A differential operator for integrating one-loop scattering equations

Wang, Tianheng; Chen, Gang; Cheung, Yeuk-Kwan E.; Xu, Feng

doi:10.1007/jhep01(2017)028

Cited by 15 publications

(24 citation statements)

References 57 publications

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“…In our previous work [44] we proposed a conjecture that enables us to compute multidimensional residues on isolated (zero-dimensional) poles by a differential operator. Here we briefly recall that conjecture.…”

Section: Jhep06(2017)015mentioning

confidence: 99%

“…In this section we introduce our new method to determine the differential operators that is more efficient than the approach taken in [44]. We begin with a warmup example for the four point one loop SYM integrand.…”

Section: Jhep06(2017)015 2 Prescription For Determining Differential mentioning

confidence: 99%

“…The generalized CHY integral for its loop integrand is given in [14,15]. A detailed analysis of the evaluation of this generalized CHY integral has already been presented in [44]. In this section we reconsider this example as a toy model to illustrate the main ideas of the method proposed in this paper.…”

Section: Toy Model: One-loop Four-point Sym Integrandmentioning

confidence: 99%

“…As shown in [44], using the global residue theorem, the integral can be rewritten as the following (a) (b) (c) Figure 1. Tableaux for the coefficients appearing in this example.…”

Section: Toy Model: One-loop Four-point Sym Integrandmentioning

confidence: 99%

“…From now on in this section we will simply write σ 4 for σ ′ 4 for notational convenience. The main idea of the method presented in [44] is to replace the contour integration…”

Section: Toy Model: One-loop Four-point Sym Integrandmentioning

confidence: 99%

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A combinatoric shortcut to evaluate CHY-forms

Wang

Chen

Cheung

et al. 2017

J. High Energ. Phys.

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In our recent work, we proposed a differential operator for the evaluation of the multi-dimensional residues on isolated (zero-dimensional) poles. In this paper we discuss some new insight on evaluating the (generalized) Cachazo-He-Yuan (CHY) forms of the scattering amplitudes using this differential operator. We introduce a tableau representation for the coefficients appearing in the proposed differential operator. Combining the tableaux with the polynomial form of the scattering equations, the evaluation of the generalized CHY form becomes a simple combinatoric problem. It is thus possible to obtain the coefficients arising in the differential operator in a straightforward way. We present the procedure for a complete solution of the n-gon amplitudes at one-loop level in a generalized CHY form. We also apply our method to fully evaluate the one-loop five-point amplitude in the maximally supersymmetric Yang-Mills theory; the final result is identical to the one obtained by Q-Cut.

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Section: Jhep06(2017)015mentioning

confidence: 99%

Section: Jhep06(2017)015 2 Prescription For Determining Differential mentioning

confidence: 99%

Section: Toy Model: One-loop Four-point Sym Integrandmentioning

confidence: 99%

“…As shown in [44], using the global residue theorem, the integral can be rewritten as the following (a) (b) (c) Figure 1. Tableaux for the coefficients appearing in this example.…”

Section: Toy Model: One-loop Four-point Sym Integrandmentioning

confidence: 99%

“…From now on in this section we will simply write σ 4 for σ ′ 4 for notational convenience. The main idea of the method presented in [44] is to replace the contour integration…”

Section: Toy Model: One-loop Four-point Sym Integrandmentioning

confidence: 99%

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A combinatoric shortcut to evaluate CHY-forms

Wang

Chen

Cheung

et al. 2017

J. High Energ. Phys.

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Aspects of Scattering Amplitudes and Moduli Space Localization

Mizera¹

2020

Springer Theses

174

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Intersection Numbers of Twisted Differential Forms

Mizera

2020

Springer Theses

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A differential operator for integrating one-loop scattering equations

Cited by 15 publications

References 57 publications

A combinatoric shortcut to evaluate CHY-forms

A combinatoric shortcut to evaluate CHY-forms

Aspects of Scattering Amplitudes and Moduli Space Localization

Intersection Numbers of Twisted Differential Forms

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