Analytical expressions of 3 and 4-loop sunrise Feynman integrals and 4-dimensional lattice integrals
Mar, 2008Citations per year
Abstract: (arXiv)
In this paper we continue a work started some years ago concerning the identification of the analytical expression of Feynman integrals whose calculation involves multiple elliptic integrals. We rewrite and simplify the analytical expression of an on-shell 3-loop equal-mass self-mass integral found previously. We collect and analyze a number of results on double and triple elliptic integrals. Therefore, we are able, for the first time, to identify a very compact analytical expression for the on-shell 4-loop self-mass integral which is one master integral of the 4-loop electron g-2. Moreover, we identify the analytical expressions of some integrals which appear in lattice perturbation theory, and in particular the 4-dimensional generalized Watson integral.- 12.38.Gc
- 12.20Ds
- 02.60.Jh
- Feynman diagram
- master integral
- elliptic integral
- lattice Green function
- Watson integral
- Feynman graph: higher-order
- two-point function
References(13)
Figures(0)