Next-to-Next-to-Next-to-Leading Order QCD Prediction for the Top AntitopS-Wave Pair Production Cross Section Near Threshold ine+e−Annihilation

Abstract

We present the third-order QCD prediction for the production of top-anti-top quark pairs in electronpositron collisions close to the threshold in the dominant S-wave state. We observe a significant reduction of the theoretical uncertainty and discuss the sensitivity to the top quark mass and width.PACS numbers: 14.65. Ha, 12.38.Bx, 13.66.Bc Among the main motivations for building a future highenergy electron-positron collider in steps of increasing center-of-mass energy are precise measurements at √ s ≈ 345 GeV close to the production threshold of top antitop quark pairs. The peculiar behaviour of the cross section allows for the precise determination of a number of Standard Model parameters, most prominently the top quark mass. To date the most precise measurement of m t = 173.34±0.27(stat)±0.71(syst) GeV comes from the hadron colliders Fermilab Tevatron and CERN LHC [1] and is based on the reconstruction of the top and antitop quarks through their decay products. This approach and the value quoted above are plagued by unknown relations of the extracted mass value m t to top quark masses in the pole or MS renormalization scheme, which may well exceed 1 GeV. At hadron colliders there are also methods to determine directly a well-defined top quark mass, such as the extraction of m t from top quark cross section measurements. However, the final precision is of the order of a few GeV and thus significantly worse. At an electron-positron collider, on the other hand, scans of the top anti-top pair production threshold can lead to very precise measurements of well-defined mass values with a statistical accuracy of only 20-30 MeV [2,3]. Besides the top quark mass also its decay width and the strong coupling constant can be extracted with an accuracy of 21 MeV [3] and 0.0009 [2], respectively. A recent study has shown that for a Higgs boson with a mass of about 125 GeV the top quark Yukawa coupling can be obtained with a statistical uncertainty of only 4.2% [3]. These numbers pose several challenges to theory.A crucial input to reach the aimed precision is a precise calculation of the top anti-top pair production cross section in the threshold region. While the fundamental theory of quantum chromodyanmics (QCD) is wellestablished, performing calculations of quantum corrections to the very high accuracies demanded here is very difficult indeed. The problem is further complicated by the fact that in the threshold region the colour Coulomb potential ∝ α s /r, where α s denotes the strong coupling, can no longer be treated as a perturbation even though α s ≪ 1. Standard perturbation theory in α s breaks down and resummation is required.The relevant techniques have been developed in the 1990s in the framework of effective field theory (EFT), which accounts for the different dynamical scales in the problem. For a heavy quark anti-quark system at threshold there are three relevant scales, the hard scale m, the potential and soft scale mv, and the ultrasoft scale mv 2 , where m denotes the mass of the quark and v its velocit...

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