Bananas: multi-edge graphs and their Feynman integrals

TL;DR

This paper analyzes multi-edge banana graphs with different masses, providing a recursive integral definition of their cut Feynman integrals, exploring their structure, differential equations, monodromy, and basis of master integrals.

Contribution

It introduces a recursive integral approach to compute cut banana graphs with varying masses and examines their mathematical structure and related differential equations.

Findings

Recursive integral definition for cut banana graphs

Detailed analysis of the integral structure and monodromy

Discussion of differential equations and master integrals

Abstract

We consider multi-edge or banana graphs $b_n$ on $n$ internal edges $e_i$ with different masses $m_i$. We focus on the cut banana graphs $\Im(\Phi_R(b_n))$ from which the full result $\Phi_R(b_n)$ can be derived through dispersion. We give a recursive definition of $\Im(\Phi_R(b_n))$ through iterated integrals. We discuss the structure of this iterated integral in detail. A discussion of accompanying differential equations, of monodromy and of a basis of master integrals is included.