Threshold Resummation and the Total Cross Section for Top Quark Production

We discuss the motivation for resummation of the effects of initial-state 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.Comment: 7 pages, 1 figure, uses aipproc.sty; Paper presented by E. L. Berger, to be published in the Proceedings of DIS'97, Fifth International Workshop on Deep Inelastic Scattering and QCD, Chicago, IL, April 14 - 18, 199

The Perturbative Resummed Series for Top Production

Our calculation of the total cross section for inclusive production of $t\bar{t}$ pairs in hadron collisions is summarized. The principal ingredient of this 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 manifestly perturbative. 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.Comment: 9 pages. Latex file plus 6 ps files of figures submitted togther in uuencoded form; invited talk presented by Harry Contopanagos at the XXXI Rencontres de Moriond on QCD and High Energy Hadronic Interactions, Les Arcs, France, March, 1996. New version to correct problem with unsuccessful posting of figures on May

Top Quark Production Dynamics in QCD

A calculation of the total cross section for top quark production in hadron-hadron collisions is presented based on an all-orders perturbative resummation of initial-state gluon radiative contributions to the basic quantum chromodynamics subprocesses. Principal-value resummation is used to evaluate all relevant large threshold contributions. In this method there are no arbitrary infrared cutoffs, and the perturbative regime of applicability is well defined, two attributes that significantly reduce the estimated uncertainty of the results. For $p\bar{p}$ collisions at center-of-mass energy $\sqrt{s}=1.8$ TeV and a top mass of 175 GeV, we obtain $\sigma(t\bar{t})=5.52^{+0.07}_{-0.45} pb$, in agreement with experiment. Predicted cross sections are provided as a function of top mass in $p\bar{p}$ collisions at $\sqrt{s}=2.0$ TeV and in $p p$ collisions at CERN LHC energies.Comment: 12 pages. Latex file plus 8 ps files of figures submitted altogther in uuencoded form; Invited talk presented by E. L. Berger at the International Symposium on Heavy Flavor and Electroweak Theory, Beijing, August 16 - 19, 199

Calculation of the Cross Section for Top Quark Production

We summarize calculations of the cross section for top quark production at hadron colliders within the context of perturbative quantum chromodynamics, including resummation of the effects of initial-state soft gluon radiation to all orders in the strong coupling strength. In our approach we resum the universal leading-logarithm contributions, and we restrict the calculation to the region of phase space that is demonstrably perturbative. We compare our approach with other methods. We present predictions of the physical cross section as a function of the top quark mass in proton-antiproton reactions at center-of-mass energies of 1.8 and 2.0 TeV, and we discuss estimated uncertainties.Comment: 13 pages, LaTeX, including 6 ps files of figures. Invited paper presented by E. L. Berger at the XIth Topical Workshop on Hadron Collider Physics, Abano Terme, Padova, Italy, May, 199

Non-leading Logarithms in Principal Value Resummation

We apply the method of principal value resummation of large momentum-dependent radiative corrections to the calculation of the Drell Yan cross section. We sum all next-to-leading logarithms and provide numerical results for the resummed exponent and the corresponding hard scattering function.Comment: 22 pages (LaTeX), 5 figures not included; available upon request from [email protected], ANL-HEP-PR-94-25, ITP-SB-94-3

Principal Value Resummation

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 $\alpha_s$, 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 $\Lambda_{QCD}/Q$. 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 $Q^2$.Comment: 28 pages, ITP-SB-93-6

Perturbative Gluon Resummation of the Top Quark Production Cross Section

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 cutoffs and specification of the perturbative regime of applicability. For $p\bar{p}$ collisions at center-of-mass energy $\sqrt{s}=1.8$TeV and a top mass of 175 GeV, we compute $\sigma(t\bar{t})=5.52^{+0.07}_{-0.45}pb$.Comment: PS file, cover page plus 12 pages, plus 4 figure

Threshold Resummation of the Total Cross Section for Heavy Quark Production in Hadronic Collisions

We discuss calculations of the inclusive total cross section for heavy quark production at hadron collider energies within the context of perturbative quantum chromodynamics, including resummation of the effects of initial-state soft gluon radiation to all orders in the strong coupling strength. We resum the universal leading-logarithm contributions, and we restrict our integrations to the region of phase space that is demonstrably perturbative. We include a detailed comparison of the differences between ours and other methods. We provide predictions of the physical cross section as a function of the heavy quark mass in proton-antiproton reactions at center-of-mass energies of 1.8 and 2.0 TeV, and we discuss estimated uncertainties.Comment: 31 pages, RevTeX, 7 figure

Sudakov Factorization and Resummation

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 $\overline{{\rm MS}}$ factorization schemes.Comment: 32 pages, phyzzx.tex macropackage, 1 figur