We present a unified derivation of the resummation of Sudakov logarithms, directly from the factorization properties of cross sections in which they occur. We rederive in this manner the well-known exponentiation of leading and nonleading logarithmic enhancements near the edge of phase space for cross sections such as deeply inelastic scattering, which are induced by an electroweak hard scattering. For QCD hard-scattering processes, such as heavy-quark production, we show that the resummation of nonleading logarithms requires in general mixing in the space of the color tensors of the hard scattering. The exponentiation of Sudakov logarithms implies that many weighted cross sections obey particular evolution equations in momentum transfer, which streamline the computation of their Sudakov exponents. We illustrate this method with the resummation of soft-gluon enhancements of the inclusive Drell-Yan cross section, in both DIS and MS factorization schemes.

We present a new resummation formula for the Drell-Yan cross section. The formal resummation of threshold corrections in Drell-Yan hard-scattering functions produces an exponent with singularities from the infrared pole of the QCD running coupling. Our reformulation treats such 'infrared renormalons' by a principal value prescription, analogous to a modified Borel transform. The resulting expression includes all large threshold corrections to the hard scattering function as an asymptotic series in α s , but is a finite function of Q 2 . We find that the ambiguities of the resummed perturbation theory imply the presence of higher twist corrections to quark-antiquark hard-scattering functions that begin at Λ QCD /Q. This suggests an important role for higher twist in the phenomonolgy of hadron-hadron inclusive cross sections. We also discuss the numerical evaluation of the exponent and its asymptotic perturbation series for representative values of Q 2 .1

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We present a calculation of the total cross section for top quark production based on a new perturbative resummation of gluon radiative corrections to the basic QCD subprocesses. We use Principal Value Resummation to calculate all relevant large threshold corrections. Advantages of this method include its independence from arbitrary infrared cuto s and speci cation of the perturbative regime of applicability. For p p collisions at center-of-mass energy p s = 1:8TeV and a top mass of 175 GeV, we compute (t t) = 5:52 +0:07 0:45 pb.

Our calculation of the total cross section for inclusive production of tt pairs in hadron collisions is presented. The principal ingredient of the calculation is resummation of the universal leading-logarithm effects of gluon radiation to all orders in the quantum chromodynamics coupling strength, restricted to the region of phase space that is demonstrably perturbative.We derive the perturbative regime of the resummed series, starting from the principal-value resummation approach, and we isolate the perturbative domain in both moment space and, upon inversion of the corresponding Mellin transform, in momentum space. We show that our perturbative result does not depend on the manner non-perturbative or infrared effects are handled in principal-value resummation. We treat both the quark-antiquark and gluon-gluon production channels consistently in the MS factorization scheme. We compare our method and results with other resummation methods that rely on the choice of infrared cutoffs. We derive the renormalization/factorization scale dependence of our resummed cross section, and we discuss factorization scheme dependence and remaining theoretical uncertainties, including estimates of possible non-perturbative contributions. We include the full content of the exact next-to-leading order calculation in obtaining our final results. We present predictions of the physical cross section as a function of top quark mass in proton-antiproton reactions at center-of-mass energies of 1.8 and 2.0 TeV. We also provide the differential cross section as a function of the parton-parton subenergy.

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Abstract. We discuss the motivation for resummation of the effects of initialstate soft gluon radiation, to all orders in the strong coupling strength, for processes in which the near-threshold region in the partonic subenergy is important. We summarize our calculation of the total cross section for top quark production at hadron colliders. Comments are included on the differences between our treatment of subleading logarithmic terms and other methods.

We discuss the existence and properties of the asymptotic S matrix in field theories with massless particles. We show for the classic case of the scattering of an electron in an external electromagnetic field that the S-matrix method yields the same results as the traditional cross-section method involving properly formed sums over physically degenerate initial as well as final states. In that case, we show that ob-servable~ are independent of the particular choice of asymptotic Hamiltonian. We argue that the massless theory is unique and discuss its relation to the massless limit of the massive theory. Although the results do not depend on it, a novel aspect of our formalism is the interpretation of physical states involving massless particles as Fock states and the occurrence of physical transitions in Fock space.