Abstract
We review the Sudakov results on the double logarithmic asymptotics of the electron form-factor which were based on his parametrization of the virtual particle momenta in the Feynman diagrams. The high energy amplitudes for various QED and QCD processes in the double-logarithmic approximation are obtained by using the Bethe-Salpeter approach and the evolution equations. The ultraviolet divergency of the graviton Regge trajectory allows to derive the infrared evolution equation for the graviton-graviton scattering amplitude with a double-logarithmic accuracy. The asymptotic behavior of this amplitude depends essentially on the rank N of the super-symmetry.
Highlights
We review the Sudakov results on the double logarithmic asymptotics of the electron form-factor which were based on his parametrization of the virtual particle momenta in the Feynman diagrams
√ The investigation of scattering amplitudes at high energies s in QED was initiated by Vladimir Vasil’evich Sudakov 60 years ago in his paper [1], devoted to the asymptotic behavior of the vertex function in the double logarithmic approximation (DLA) valid in the region α ln2 s me
A simple approach for the derivation of scattering amplitudes in QED and QCD at DLA was suggested in the paper [6]
Summary
√ The investigation of scattering amplitudes at high energies s in QED was initiated by Vladimir Vasil’evich Sudakov 60 years ago in his paper [1], devoted to the asymptotic behavior of the vertex function in the double logarithmic approximation (DLA) valid in the region α ln s me. Sudakov considered the case of the high energy scattering of the virtual electron off a charged center. In the case of the real electron there are infrared divergencies which can be removed by the introduction of the photon mass λ. These divergencies are canceled in the inclusive cross-section for the inelastic scattering with the emission of an arbitrary number of photons [2]. But one should take into account the energy conservation for the total frequency ω of the emitted photons It turns out, that the QED radiative corrections to the production of narrow resonances aprreodlaurcgtieo.nFionrthexeaem+ep−lec,otlhleisidoonusbalet -√losga−riMthZm≪ic result for the cross-section MZ has the form (cf [3]). That σe+e−→Z+photons does not depend on λ and behaves as ∼ 1/(W − MZ) above the resonance
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