ar X iv : 0 90 2 . 32 67 v 1 [ he p - ph ] 1 8 Fe b 20 09 Threshold corrections to the γtt̄ vertex at O ( αα s )

The measurement of the total tt̄ cross section constitutes a major part of the top physics program at a future ee International Linear Collider (ILC). Due to the large top quark mass and the large width Γt ≫ ΛQCD, non perturbative effects are strongly suppressed at energies around the threshold. Therefore it is possible to determine top quark properties like the mass mt and the width Γt, but also the strong coupling αs with high precision. In Ref. [2] it has been shown that an uncertainty of below 100 MeV can be obtained for mt from a threshold scan of the cross section. The feasibility of such high-precision measurements requires a theory prediction of the total cross section σ(ee → tt̄) with high accuracy (preferably δσ/σ ≤ 3%). The study of tt̄ threshold production is performed in the framework of non-relativistic QCD (NRQCD) [3] which separates the hard and soft scales involved in the process. The next-to-next-to-leading order (NNLO) calculation [4] turned out to be as large as the NLO one. Only the (partial) NNNLO [5, 6] results show a good convergence of the perturbative expansion and a strong reduction of the scale dependence from NNLO to NNNLO can be observed. The remaining uncertainty turns out to be of the order of 10%. A similar value is obtained from the approach based on the resummation of logarithmically enhanced terms which have been considered in Refs. [7, 8]. In order to reach a theory goal of δσ/σ ≤ 3% it is necessary to include in the prediction next to the one-loop electroweak corrections, which are known since quite some time [9] (see also [10]), also higher order effects. The evaluation of O(ααs) corrections has been started in Ref. [11], where the two-loop mixed electroweak and QCD corrections to the matching coefficient of the vector current has been computed due to a Higgs or Z boson exchange in addition to a gluon. In these proceedings the calculation of O(ααs) for the two-loop vertex diagrams mediated by a W boson and gluon exchange is summarised [12]. This result completes the vertex corrections of order ααs — a building block for the top quark production cross section. Assuming the (numerically well justified) power counting α ∼ αs one can see that these corrections are formally of NNNLO. In order to complete the matching corrections of order ααs also the two-loop box diagrams contributing to ee → tt̄ have to be considered. Actually, only the proper combination of the box, vertex and self-energy contributions (the latter can, e.g., be found in Refs. [13, 14]) forms a gauge independent set.