The four-loop $$ \mathcal{N} $$ = 4 SYM Sudakov form factor

Lee, Roman N.; Manteuffel, Andreas von; Schabinger, Robert M.; Smirnov, Alexander V.; Smirnov, Vladimir A.; Steinhauser, Matthias

doi:10.1007/jhep01(2022)091

Cited by 13 publications

(5 citation statements)

References 78 publications

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“…At four-loops, there is also N c -subleading contribution to these anomalous dimensions, see e.g. [145][146][147][148][149][150]. We can compare the above convention with the Sudakov form factor result in [93]: Next, we provide some details on the calculation from (5.5) to (5.6).…”

Section: Ir Conventions and Non-dipole Termsmentioning

confidence: 97%

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: Ir Conventions and Non-dipole Termsmentioning

confidence: 97%

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

Lin

Yang

Zhang

2022

J. High Energ. Phys.

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“…In supersymmetric theories, many amplitudes with two or more loops and/or five or more particles have been computed [1][2][3][4][5][6][7][8][9][10][11][12][13]. Substantial progress in non-supersymmetric theories has also been made with the computation of 2 Ñ 3 scattering amplitudes at NNLO [14][15][16][17][18][19][20][21][22][23][24][25] and beyond [26][27][28][29][30][31][32][33][34][35][36][37][38]. Much of this progress has been facilitated by a firm mathematical understanding of the MPL function space.…”

Section: Introductionmentioning

confidence: 99%

Loop-by-loop differential equations for dual (elliptic) Feynman integrals

Giroux

Pokraka

2023

J. High Energ. Phys.

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We present a loop-by-loop method for computing the differential equations of Feynman integrals using the recently developed dual form formalism. We give explicit prescriptions for the loop-by-loop fibration of multi-loop dual forms. Then, we test our formalism on a simple, but non-trivial, example: the two-loop three-mass elliptic sunrise family of integrals. We obtain an ε-form differential equation within the correct function space in a sequence of relatively simple algebraic steps. In particular, none of these steps relies on the analysis of q-series. Then, we discuss interesting properties satisfied by our dual basis as well as its simple relation to the known ε-form basis of Feynman integrands. The underlying K3-geometry of the three-loop four-mass sunrise integral is also discussed. Finally, we speculate on how to construct a “good” loop-by-loop basis at three-loop.

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“…Over the last decade, it has become clear that a broad range of scattering amplitudes can be expressed in terms of functions called multiple polylogarithms. This realization has led to enormous advances in our computational power, both in supersymmetric gauge theory and in QCD, where substantial progress has recently been made computing 2 → 3 scattering processes to NNLO , and obtaining the first results at N 3 LO and beyond [85][86][87][88][89][90]. In particular, much of this rapid progress has been facilitated by a deep understanding of the mathematical properties exhibited by multiple polylogarithms and the development of tools for working with these functions [91][92][93][94][95][96][97], as well as by the availability of public codes for polylogarithmic integration and numerical evaluation [98][99][100][101][102][103][104][105].…”

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confidence: 99%

Functions Beyond Multiple Polylogarithms for Precision Collider Physics

Bourjaily¹,

Broedel²,

Chaubey³

et al. 2022

Preprint

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Feynman diagrams constitute one of the essential ingredients for making precision predictions for collider experiments. Yet, while the simplest Feynman diagrams can be evaluated in terms of multiple polylogarithms-whose properties as special functions are well understood-more complex diagrams often involve integrals over complicated algebraic manifolds. Such diagrams already contribute at NNLO to the self-energy of the electron, t t production, γγ production, and Higgs decay, and appear at two loops in the planar limit of maximally supersymmetric Yang-Mills theory. This makes the study of these more complicated types of integrals of phenomenological as well as conceptual importance.In this white paper contribution to the Snowmass community planning exercise, we provide an overview of the state of research on Feynman diagrams that involve special functions beyond multiple polylogarithms, and highlight a number of research directions that constitute essential avenues for future investigation.

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The four-loop $$ \mathcal{N} $$ = 4 SYM Sudakov form factor

Abstract: We present the Sudakov form factor in full color $$ \mathcal{N} $$ N = 4 supersymmetric Yang- Mills theory to four loop order and provide uniformly transcendental results for the relevant master integrals through to weight eight.

Cited by 13 publications

References 78 publications

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

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

Loop-by-loop differential equations for dual (elliptic) Feynman integrals

Functions Beyond Multiple Polylogarithms for Precision Collider Physics

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