Resummation of non-global QCD observables

We discuss issues related to the resummation of non-global observables in QCD, those that are sensitive to radiation in only a part of phase space. Examples of such observables are certain single-hemisphere event shapes in e+e- and DIS. Compared to global observables (those sensitive to all emissions, e.g. the e+e- thrust) a new class of single-logarithmic terms arises. These have been neglected in recent calculations in the literature. For a whole set of single hemisphere e+e- and DIS event shapes, we analytically evaluate the first such term, at order alpha_s^2, and give numerical results for the resummation of these terms in the large-Nc limit.Comment: 10 page

Momentum Conservation at Small x

We discuss how momentum conservation is implemented in perturbative computations based on expansions of anomalous dimensions appropriate at small $x$. We show that for any given choice of $F_2$ coefficient functions there always exists a factorization scheme where the gluon is defined in such a way that momentum is conserved at next to leading order.Comment: 11 pages, plain TeX with harvma

Multijet rates in e+e- annihilation: perturbation theory versus LEP data

We show that the next-to-leading order perturbative prediction, matched with the next-to-leading logarithmic approximation for predicting both two-, three- and four-jet rates using the Durham jet-clustering algorithm, in the 0.001 < ycut < 0.1 range gives a very accurate description of the data obtained at the Large Electron Positron collider. This information can be utilized either for simultaneous measurement of the strong coupling and the QCD colour charges, or for improving the QCD background prediction in new particle searches at LEP2.Comment: 6 pages, 3 figures, 1 table, LaTeX with twoside,fleqn,espcrc2,epsf styles, Contribution to "QCD98 Euroconference", Montpellier, July 2-8, 1998 duplicate reference eliminated, typos in text corrected, important reference adde

Next-to-next-to-leading logarithmic threshold resummation for deep-inelastic scattering and the Drell-Yan process

The soft-gluon resummation exponents G^N in moment space are investigated for the quark coefficient functions in deep-inelastic structure functions and the quark-antiquark contribution to the Drell-Yan cross section dsigma/dM. Employing results from two- and three-loop calculations we obtain the next-to-next-to-leading logarithmic terms alpha_s (alpha_s ln N)^n of G^N to all orders in the strong coupling constant alpha_s. These new contributions facilitate a reliable assessment of the numerical effect and the stability of the large-N expansion.Comment: 9 pages, LaTeX, 2 eps-figure

Direct Estimation of Sizes of Higher-Order Graphs

With the aid of simple examples we show how to make simple estimates of the sizes of higher-order Feynman graphs. Our methods enable appropriate values of renormalization and factorization scales to be made. They allow the diagnosis of the source of unusually large corrections that are in need of resummation.Comment: 22 pages Revtex with epsf, postscript figures. Replacement is due to author error. Version is same as origina

QCD Calculations by Numerical Integration

Calculations of observables in Quantum Chromodynamics are typically performed using a method that combines numerical integrations over the momenta of final state particles with analytical integrations over the momenta of virtual particles. I discuss a method for performing all of the integrations numerically.Comment: 9 pages including 2 figures. RevTe

Electroweak double logarithms in inclusive observables for a generic initial state

High energy observables are characterized by large electroweak radiative corrections of infrared origin; double logarithms are present even for inclusive cross sections, thus violating the Bloch Nordsieck theorem. This effect, related to the initial states carrying nonabelian isospin charges, is here investigated for {\sl any} inclusive cross section in the SU(2)$\otimes$U(1) symmetric limit, that is appropriate for energies much higher than the weak scale. We develop a general formalism allowing to calculate the all order double log resummed cross sections once the hard (tree level) ones are known. The relevant cases of fermion-fermion, fermion-boson and boson-boson scattering are discussed.Comment: 6 pages, 2 figure

Resummed jet rates for e+e−e^+e^- annihilation into massive quarks

Expressions for Sudakov form factors for heavy quarks are presented. They are used to construct resummed jet rates for up to four jets in $e^+e^-$ annihilation. The coefficients of leading and next-to-leading logarithmic corrections, mandatory for a combination with higher order matrix elements, are evaluated up to second order in $\alpha_s$.Comment: 7 pages, 4 figures, revtex. Text improved, references added. Final version to appear in Phys. Lett.