Hypergeometric series representations of Feynman integrals by GKZ hypergeometric systems

Abstract

Abstract We show that almost all Feynman integrals as well as their coefficients in a Laurent series in dimensional regularization can be written in terms of Horn hypergeometric functions. By applying the results of Gelfand-Kapranov-Zelevinsky (GKZ) we derive a formula for a class of hypergeometric series representations of Feynman integrals, which can be obtained by triangulations of the Newton polytope ∆ G corresponding to the Lee- Pomeransky polynomial G. Those series can be of higher dimension, but converge fast for convenient kinematics, which also allows numerical applications. Further, we discuss possible difficulties which can arise in a practical usage of this approach and give strategies to solve them.

Keywords

• Differential and Algebraic Geometry
• Scattering Amplitudes