Multi-fold contour integrals of certain ratios of Euler gamma functions from Feynman diagrams: orthogonality of triangles

González, Iván; Kondrashuk, Igor; Notte-Cuello, Eduardo A.; Parra-Ferrada, Ivan

doi:10.1007/s13324-018-0252-6

Cited by 4 publications

(4 citation statements)

References 30 publications

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“…For this purpose, we first consider a scalar triangle diagram of Ref. [74] and note that any term in the one-loop contribution in Lcc vertex (5) may be considered as such a scalar triangle diagram depicted in Figure 2…”

Section: Three-point Green Function Of Dressed Mean Fieldsmentioning

confidence: 99%

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Finiteness of N=4 Super-Yang–Mills Effective Action in Terms of Dressed N=1 Superfields

Kondrashuk,

Schmidt

2023

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We argue in favor of the independence on any scale, ultraviolet or infrared, in kernels of the effective action expressed in terms of dressed N=1 superfields for the case of N=4 super-Yang–Mills theory. Under “scale independence” of the effective action of dressed mean superfields, we mean its “finiteness in the off-shell limit of removing all the regularizations”. This off-shell limit is scale independent because no scale remains inside these kernels after removing the regularizations. We use two types of regularization: regularization by dimensional reduction and regularization by higher derivatives in its supersymmetric form. Based on the Slavnov–Taylor identity, we show that dressed fields of matter and of vector multiplets can be introduced to express the effective action in terms of them. Kernels of the effective action expressed in terms of such dressed effective fields do not depend on the ultraviolet scale. In the case of dimensional reduction, by using the developed technique, we show how the problem of inconsistency of the dimensional reduction can be solved. Using Piguet and Sibold formalism, we indicate that the dependence on the infrared scale disappears off shell in both the regularizations.

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Section: Three-point Green Function Of Dressed Mean Fieldsmentioning

confidence: 99%

“…With all these definitions made, we consider the triangle scalar diagram in Figure 2 in position space, repeating in part the integral transformations used in Ref. [74].…”

Section: Three-point Green Function Of Dressed Mean Fieldsmentioning

confidence: 99%

Finiteness of N=4 Super-Yang–Mills Effective Action in Terms of Dressed N=1 Superfields

Kondrashuk,

Schmidt

2023

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“…Remark 1.2 In high energy physics Mellin-Barnes integrals appear frequently at the intermediate steps in the process of calculations [2,3,12,[14][15][16]21,25]. These are contour integrals in which the integrands are quotients of Euler Gamma functions, as in (1.8).…”

Section: (): V-volmentioning

confidence: 99%

Mellin–Barnes integrals and the method of brackets

et al. 2022

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The method of brackets is a method for the evaluation of definite integrals based on a small number of rules. This is employed here for the evaluation of Mellin–Barnes integral. The fundamental idea is to transform these integral representations into a bracket series to obtain their values. The expansion of the gamma function in such a series constitute the main part of this new application. The power and flexibility of this procedure is illustrated with a variety of examples.

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“…Remark 1.2. In high energy physics Mellin-Barnes integrals appear frequently at the intermediate steps in the process of calculations [2,3,10,11,12,17,14,21]. These are contour integrals in which the integrands are quotients of Euler Gamma functions, as in (1.10).…”

Section: Introductionmentioning

confidence: 99%

Mellin-Barnes and the method of brackets

Gonzalez,

Kondrashuk,

Moll

et al. 2021

Preprint

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The method of brackets is a method for the evaluation of definite integrals based on a small number of rules. This is employed here for the evaluation of Mellin-Barnes integral. The fundamental idea is to transform these integral representations into a bracket series to obtain their values. The expansion of the gamma function in such a series constitute the main part of this new application. The power and flexibility of this procedure is illustrated with a variety of examples.

show abstract

Multi-fold contour integrals of certain ratios of Euler gamma functions from Feynman diagrams: orthogonality of triangles

Cited by 4 publications

References 30 publications

Finiteness of N=4 Super-Yang–Mills Effective Action in Terms of Dressed N=1 Superfields

Finiteness of N=4 Super-Yang–Mills Effective Action in Terms of Dressed N=1 Superfields

Mellin–Barnes integrals and the method of brackets

Mellin-Barnes and the method of brackets

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