Feynman integrals and iterated integrals of modular forms

DOI10.4310/CNTP.2018.V12.N2.A1zbMATH Open1393.81015arXiv1704.08895MaRDI QIDQ1651395

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Publication date: 12 July 2018

Published in: (Search for Journal in Brave)

Abstract: In this paper we show that certain Feynman integrals can be expressed as linear combinations of iterated integrals of modular forms to all orders in the dimensional regularisation parameter $varepsilon$ . We discuss explicitly the equal mass sunrise integral and the kite integral. For both cases we give the alphabet of letters occurring in the iterated integrals. For the sunrise integral we present a compact formula, expressing this integral to all orders in $varepsilon$ as iterated integrals of modular forms.

Full work available at URL: https://arxiv.org/abs/1704.08895

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