We present an analytic calculation of the O(mα 6 ) recoil and radiative recoil corrections to energy levels of positronium nS states and their hyperfine splitting. A complete analytic formula valid to O(mα 6 ) is given for the spectrum of S states. Technical aspects of the calculation are discussed in detail. Theoretical predictions are given for various energy intervals and compared with experimental results.

The b quark low-scale running mass m kin is determined from an analysis of the ⌼ sum rules in the next-to-next-to-leading order ͑NNLO͒. It is demonstrated that using this mass one can significantly improve the convergence of the perturbation series for the spectral density moments. We obtain m kin (1 GeV)ϭ4.56 Ϯ0.06 GeV. Using this result we derive the value of the modified minimal subtraction scheme mass m : m (m )ϭ4.2Ϯ0.1 GeV. Contrary to the low-scale running mass, the pole mass of the b quark cannot be reliably determined from the sum rules. As a by-product of our study we find the NNLO analytical expression for the cross section e ϩ e Ϫ →QQ of the quark-antiquark pair production in the threshold region, as well as the energy levels and the wave functions at the origin for the 1 S 3 bound states of QQ . ͓S0556-2821͑99͒08009-1͔

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Using non-relativistic effective theories, new next-to-next-to-leading order (NNLO) QCD corrections to the total tt production cross section at the Linear Collider have been calculated recently. In this article the NNLO calculations of several groups are compared and the remaining uncertainties are discussed. The theoretical prospects for an accurate determination of top quark mass parameters are discussed in detail. An outlook on possible future improvements is given.

We present an analytic calculation of the O ͑ma 6 ͒ recoil corrections to the hyperfine splitting (HFS) of the ground state energy levels in positronium. We find DE rec ma 6 ͑2