6533b839fe1ef96bd12a5a27
RESEARCH PRODUCT
Feynman integrals and iterated integrals of modular forms
Luise AdamsStefan Weinzierlsubject
High Energy Physics - TheoryPure mathematicsAlgebra and Number Theory010308 nuclear & particles physicsFeynman integralDifferential equationModular formGeneral Physics and AstronomyFOS: Physical sciencesMathematical Physics (math-ph)01 natural sciencesLoop integralHigh Energy Physics - PhenomenologyHigh Energy Physics - Phenomenology (hep-ph)High Energy Physics - Theory (hep-th)Iterated integrals0103 physical sciencesAlphabet010306 general physicsLinear combinationGroup theoryMathematical PhysicsMathematicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2017-04-28 |