Coordinate space calculation of two- and three-loop sunrise-type diagrams, elliptic functions and truncated Bessel integral identities

Abstract

We integrate three-loop sunrise-type vacuum diagrams in $D_0=4$ dimensions with four different masses using configuration space techniques. The finite parts of our results are in numerical agreement with corresponding three-loop calculations in momentum space. Using some of the closed form results of the momentum space calculation we arrive at new integral identities involving truncated integrals of products of Bessel functions. For the non-degenerate finite two-loop sunrise-type vacuum diagram in $D_0=2$ dimensions we make use of the known closed form $p$-space result to express the moment of a product of three Bessel functions in terms of a sum of Claussen polylogarithms. Using results for the nondegenerate two-loop sunrise diagram from the literature in $D_0=2$ dimensions we obtain a Bessel function integral identity in terms of elliptic functions.

14 pages, 1 figure

References in corpus (8)

• The two-loop sunrise graph in two space-time dimensions with arbitrary masses in terms of elliptic dilogarithms
• Elliptic polylogarithms and iterated integrals on elliptic curves II: an application to the sunrise integral
• Elliptic integral evaluations of Bessel moments
• A numerical test of differential equations for one- and two-loop sunrise diagrams using configuration space techniques
• Elliptic integral evaluation of a Bessel moment by contour integration of a lattice Green function
• TVID: Three-loop Vacuum Integrals from Dispersion relations
• Laurent series expansion of sunrise-type diagrams using configuration space techniques
• Virtual and real processes, the Källén function, and the relation to dilogarithms

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