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arXiv · hep-ph/9512442

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

Leo. V. Avdeev
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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.

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Leo. V. Avdeev. 1995-12-29. Recurrence Relations for Three-Loop Prototypes of Bubble Diagrams with a Mass. https://doi.org/10.1016/0010-4655(96)00090-2

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