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.

arXiv comment43 pages, 7 figures, minor corrections

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• On a procedure to derive $\epsilon$-factorised differential equations beyond polylogarithms
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• The ice cone family and iterated integrals for Calabi-Yau varieties
• The SAGEX Review on Scattering Amplitudes, Chapter 4: Multi-loop Feynman Integrals
• Three-loop banana integrals with four unequal masses
• Feynman Integrals from Positivity Constraints
• A Calabi-Yau-to-Curve Correspondence for Feynman Integrals
• Analytic and numerical approaches for depictive 3-loop integrals using sector decomposition