Recurrence Relations for Three-Loop Prototypes of Bubble Diagrams with a Mass

Abstract

Recurrence relations derived via the Chetyrkin--Tkachov method of integration by parts are applied to reduce scalar three-loop bubble (vacuum) diagrams with a mass to a limited number of master integrals. The reduction is implemented as a package of computer programs for analytic evaluation in FORM. The algorithms are applicable to diagrams with any integer powers on the lines in an arbitrary dimension. A physical application is the evaluation of the three-loop QCD correction to the electroweak rho parameter.

9 pages in LaTeX

References in corpus (4)

• Two-loop two-point functions with masses: asymptotic expansions and Taylor series, in any dimension
• $O(\alpha {\alpha }_s^2)$ correction to the electroweak $\rho$ parameter
• Corrections of order ${\cal O}(G_F M_t^2 \as^2)$ to the $\rho$ parameter
• Calculation of Feynman Diagrams from their Small Momentum Expansion

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