Abstract
We use the method of differential equations to analytically evaluate all planar three-loop Feynman integrals relevant for form factor calculations involving massive particles. Our results for ninety master integrals at general $q^2$ are expressed in terms of multiple polylogarithms, and results for fiftyone master integrals at the threshold $q^2=4m^2$ are expressed in terms of multiple polylogarithms of argument one, with indices equal to zero or to a sixth root of unity.
Highlights
When considering Feynman integrals with less than 9 propagators, it typically happens that their graph can be represented as a subdiagram of more than one of the families shown in figure 1
A given diagram can be represented in many equivalent ways
We have presented two more applications of the strategy to solve DE for Feynman integrals initiated in [4]
Summary
Smirnovd,e a PRISMA Cluster of Excellence, Johannes Gutenberg Universität Mainz, Mainz, Germany b. Kavli Institute for Theoretical Physics, UC Santa Barbara, Santa Barbara, U.S.A. Skobeltsyn Institute of Nuclear Physics of Moscow State University, Moscow, Russia e. Institut für Theoretische Teilchenphysik, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
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