The all-loop conjecture for integrands of reggeon amplitudes in $$ \mathcal{N}=4 $$ SYM

Bolshov, A.; Bork, L. V.; Onishchenko, A. I.

doi:10.1007/jhep06(2018)129

Cited by 9 publications

(5 citation statements)

References 79 publications

(190 reference statements)

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“…2 Form factors of a variety of operators have been calculated in N = 4 sYM theory using modern techniques originally developed in the context of scattering amplitudes. These include recursion relations [14][15][16][17], on-shell diagrams, polytopes and Graßmannians [18][19][20][21][22][23], twistor space actions [24][25][26][27], a connected prescription [28][29][30], color-kinematics duality [31][32][33], and a dual description via the AdS/CFT correspondence [14,[34][35][36][37][38]. These results are currently limited to two loops for n ≥ 3.…”

Section: Jhep04(2021)147mentioning

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: Jhep04(2021)147mentioning

confidence: 99%

A three-point form factor through five loops

Dixon

McLeod

Wilhelm

2021

J. High Energ. Phys.

106

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“…Bootstrap methods have also proved to be successful for form factors: the symbol bootstrap method has been applied to form factors at two loops [23] and recently at much higher loops in [31] with the help of the form factor operator product expansion (OPE) [32,33]; besides, a new bootstrap strategy based on the master-integral ansatz has been developed to compute a two-loop four-point form factor in [34]. See also some other studies in [35][36][37][38][39][40][41][42][43]. A recent introduction and review of form factors in N = 4 SYM can be found in [44].…”

Section: Introductionmentioning

confidence: 99%

Full-color three-loop three-point form factors in 𝒩 = 4 SYM

Lin

Yang

Zhang

2022

J. High Energ. Phys.

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We present the detailed computation of full-color three-loop three-point form factors of both the stress-tensor supermultiplet and a length-three BPS operator in 𝒩 = 4 SYM. The integrands are constructed based on the color-kinematics (CK) duality and generalized unitarity method. An interesting observation is that the CK-dual integrands contain a large number of free parameters. We discuss the origin of these free parameters in detail and check that they cancel in the simplified integrands. We further perform the numerical evaluation of the integrals at a special kinematics point using public packages FIESTA and pySecDec based on the sector-decomposition approach. We find that the numerical computation can be significantly simplified by expressing the integrals in terms of uniformly transcendental basis, although the final three-loop computations still require large computational resources. Having the full-color numerical results, we verify that the non-planar infrared divergences reproduce the non-dipole structures, which firstly appear at three loops. As for the finite remainder functions, we check that the numerical planar remainder for the stress-tensor supermultiplet is consistent with the known result of the bootstrap computation. We also obtain for the first time the numerical results of the three-loop non-planar remainder for the stress-tensor supermultiplet as well as the three-loop remainder for the length-three operator.

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Section: Introductionmentioning

confidence: 99%

A Three-Point Form Factor Through Five Loops

Dixon,

McLeod,

Wilhelm

2020

Preprint

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We bootstrap the three-point form factor of the chiral part of the stress-tensor supermultiplet in planar 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. Moreover, we conjecture that 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 qg. We present evidence that the planar 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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The all-loop conjecture for integrands of reggeon amplitudes in $$ \mathcal{N}=4 $$ SYM

Cited by 9 publications

References 79 publications

A three-point form factor through five loops

A three-point form factor through five loops

Full-color three-loop three-point form factors in 𝒩 = 4 SYM

A Three-Point Form Factor Through Five Loops

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