Complete form factors in Yang-Mills from unitarity and spinor helicity in six dimensions

Huber, Manuel Accettulli; Brandhuber, Andreas; Angelis, Stefano De; Travaglini, Gabriele

doi:10.1103/physrevd.101.026004

Cited by 9 publications

(4 citation statements)

References 78 publications

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“…Possible operators include those studied in refs. [33,102,[136][137][138][139][140][141][142][143][144][145][146]. In particular, in the case of the two-loop three-point form factor for tr(F 3 ) it has been shown that the next-to-leading order contribution to the Higgs amplitude remainder in the heavy-top limit of QCD shares its maximally transcendental part with its counterpart in N = 4 sYM theory [122,[147][148][149].…”

Section: Discussionmentioning

confidence: 99%

A three-point form factor through five loops

Dixon

McLeod

Wilhelm

2021

J. High Energ. Phys.

106

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We bootstrap the three-point form factor of the chiral part of the stresstensor supermultiplet in planar $$ \mathcal{N} $$ N = 4 super-Yang-Mills theory, obtaining new results at three, four, and five loops. Our construction employs known conditions on the first, second, and final entries of the symbol, combined with new multiple-final-entry conditions, “extended-Steinmann-like” conditions, and near-collinear data from the recently-developed form factor operator product expansion. Our results are expected to give the maximally transcendental parts of the gg → Hg and H → ggg amplitudes in the heavy-top limit of QCD. At two loops, the extended-Steinmann-like space of functions we describe contains all transcendental functions required for four-point amplitudes with one massive and three massless external legs, and all massless internal lines, including processes such as gg → Hg and γ* → $$ q\overline{q}g $$ q q ¯ g . We expect the extended-Steinmann-like space to contain these amplitudes at higher loops as well, although not to arbitrarily high loop order. We present evidence that the planar $$ \mathcal{N} $$ N = 4 three-point form factor can be placed in an even smaller space of functions, with no independent ζ values at weights two and three.

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Section: Discussionmentioning

confidence: 99%

A three-point form factor through five loops

Dixon

McLeod

Wilhelm

2021

J. High Energ. Phys.

106

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“…We will systematically ignore such contact terms at four points, except for the four-scalar contact term (corresponding in the Lagrangian formalism to the λφ 4 interaction). Indeed, such terms are usually computed through d-dimensional generalised unitarity techniques as one-loop finite rational terms [114,117,[149][150][151][152][153][154], hence they must be vanishing at tree-level. 16 In particular, in the case of the four-scalar amplitude we will add to the factorisable part a contact term whose kinematic dependence is trivial:…”

Section: Jhep11(2021)221mentioning

confidence: 99%

Standard Model EFTs via on-shell methods

Huber

Angelis

2021

J. High Energ. Phys.

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We present the Standard Model Effective Field Theories (SMEFT) from purely on-shell arguments. Starting from few basics assumptions such as Poincaré invariance and locality, we classify all the renormalisable and non-renormalisable interactions at lowest order in the couplings. From these building blocks, we review how locality and unitarity enforce Lie algebra structures to appear in the S-matrix elements together with relations among couplings (and hypercharges). Furthermore, we give a fully on-shell algorithm to compute any higher-point tree-level amplitude (or form factor) in generic EFTs, bypassing BCFW-like recursion relations which are known to be problematic when non-renormalisable interactions are involved. Finally, using known amplitudes techniques we compute the mixing matrix of SMEFT marginal interactions up to mass dimension 8, to linear order in the effective interactions.

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“…Among the various results, they satisfy BCFW recursion relations [57], also at loop level [173], can be computed using (generalised) unitarity, and are invariant under a form of dual conformal symmetry [174], which is broken at loop level. Analytic non-supersymmetric form factors were recently computed at one loop [175] using dimensional reconstruction [176][177][178][179].…”

Section: General Propertiesmentioning

confidence: 99%

The SAGEX review on scattering amplitudes Chapter 1: Modern fundamentals of amplitudes

Brandhuber¹,

Plefka²,

Travaglini³

2022

J. Phys. A: Math. Theor.

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This chapter introduces the foundational concepts and techniques for scattering amplitudes. It is meant to be accessible to readers with only a basic understanding of quantum field theory. Topics covered include: the four-dimensional spinor-helicity formalism and the colour decomposition of Yang-Mills scattering amplitudes; the study of soft and collinear limits of Yang-Mills and gravity amplitudes; the BCFW recursion relation and generalised unitarity, also in the superamplitudes formalism of $\cN{=}4$ supersymmetric Yang-Mills; an overview of standard and hidden symmetries of the S-matrix of N=4 supersymmetric Yang-Mills, such as the conformal, dual conformal and Yangian symmetries; and a brief excursus on form factors of protected and non-protected operators in Yang-Mills theory. Several examples and explicit calculations are also provided.

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Complete form factors in Yang-Mills from unitarity and spinor helicity in six dimensions

Cited by 9 publications

References 78 publications

A three-point form factor through five loops

A three-point form factor through five loops

Standard Model EFTs via on-shell methods

The SAGEX review on scattering amplitudes Chapter 1: Modern fundamentals of amplitudes

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