Differential equations for loop integrals without squared propagators

Abstract

We provide a sufficient condition for avoiding squared propagators in the intermediate stages of setting up differential equations for loop integrals. This condition is satisfied in a large class of two- and three-loop diagrams. For these diagrams, the differential equations can thus be computed using "unitarity-compatible" integration-by-parts reductions, which simplify the reduction problem by avoiding integrals with higher-power propagators.

8 pages, 3 figures. Contribution to the proceedings of Loops and Legs 2018, 29 April--4 May 2018, St. Goar, Germany