Nine-Propagator Master Integrals for Massless Three-Loop Form Factors

Abstract

We complete the calculation of master integrals for massless three-loop form factors by computing the previously-unknown three diagrams with nine propagators in dimensional regularisation. Each of the integrals yields a six-fold Mellin-Barnes representation which we use to compute the coefficients of the Laurent expansion in epsilon. Using Riemann zeta functions of up to weight six, we give fully analytic results for one integral; for a second, analytic results for all but the finite term; for the third, analytic results for all but the last two coefficients in the Laurent expansion. The remaining coefficients are given numerically to sufficiently high accuracy for phenomenological applications.

15 pages, 2 figures. Minor modifications and reference added. Matches published version

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• Planar master integrals for four-loop form factors
• Cutting massless four-loop propagators
• Three loop form factors of a massive spin-2 particle with nonuniversal coupling
• Methods for the Reduction of Three-Loop QCD Form Factors
• Fermionic corrections to quark and gluon form factors in four-loop QCD
• Singlet and non-singlet three-loop massive form factors