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.
Highlights
A major goal of a future international linear collider (ILC) is the precise measurement of the top-quark production cross section close to threshold
The theoretical calculation of the threshold cross section is based on an effective theory [1,2] which is constructed from Quantum Chromodynamics (QCD) by integrating out the hard scale given by the top-quark mass
In this paper we provide a further building block needed for the completion of the next-to-next-to-next-to leading order (NNNLO) calculation: the heavy-fermion contribution to the three-loop matching coefficient
Summary
A major goal of a future international linear collider (ILC) is the precise measurement of the top-quark production cross section close to threshold. The theoretical calculation of the threshold cross section is based on an effective theory [1,2] (for a review see [3]) which is constructed from QCD by integrating out the hard scale given by the top-quark mass. In this paper we provide a further building block needed for the completion of the NNNLO calculation: the heavy-fermion contribution to the three-loop matching coefficient. One has to consider vertex diagrams with massive quarks on their mass shell and the external momentum q2 = 4m2Q. This kinematical configuration in combination with an involved reduction to master integrals makes the calculation quite challenging.
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