Form factor and boundary contribution of amplitude

Huang, Rijun; Jin, Qingjun; Feng, Bo

doi:10.1007/jhep06(2016)072

Cited by 17 publications

(8 citation statements)

References 109 publications

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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%

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

Lin

Yang

Zhang

2022

J. High Energ. Phys.

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“…Finally, one needs to check against unitarity cuts in Figure 10. As in the last subsection, it is straightforward to check that the numerator ansatz (80) passes all checks. 8 The results for various factors are summarized in Table 2.…”

Section: The Two-loop Example Revisitedmentioning

confidence: 99%

“…(3) Construct ansatz of master numerators. We construct an ansatz for N d by applying the following constraints: a) With the power counting property discussed above (80), the numerator should depend linearly on the loop momentum l, since the topology contains a sub-box form factor. A general ansatz can be given as…”

Section: Three-loop Construction and Beyondmentioning

confidence: 99%

On-shell methods for form factors in $$\mathcal{N}=4$$ SYM and their applications

Yang

2020

Sci. China Phys. Mech. Astron.

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Form factors are quantities that involve both asymptotic on-shell states and gauge invariant operators. They provide a natural bridge between on-shell amplitudes and off-shell correlation functions of operators, thus allowing us to use modern on-shell amplitude techniques to probe into the off-shell side of quantum field theory. In particular, form factors have been successfully used in computing the cusp (soft) anomalous dimensions and anomalous dimensions of general local operators. This review is intended to provide a pedagogical introduction to some of these developments. We will first review some amplitudes background using four-point amplitudes as main examples. Then we generalize these techniques to form factors, including (1) tree-level form factors, (2) Sudakov form factor and infrared singularities, and (3) form factors of general operators and their anomalous dimensions. Although most examples we consider are in N = 4 super-Yang-Mill theory, the on-shell methods are universal and are expected to be applicable to general gauge theories. *

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“…Twistor space based representations of 1/2-BPS and more general form factors were considered in [44,45], see also [46][47][48] for Lorentz harmonic chiral formulation. Special case of form factors of operators corresponding to "defect insertions" was considered in [49]. Integrability properties of 1/2-BPS form factors where investigated in [50][51][52][53][54] and in an important paper [55] with an explicit construction based on quantum inverse scattering method.…”

Section: Jhep12(2016)076mentioning

confidence: 99%

Grassmannians and form factors with q 2 = 0 in N $$ \mathcal{N} $$ =4 SYM theory

Bork¹,

Onishchenko²

2016

J. High Energ. Phys.

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In this paper we consider tree level form factors of operators from stress tensor operator supermultiplet with light-like operator momentum q 2 = 0. We present a conjecture for the Grassmannian integral representation both for these tree level form factors as well as for leading singularities of their loop counterparts. The presented conjecture was successfully checked by reproducing several known answers in MHV and N k−2 MHV, k ≥ 3 sectors together with appropriate soft limits. We also discuss the cancellation of spurious poles and relations between different BCFW representations for such form factors on simple examples.

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Form factor and boundary contribution of amplitude

Cited by 17 publications

References 109 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

On-shell methods for form factors in $$\mathcal{N}=4$$ SYM and their applications

Grassmannians and form factors with q 2 = 0 in N $$ \mathcal{N} $$ =4 SYM theory

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