6533b7d8fe1ef96bd126a53a

RESEARCH PRODUCT

Modular transformations of elliptic Feynman integrals

Stefan Weinzierl

subject

PhysicsHigh Energy Physics - TheoryNuclear and High Energy PhysicsClass (set theory)Basis (linear algebra)010308 nuclear & particles physicsbusiness.industryCoordinate systemFOS: Physical sciencesModular designBase (topology)01 natural sciencesManifoldAlgebraHigh Energy Physics - PhenomenologyTransformation (function)High Energy Physics - Phenomenology (hep-ph)High Energy Physics - Theory (hep-th)0103 physical scienceslcsh:QC770-798lcsh:Nuclear and particle physics. Atomic energy. Radioactivity010306 general physicsbusinessVariable (mathematics)

description

We investigate the behaviour of elliptic Feynman integrals under modular transformations. This has a practical motivation: Through a suitable modular transformation we can achieve that the nome squared is a small quantity, leading to fast numerical evaluations. Contrary to the case of multiple polylogarithms, where it is sufficient to consider just variable transformations for the numerical evaluations of multiple polylogarithms, it is more natural in the elliptic case to consider a combination of a variable transformation (i.e. a modular transformation) together with a redefinition of the master integrals. Thus we combine a coordinate transformation on the base manifold with a basis transformation in the fibre. Only in the combination of the two transformations we stay within the same class of functions.

https://dx.doi.org/10.48550/arxiv.2011.07311