Double box and hexagon conformal Feynman integrals

Ananthanarayan, B.; Banik, Sumit; Friot, Samuel; Ghosh, Shayan

doi:10.1103/physrevd.102.091901

Cited by 33 publications

(62 citation statements)

References 7 publications

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“…Let us note here that the AppellF2 package can be used to develop a Mathematica realization of the ten second order complete hypergeometric functions in two variables which F 2 is linked to, which is a work in progress [19]. As another extension of the present study, we will also consider, in a subsequent work, the logarithmic situation where some of the Pochhammer parameters can be identical.…”

Section: Discussionmentioning

confidence: 99%

“…Therefore, by the study of appropriate classes of multiple MB integrals, the method of [5] opens promising horizons in hypergeometric functions theory and, in particular, for the determination of the analytic continuations of many classes of hypergeometric series, whatever the number of their variables is, in terms of others multivariable hypergeometric series. Obviously, a large number of applications can follow in physics, as already shown in the recent works [10] and [11] in the context of the study of Feynman integrals in quantum field theory.…”

Section: Introductionmentioning

confidence: 93%

“…These links can be obtained from the transformation theory of F 2 and are summarized in Chapter 5 of [3]. Hence, in the present work, by studying the linear transformations 1 of F 2 and by building the AppellF2 Mathematica package based on the obtained formulas and dedicated to its numerical evaluation, we provide the basis of a future Mathematica package for the evaluation of all the double series above [19], with the exception of F 4 , H 1 and H 5 . These three lacking series will be considered separately in subsequent publications.…”

Section: Introductionmentioning

confidence: 99%

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On the evaluation of the Appell $F_2$ double hypergeometric function

Ananthanarayan,

Bera,

Friot

et al. 2021

Preprint

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The transformation theory of the Appell F2(a, b1, b2; c1, c2; x, y) double hypergeometric function is used to obtain a set of series representations of F2 which provide an efficient way to evaluate F2 for real values of its arguments x and y and generic complex values of its parameters a, b1, b2, c1 and c2 (i.e. in the nonlogarithmic case). This study rests on a classical approach where the usual double series representation of F2 and other double hypergeometric series that appear in the intermediate steps of the calculations are written as infinite sums of one variable hypergeometric series, such as the Gauss 2F1 or the 3F2, various linear transformations of the latter being then applied to derive known and new formulas. Using the three well-known Euler transformations of F2 on these results allows us to obtain a total of 44 series which form the basis of the Mathematica package AppellF2, dedicated to the evaluation of F2. A brief description of the package and of the numerical analysis that we have performed to test it are also presented.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

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On the evaluation of the Appell $F_2$ double hypergeometric function

Ananthanarayan,

Bera,

Friot

et al. 2021

Preprint

Self Cite

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“…This integral was found to satisfy a first-order differential equation relating it to the 6D hexagon [63,64], as well as a further second-order differential equation [65]. A four-fold rational integral representation -and a one-fold polylogarithmic one - were found [66], as well as a sum representation [67,68]. So far, however, it has not been possible to express the elliptic double-box integral in terms of eMPLs.…”

Section: Introductionmentioning

confidence: 99%

The elliptic double box and symbology beyond polylogarithms

Kristensson,

Wilhelm,

Zhang

2021

Preprint

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We study the elliptic double-box integral, which contributes to generic massless QFTs and is the only contribution to a particular 10-point scattering amplitude in N = 4 SYM theory. Based on a Feynman parametrization, we express this integral in terms of elliptic polylogarithms. We then study its symbol, finding a rich structure and remarkable similarity with the non-elliptic case. In particular, the first entry of the symbol is expressible in terms of logarithms of dual-conformal crossratios, and elliptic letters only occur in the last two entries. Moreover, the symbol makes manifest a differential equation relating the double-box integral to a 6D hexagon integral, suggesting that it can be bootstrapped based on the latter integral alone.

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“…While the 2variable box integral was shown to be completely fixed by its symmetries, in this first approach it was not possible to fix the linear combination of formal Yangian invariant building blocks for the 9-variable hexagon and double box integrals. Here an important step was recently made in [20], where this linear combination was determined using a multi-variable extension of the Mellin-Barnes techniques, cf. [21,22].…”

Section: Introductionmentioning

confidence: 99%

Yangian bootstrap for massive Feynman integrals

Loebbert¹,

Miczajka²,

Müller³

et al. 2021

SciPost Phys.

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We extend the study of the recently discovered Yangian symmetry of massive Feynman integrals and its relation to massive momentum space conformal symmetry. After proving the symmetry statements in detail at one and two loop orders, we employ the conformal and Yangian constraints to bootstrap various one-loop examples of massive Feynman integrals. In particular, we explore the interplay between Yangian symmetry and hypergeometric expressions of the considered integrals. Based on these examples we conjecture single series representations for all dual conformal one-loop integrals in D spacetime dimensions with generic massive propagators.

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Double box and hexagon conformal Feynman integrals

Cited by 33 publications

References 7 publications

On the evaluation of the Appell $F_2$ double hypergeometric function

On the evaluation of the Appell $F_2$ double hypergeometric function

The elliptic double box and symbology beyond polylogarithms

Yangian bootstrap for massive Feynman integrals

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