Numerical evaluation of master integrals from differential equations

Abstract

The 4-th order Runge-Kutta method in the complex plane is proposed for numerically advancing the solutions of a system of first order differential equations in one external invariant satisfied by the master integrals related to a Feynman graph. The particular case of the general massive 2-loop sunrise self-mass diagram is analyzed. The method offers a reliable and robust approach to the direct and precise numerical evaluation of master integrals.

Latex, 5 pages, 4 ps-figures, uses included npb.sty, presented at RADCOR 2002 and Loops and Legs in Quantum Field Theory, 8-13 September 2002, Kloster Banz, Germany

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• TSIL: a program for the calculation of two-loop self-energy integrals
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• Strong and Yukawa two-loop contributions to Higgs scalar boson self-energies and pole masses in supersymmetry
• Two-loop QCD corrections to the MSSM Higgs masses beyond the effective-potential approximation
• Two-loop scalar self-energies and pole masses in a general renormalizable theory with massless gauge bosons
• Numerical evaluation of loop integrals
• Evaluation of the general 3-loop vacuum Feynman integral
• BOKASUN: a fast and precise numerical program to calculate the Master Integrals of the two-loop sunrise diagrams
• Two-Loop Vertices in Quantum Field Theory: Infrared Convergent Scalar Configurations
• Refined gluino and squark pole masses beyond leading order
• Renormalized $\epsilon$-finite master integrals and their virtues: the three-loop self energy case
• Evaluation of three-loop self-energy master integrals with four or five propagators
• Lectures on configuration space methods for sunrise-type diagrams
• Evaluating massive planar two-loop tensor vertex integrals