On the Method of Brackets

Ananthanarayan, B.; Banik, Sumit; Friot, Samuel; Pathak, Tanay

doi:10.48550/arxiv.2112.09679

Cited by 4 publications

(4 citation statements)

References 21 publications

(63 reference statements)

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“…[34]. The very problem of finding series representations for a given MB integrals was recently analyzed in [35,36] making use of an approach based on conic hulls. A public computer code was also given there.…”

Section: Discussionmentioning

confidence: 99%

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Belitsky¹,

Smirnov²,

A.³

2022

Preprint

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We address the problem of evaluation of multiloop Feynman integrals by means of their Mellin-Barnes representation. After a brief overview of available capabilities though open source toolkits and their application in various circumstances, we introduce a new code MBcreate which allows one to automatically deduce a concise Mellin-Barnes representation for a given parametric integral. A thorough discussion of its implementation and use is provided.

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Section: Discussionmentioning

confidence: 99%

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Belitsky¹,

Smirnov²,

A.³

2022

Preprint

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“…The several variable generalization of Ramanujan's master theorem has also been useful in computing multi-loop Feynman integrals [58][59][60][61].…”

Section: E Positivity Of D (N) M : Further Examplesmentioning

confidence: 99%

Celestial insights into the S-matrix bootstrap

Ghosh

Raman

Sinha

2022

J. High Energ. Phys.

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We consider 2-2 scattering in four spacetime dimensions in Celestial variables. Using the crossing symmetric dispersion relation (CSDR), we recast the Celestial amplitudes in terms of crossing symmetric partial waves. These partial waves have spurious singularities in the complex Celestial variable, which need to be removed in local theories. The locality constraints (null constraints) admit closed form expressions, which lead to novel bounds on partial wave moments. These bounds allow us to quantify the degree of low spin dominance(LSD) for scalar theories. We study a new kind of positivity that seems to be present in a wide class of theories. We prove that this positivity arises only in theories with a spin-0 dominance. The crossing symmetric partial waves with spurious singularities removed, dubbed as Feynman blocks, have remarkable properties in the Celestial variable, namely typically realness, in the sense of Geometric Function Theory (GFT). Using GFT techniques we derive non-projective bounds on Wilson coefficients in terms of partial wave moments.

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“…It seems that Regge was the first to show that Feynman integrals are linked to multivariable hypergeometric functions [2] (for a recent review of the relation between hypergeometric functions and Feynman integrals, we refer the reader to [3]). Nowadays, methods like the Mellin-Barnes (MB) representation [4,5], the method of brackets [6,7,8], the negative-dimension approach [9,10], etc. can provide hypergeometric representations of Feynman integrals.…”

Section: Introductionmentioning

confidence: 99%

Olsson.wl : a Mathematica package for the computation of linear transformations of multivariable hypergeometric functions

Ananthanarayan,

Bera,

Friot

et al. 2022

Preprint

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We present the Olsson.wl Mathematica package which aims to find linear transformations for some classes of multivariable hypergeometric functions. It is based on a well-known method developed by P. O. M. Olsson in J. Math. Phys. 5, 420 (1964) in order to derive the analytic continuations of the Appell F 1 double hypergeometric series from the linear transformations of the Gauss 2 F 1 hypergeometric function. We provide a brief description of Olsson's method and demonstrate the commands of the package, along with examples. We also provide a companion package, called ROC2.wl and dedicated to the derivation of the regions of convergence of double hypergeometric series. This package can be used independently of Olsson.wl.

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On the Method of Brackets

Cited by 4 publications

References 21 publications

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Celestial insights into the S-matrix bootstrap

Olsson.wl : a Mathematica package for the computation of linear transformations of multivariable hypergeometric functions

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