Bananas: multi-edge graphs and their Feynman 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.

43 pages, 7 figures, minor corrections

References in corpus (1)

• Singularities, swallowtails and Dirac points. An analysis for families of Hamiltonians and applications to wire networks, especially the Gyroid

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