Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2008-03-07
Int.J.Mod.Phys.A23:5007-5020,2008
Physics
High Energy Physics
High Energy Physics - Phenomenology
13 pages, 1 figure, LaTex; v2: some rephrasing of text; v3: reference added, minor modifications; v4: checks of lattice integr
Scientific paper
10.1142/S0217751X08042869
In this paper we continue the work begun in 2002 on the identification of the analytical expressions of Feynman integrals which require the evaluation of multiple elliptic integrals. We rewrite and simplify the analytical expression of the 3-loop self-mass integral with three equal masses and on-shell external momentum. We collect and analyze a number of results on double and triple elliptic integrals. By using very high-precision numerical fits, for the first time we are able to identify a very compact analytical expression for the 4-loop on-shell self-mass integral with 4 equal masses, that is one of the master integrals of the 4-loop electron g-2. Moreover, we fit the analytical expressions of some integrals which appear in lattice perturbation theory, and in particular the 4-dimensional generalized Watson integral.
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