In this paper we consider the matching coefficient of the vector
current between Quantum Chromodynamics (QCD) and Non-Relativistic QCD
(NRQCD) to three-loop order in perturbation theory.
We evaluate the fermionic corrections containing a closed massless
fermion loop.
The results are building blocks both for the bottom and top quark system
at threshold. We explain in detail the methods used for the evaluation
of the Feynman diagrams, classify the occurring master integrals and
provide results for the latter. The numerical effects are significant.
They have the tendency to improve the behaviour of the perturbative
series — both for the bottom and top quark system.
