Completely automated computation of the heavy-fermion corrections to the three-loop matching coefficient of the vector current

Abstract

We evaluate the corrections to the matching coefficient of the vector current between Quantum Chromodynamics (QCD) and Non-Relativistic QCD (NRQCD) to three-loop order containing a closed heavy-fermion loop. The result constitutes a building block both for the bottom- and top-quark system at threshold. Strong emphasis is put on our completely automated approach of the calculation including the generation of the Feynman diagrams, the identification of the topologies, the reduction to master integrals and the automated numerical computation of the latter.

arXiv comment14 pages

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• Analytic results for planar three-loop integrals for massive form factors
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• Three-loop QCD matching of the flavor-changing scalar current involving the heavy charm and bottom quark
• Non-relativistic high-energy physics: top production and dark matter annihilation
• Supersymmetric Corrections to the Threshold Production of Top Quark Pairs
• Nonrelativistic effective field theory of unstable top