GKZ-system of the 2-loop self energy with 4 propagators

TL;DR

This paper derives a GKZ-system of linear PDEs for a 2-loop self energy Feynman integral with 4 propagators, revealing its hypergeometric structure and fundamental solutions.

Contribution

It introduces a novel GKZ-system framework for analyzing complex Feynman integrals with multiple propagators and ratios.

Findings

536 hypergeometric functions identified

30 linearly independent fundamental solutions found

Convergent regions intersect, enabling solution construction

Abstract

Applying the system of linear partial differential equations derived from the Mellin-Barnes representation and the Miller transformation, we present the GKZ-system of the Feynman integral of the 2-loop self energy diagram with 4 propagators. The codimension of the derived GKZ-system equals the number of independent dimensionless ratios among the external momentum squared and virtual mass squared. In total 536 hypergeometric functions are obtained in the neighborhoods of the origin and infinity, in which 30 linearly independent hypergeometric functions whose convergent regions have nonempty intersection constitute a fundamental solution system in a proper subset of the whole parameter space.