The Double Box and Hexagon Conformal Feynman Integrals

TL;DR

This paper derives explicit hypergeometric series representations for off-shell massless six-point conformal Feynman integrals, linking double box and hexagon topologies via Mellin-Barnes techniques and differential equations.

Contribution

It provides new hypergeometric series formulas for complex conformal integrals, connecting different topologies and dimensions through Mellin-Barnes and differential equation methods.

Findings

Explicit hypergeometric series for conformal integrals

Connection between double box and hexagon integrals

Differential equations relating integrals in different dimensions

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.