The Double Box and Hexagon Conformal Feynman Integrals

Abstract

The off-shell massless six-point double box and hexagon conformal Feynman integrals with generic propagator powers are expressed in terms of linear combinations of multiple hypergeometric series of the generalized Horn type. These results are derived from 9-fold Mellin-Barnes representations obtained from their dual conformal Feynman parameter representations. The individual terms in the presented expressions satisfy the differential equation that relates the double box in $D$ dimensions to the hexagon in $D+2$ dimensions.

26 pages, 1 figure

References in corpus (5)

• Yangian Symmetry for Fishnet Feynman Graphs
• Yangian Symmetry for Bi-Scalar Loop Amplitudes
• Yangian Bootstrap for Conformal Feynman Integrals
• On convergent series representations of Mellin-Barnes integrals
• Multiple Mellin-Barnes Integrals as Periods of Calabi-Yau Manifolds With Several Moduli

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• Yangian-invariant fishnet integrals in 2 dimensions as volumes of Calabi-Yau varieties
• Multiple Series Representations of $N$-fold Mellin-Barnes Integrals
• The elliptic double box and symbology beyond polylogarithms
• Yangian Bootstrap for Massive Feynman Integrals
• Massive One-loop Conformal Feynman Integrals and Quadratic Transformations of Multiple Hypergeometric Series
• Yangian Ward Identities for Fishnet Four-Point Integrals
• Multiple Mellin-Barnes integrals with straight contours
• Analytic continuations of the Horn $H_1$ and $H_5$ functions
• Chiral Perturbation Theory Reflections on Effective Theories of the Standard Model
• On the evaluation of the Appell $F_2$ double hypergeometric function
• Singularities of Feynman Integrals
• Closed Form Expressions for Certain Improper Integrals of Mathematical Physics