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

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.Comment: 14 page

Relation between the pole and the minimally subtracted mass in dimensional regularization and dimensional reduction to three-loop order

We compute the relation between the pole quark mass and the minimally subtracted quark mass in the framework of QCD applying dimensional reduction as a regularization scheme. Special emphasis is put on the evanescent couplings and the renormalization of the epsilon-scalar mass. As a by-product we obtain the three-loop on-shell renormalization constants Zm(OS) and Z2(OS) in dimensional regularization and thus provide the first independent check of the analytical results computed several years ago.Comment: 22 page

Three-Loop Chromomagnetic Interaction in HQET

We compute the three-loop QCD corrections to the quark chromomagnetic moment and thus obtain the matching coefficient and the anomalous dimension of the chromomagnetic interaction in HQET. As a byproduct we obtain the three-loop corrections to the quark anomalous magnetic moment.Comment: 22 page

Fermionic Corrections to the Three-Loop Matching Coefficient of the Vector Current

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.Comment: 21 page

Matching QCD and HQET heavy-light currents at three loops

We consider the currents formed by a heavy and a light quark within Quantum Chromodynamics and compute the matching to Heavy Quark Effective Theory to three-loop accuracy. As an application we obtain the third-order perturbative corrections to ratios of B-meson decay constants.Comment: 23 pages, full results are available as Mathematica files at http://www-ttp.particle.uni-karlsruhe.de/Progdata/ttp09/ttp09-41/ ; v2: an error in comparison with Ref. [8] fixed ; v3: Journal versio

O(ααs){\cal O}(\alpha\alpha_s) corrections to the γttˉ\gamma t\bar{t} vertex at the top quark threshold

We compute the last missing piece of the two-loop ${\cal O}(\alpha \alpha_s)$ corrections to $\gamma t \bar{t}$ vertex at the $t \bar{t}$ threshold due to the exchange of a $W$ boson and a gluon. This contribution constitutes a building block of the top quark threshold production cross section at electron positron colliders.Comment: 22 pages, 8 figure

Two-loop Matching Coefficients for Heavy Quark Currents.

In this paper we consider the matching coefficients up to two loops between Quantum Chromodynamics (QCD) and Non-Relativistic QCD (NRQCD) for the vector, axial-vector, scalar and pseudo-scalar currents. The structure of the effective theory is discussed and analytical results are presented. Particular emphasis is put on the singlet diagrams.Comment: 9 page