on-shell recursion.
Color-factor symmetry using perturbiner methods for tree-level amplitudes of Yang-Mills theory coupled to matter
hep-th 2026-07 accept novelty 6.0 of 10

Perturbiner recursion proves color-factor symmetry (hence BCJ relations) for all tree-level YM+matter amplitudes with at least one gluon.
Scalar-Graviton Amplitudes
hep-th 2019-08 conditional novelty 6.0 of 10

The paper gives recursive, covariant, D-dimensional tree amplitudes for two massive scalars and any number of gluons or gravitons, extending known four-dimensional results.
Scattering equations and BCJ relations for gauge and gravitational amplitudes with massive scalar particles
hep-th 2014-07 accept novelty 6.0 of 10

The scattering equations and CHY amplitude formulas are generalized to include a pair of massive scalars, producing new BCJ relations and explicit tree-level expressions for gauge and gravity amplitudes with massive matter.

Show 9 more citing papers

Integrand Oxidation and One-Loop Colour-Dual Numerators in N=4 Gauge Theory
hep-th 2013-03 conditional novelty 6.0 of 10

A bottom-up 'integrand oxidation' procedure builds colour-kinematics dual one-loop numerators starting from box numerators, and is carried out explicitly for six- and seven-point MHV and NMHV amplitudes in N=4 Yang-Mills.
Scattering amplitudes with massive fermions using BCFW recursion
hep-ph 2006-03 accept novelty 6.0 of 10

Massive quark-antiquark to two and three gluon partial helicity amplitudes are expressed in compact spinor-product form using BCFW recursion, with helicity-flip cases treated by Feynman diagrams.
The Cut-Constructible Part of QCD Amplitudes
hep-ph 2006-02 conditional novelty 6.0 of 10

The authors complete the cut-constructible part of the one-loop six-gluon QCD amplitude by turning unitarity-cut integrals into algebraic residue extraction.
The Amplitude for Classical Gravitational Scattering at Third Post-Minkowskian Order
hep-th 2021-05 accept novelty 5.0 of 10

A complete amplitude-level derivation of the third post-Minkowskian gravitational scattering angle, including radiation reaction, confirms the Di Vecchia-Heissenberg-Russo-Veneziano conjecture and Damour's general-rel...
The Rise of SMEFT On-shell Amplitudes
hep-ph 2019-05 conditional novelty 5.0 of 10

A tree-level map connects the 11 bosonic dimension-six SMEFT operators to massive three-point on-shell amplitudes, fixing a basis that determines higher-point amplitudes.
Direct Extraction Of One Loop Rational Terms
hep-ph 2008-06 conditional novelty 5.0 of 10

Rational terms in one-loop QCD amplitudes can be extracted directly from quadruple, triple and double cuts by taking a large effective-mass limit, with no separate pentagon contributions.
The SM and NLO multileg working group: Summary report
hep-ph 2010-03 accept novelty 4.0 of 10

A workshop summary cataloguing the state of next-to-leading-order multileg calculations for LHC physics in 2009, with new results on top-pair-plus-bottom-pair production and a three-way comparison of W-plus-three-jet ...
The NLO multileg working group: summary report
hep-ph 2008-03 accept novelty 3.0 of 10

The Les Houches 2007 NLO multileg working group reports progress on automated one-loop amplitude methods, a three-way comparison of WW+jet calculations, and the remaining gaps in the LHC theory wishlist.
Scattering Amplitudes
hep-th 2013-08 accept novelty 2.0 of 10

A graduate-level textbook review that reconstructs the on-shell amplitudes program, from spinor helicity and BCFW recursion through superamplitudes, twistors, Grassmannians, and polytopes, with worked examples and exercises.

How the literature uses it

20 arXiv papers cite this in 33 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 · 24 sentences without a confident label

Uses its method or tool 2 papers

The rational part contribution to a scalar amplitude can be extracted by introducing an effective mass $μ^2$ for the scalar and by evaluating the integral coefficient in four dimensions with the tree-level amplitudes for massive scalars [ref] .

Simplicity in the Structure of QED and Gravity Amplitudes · Absence of rational terms · 0.90
The required tree level amplitudes have been generated using on-shell recursion relations literature [ref] .

Direct Extraction Of One Loop Rational Terms · Remaining helicity configurations · 0.99

Compares with it 4 papers

Evaluated on the solution to the scattering equations, this gives: [equation] We can now evaluate the amplitude for different helicity assignments: [equation] These expressions match the results obtained in [ref] .

Massive ambitwistor-strings; twistorial models · Amplitudes · 0.99
Using the prescription [ref] for both the internal off-shell momenta and the external scalars, the remaining two diagrams give (using the notation $y_i,j=k_i,j^2-m^2$) [equation] This can be shown to be equivalent to the known result [ref] .

Deriving CSW rules for massive scalar legs and pure Yang-Mills loops · Tree level examples · 0.98
Each such split introduces a relative factor of [equation] It follows that we can write the full amplitude as [equation] This should be compared to the known expression for this amplitude [ref] (see also [ref] ), [equation] We have confirmed the equivalence of these two expressions numerically for $n=3,4,5,6$.

The Coulomb-branch S-matrix from massless amplitudes · Examples · 1.00

Cites it as background 2 papers

After initial explorations of BCFW recursion for amplitudes with massive particles [ref] , it was shown that amplitudes in QCD with massive quarks can be constructed using at most three-line shifts [ref] whereas the on-shell constructibility of amplitudes in massive, power-counting renormalizable theories using all-line shifts was proven in [ref] .

On-shell constructibility of Born amplitudes in spontaneously broken gauge theories · Introduction · 0.85
The application to massive particles is less explored, although processes involving massive quarks were calculated in [ref] and massive gauge bosons in [ref] .

The Rise of SMEFT On-shell Amplitudes · Introduction · 0.86

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