On the evaluation of three--loop scalar integrals in the massive case

Abstract

I describe a method to calculate a class of three-loop selfenergy diagrams for arbitrary internal masses and external momentum. This method combines analytical results and numerical integration, and is suitable for implementation in a computer program to produce fast and accurate results. For the class of Feynman diagrams considered in this paper this method leads to a two-fold integral which needs to be evaluated numerically. Results are given for a range of masses and external momentum.

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• Nonperturbative Higgs propagator: NLO correction in the 1/N expansion
• New developments in the 1/N expansion and nonperturbative Higgs physics
• Direct numerical evaluation of multi-loop integrals without contour deformation
• NLO correction to Higgs boson parameters in the 1/N expansion
• Testing nonperturbative techniques in the scalar sector of the standard model
• Nonperturbative three-point functions of the O(N) sigma model in the 1/N expansion at NLO
• Loops and legs beyond perturbation theory