Counting master integrals: integration by parts vs. differential reduction

Abstract

The techniques of integration by parts and differential reduction differ in the counting of master integrals. This is illustrated using as an example the two-loop sunset diagram with on-shell kinematics. A new algebraic relation between the master integrals of the two-loop sunset diagram that does not follow from the integration-by-parts technique is found.

6 pages, 1 figure; minor changes to the text, figure added; to appear in Phys. Lett. B

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