3,524 research outputs found
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 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
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