Communications in Number Theory and Physics

Volume 12 (2018)

Number 2

Feynman integrals and iterated integrals of modular forms

Pages: 193 – 251

DOI: http://dx.doi.org/10.4310/CNTP.2018.v12.n2.a1

Authors

Luise Adams (PRISMA Cluster of Excellence, Institut für Physik, Johannes Gutenberg-Universität Mainz, Germany)

Stefan Weinzierl (PRISMA Cluster of Excellence, Institut für Physik, Johannes Gutenberg-Universität Mainz, Germany)

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 Text (PDF format)

Received 1 May 2017

Accepted 1 February 2018