Analytic results for planar three-loop integrals for massive form factors

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.

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• Solving differential equations for Feynman integrals by expansions near singular points
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• The Heavy Quark Form Factors at Two Loops
• The Heavy Fermion Contributions to the Massive Three Loop Form Factors
• Heavy Quark Form Factors at Three Loops in the Planar Limit
• Massive three-loop form factor in the planar limit
• A Numerical Routine for the Crossed Vertex Diagram with a Massive-Particle Loop
• Three-loop massive form factors: complete light-fermion and large-$N_c$ corrections for vector, axial-vector, scalar and pseudo-scalar currents
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• Systematic approximation of multi-scale Feynman integrals
• Three-loop planar master integrals for heavy-to-light form factors
• Three loop QCD corrections to heavy quark form factors
• Massive quark form factors
• The canonical form has got baubles