Next-to-eikonal corrections to soft gluon radiation: a diagrammatic approach

We consider the problem of soft gluon resummation for gauge theory amplitudes and cross sections, at next-to-eikonal order, using a Feynman diagram approach. At the amplitude level, we prove exponentiation for the set of factorizable contributions, and construct effective Feynman rules which can be used to compute next-to-eikonal emissions directly in the logarithm of the amplitude, finding agreement with earlier results obtained using path-integral methods. For cross sections, we also consider sub-eikonal corrections to the phase space for multiple soft-gluon emissions, which contribute to next-to-eikonal logarithms. To clarify the discussion, we examine a class of log(1 - x) terms in the Drell-Yan cross-section up to two loops. Our results are the first steps towards a systematic generalization of threshold resummations to next-to-leading power in the threshold expansion.Comment: 66 pages, 19 figure

All-order results for soft and collinear gluons

I briefly review some general features and some recent developments concerning the resummation of long-distance singularities in QCD and in more general non-abelian gauge theories. I emphasize the field-theoretical tools of the trade, and focus mostly on the exponentiation of infrared and collinear divergences in amplitudes, which underlies the resummation of large logarithms in the corresponding cross sections. I then describe some recent results concerning the conformal limit, notably the case of N = 4 superymmetric Yang-Mills theoryComment: 15 pages, invited talk presented at the 10th Workshop in High Energy Physics Phenomenology (WHEPP X), Chennai, India, January 200

A Generic Approach to Searching for Jacobians

We consider the problem of finding cryptographically suitable Jacobians. By applying a probabilistic generic algorithm to compute the zeta functions of low genus curves drawn from an arbitrary family, we can search for Jacobians containing a large subgroup of prime order. For a suitable distribution of curves, the complexity is subexponential in genus 2, and O(N^{1/12}) in genus 3. We give examples of genus 2 and genus 3 hyperelliptic curves over prime fields with group orders over 180 bits in size, improving previous results. Our approach is particularly effective over low-degree extension fields, where in genus 2 we find Jacobians over F_{p^2) and trace zero varieties over F_{p^3} with near-prime orders up to 372 bits in size. For p = 2^{61}-1, the average time to find a group with 244-bit near-prime order is under an hour on a PC.Comment: 22 pages, to appear in Mathematics of Computatio

Instanton effects in quark form factor and quark-quark scattering at high energy

The nonperturbative effects in the high-energy processes involving strongly interacting particles are studied within the instanton liquid model of the QCD vacuum (ILM) by using the Wilson integral framework. The detailed analysis of nonperturbative contributions to the electromagnetic quark form factor is presented considering the structure of the instanton induced effects in the evolution equation describing the high energy behaviour of the form factor. It is shown that the instantons yield in high energy limit the logarithmic corrections to the amplitudes which are exponentiated in small instanton density parameter. By using the Gaussian interpolation of the constrained instanton solution, we show that the all-order multi-instanton contribution is well approximated by the weak field limit result. The role of the instantons in high energy diffractive quark-quark scattering, in particular, in formation of the soft Pomeron, is also considered. We show that within the ILM the C-odd diffractive amplitude is suppressed as 1/s compared to the C-even one. The further applications of the developed approach in studying the nonperturbative effects in high energy hadronic processes are briefly discussed.Comment: 37 pages + 9 figures; JHEP styl

Multiphoton Radiation in Leptonic W-Boson Decays

We present the calculation of multiphoton radiation effects in leptonic W-boson decays in the framework of the Yennie-Frautschi-Suura exclusive exponentiation. This calculation is implemented in the Monte Carlo event generator WINHAC for single W-boson production in hadronic collisions at the parton level. Some numerical results obtained with the help of this program are also presented.Comment: 26 pages, 16 Postscript figure

Resummation of double logarithms in electroweak high energy processes

At future linear $e^+e^-$ collider experiments in the TeV range, Sudakov double logarithms originating from massive boson exchange can lead to significant corrections to the cross sections of the observable processes. These effects are important for the high precision objectives of the Next Linear Collider. We use the infrared evolution equation, based on a gauge invariant dispersive method, to obtain double logarithmic asymptotics of scattering amplitudes and discuss how it can be applied, in the case of broken gauge symmetry, to the Standard Model of electroweak processes. We discuss the double logarithmic effects to both non-radiative processes and to processes accompanied by soft gauge boson emission. In all cases the Sudakov double logarithms are found to exponentiate. We also discuss double logarithmic effects of a non-Sudakov type which appear in Regge-like processes.Comment: 26 pages, 3 figures, Latex2

Two-Fermion Production in Electron-Positron Collisions

This report summarizes the results of the two-fermion working group of the LEP2-MC workshop, held at CERN from 1999 to 2000. Recent developments in the theoretical calculations of the two fermion production process in the electron-positron collision at LEP2 center of the mass energies are reported. The Bhabha process and the production of muon, tau, neutrino and quark pairs is covered. On the basis of comparison of various calculations, theoretical uncertainties are estimated and compared with those needed for the final LEP2 data analysis. The subjects for the further studies are identified.Comment: 2-fermion working group report of the LEP2 Monte Carlo Workshop 1999/2000, 113 pages, 24 figures, 35 table