English

Feynman integrals and iterated integrals of modular forms

High Energy Physics - Phenomenology 2018-02-02 v3 High Energy Physics - Theory Mathematical Physics math.MP

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 ε\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 ε\varepsilon as iterated integrals of modular forms.

Keywords

Cite

@article{arxiv.1704.08895,
  title  = {Feynman integrals and iterated integrals of modular forms},
  author = {Luise Adams and Stefan Weinzierl},
  journal= {arXiv preprint arXiv:1704.08895},
  year   = {2018}
}

Comments

53 pages, v2: section on relation to Gamma_1(6) added, v3: section on the choice of the periods added

R2 v1 2026-06-22T19:30:46.185Z