One-and two-jet inclusive quantities in hadron collisions have already been calculated to next-to-leading order accuracy, using both the subtraction and the cone method. Since the one-loop corrections have recently been obtained for all five-parton amplitudes, three-jet inclusive quantities can also be predicted to next-to-leading order. The subtraction method presented in the literature is based on a systematic use of boost-invariant kinematical variables, and therefore its application to three-jet production is quite cumbersome. In this paper we reanalyze the subtraction method and point out the advantage of using angle and energy variables. This leads to simpler results and it has complete generality, extending its validity to n-jet production. The formalism is also applicable to n-jet production in e + e − annihilation and in photon-hadron collisions. All the analytical results necessary to construct an efficient numerical program for next-to-leading order three-jet inclusive quantities in hadroproduction are given explicitly. As new analytical result, we also report the collinear limits of all the two-to-four processes.

Applying asymptotic expansions at threshold, we compute the two-loop quantum chromodynamics (QCD) correction to the short-distance coefficient that governs the leptonic decay c ! l 1 l 2 of an S-wave quarkonium state and discuss its impact on the relation between the quarkonium nonrelativistic wave function at the origin and the quarkonium decay constant in full QCD. [S0031-9007(98)

One-loop corrections to the helicity amplitudes of all 2 → 2 subprocesses are calculated in QCD and in N=1 supersymmetric Yang-Mills theory using two versions of dimensional regularization: the 't Hooft-Veltman scheme and dimensional reduction. Studying the structure of the soft and collinear singularities, we found universal transition rules for the squared matrix element which can be used to translate the results obtained in these schemes to the results valid in the conventional dimensional regularization scheme. With explicit calculation it is demonstrated that the one-loop helicity amplitudes of the 2 → 2 subprocesses calculated using dimensional reduction in the N=1 supersymmetric SU (N ) gauge theory respect the supersymmetry Ward identities. Our transition rules can also be used to calculate the next-to-leading order Altarelli-Parisi kernels in the dimensional reduction scheme when they satisfy supersymmetry Ward identities as well.

We consider top-anti-top production near threshold in $e^+ e^-$ collisions, resumming Coulomb-enhanced corrections at next-to-next-to-leading order (NNLO). We also sum potentially large logarithms of the small top quark velocity at the next-to-leading logarithmic level using the renormalization group. The NNLO correction to the cross section is large, and it leads to a significant modification of the peak position and normalization. We demonstrate that an accurate top quark mass determination is feasible if one abandons the conventional pole mass scheme and if one uses a subtracted potential and the corresponding mass definition. Significant uncertainties in the normalization of the $t\bar{t}$ cross section, however, remain.Comment: 14 pages, LaTeX, 2 figures included via epsf.st

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