Multivariate elliptic kites and tetrahedral tadpoles
Abstract
This work deals with two types of Feynman integrals in perturbative quantum field theory: the 2-loop 2-point kite, with 5 arbitrary internal masses, and its completion by a sixth propagator, to give a 3-loop tetrahedral tadpole, with 6 arbitrary masses. These general-mass cases cover broken and unbroken gauge theories, based on the Lie algebras U(1), SU(2) and SU(3), for the electromagnetic, weak and strong interactions. The elliptic substructure of these integrals should not be regarded as an obstruction. Rather, it is a bonus, thanks to the arithmetic-geometric mean of Gauss. Compact formulae are given, to handle all cases. Zero-mass limits are carefully considered. Anomalous thresholds of triangles in the kite pose no problem. The number theory of tadpoles is investigated, with intriguing results.
Cite
@article{arxiv.2212.01962,
title = {Multivariate elliptic kites and tetrahedral tadpoles},
author = {David Broadhurst},
journal= {arXiv preprint arXiv:2212.01962},
year = {2024}
}
Comments
16 pages, to appear in the proceedings of the 15th International Workshop on Lie Theory and Its Applications in Physics (LT-15), 19-25 June 2023, Varna, Bulgaria