Asymptotic behaviour of the scattering amplitude at high energies

doi:10.1016/0029-5582(61)90457-6

Nuclear Physics

Volume 22, Issue 2, January 1961, Pages 249-261

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Abstract

The asymptotic behaviour of the scattering amplitude is investigated at high energies. It is shown that at high energies the usual diffraction picture of scattering contradicts the unitarity conditions and analytic properties of the scattering amplitude formulated with the help of Mandelstam's representations. In terms of these conditions it is natural to expect that the cross section should decrease faster than 1/ln E.

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The interaction of spatially small dipoles with nucleons, nuclei is calculated in the DGLAP approximation at the top of HERA energies and found to be close to the S-channel unitarity limit in the case of the color octet dipoles. The DGLAP analyses of the current diffractive data appear to support this conclusion as they indicate a ∼ 30 – 40% probability of the gluon induced diffraction for Q² ∼ 4 GeV². The need for the high-precision measurements of the t-dependence of inclusive and exclusive diffraction for pinpointing higher twist effects in the gluon sector is emphasized. The eA collisions at HERA would provide a strong amplification of the gluon densities allowing to reach deep into the regime of nonlinear QCD evolution. Connection between the leading twist nuclear shadowing and leading twist diffraction in ep scattering is explained. The presented model independent results for the nuclear shadowing for light nuclei indicate much larger shadowing for the gluon sector than for the sea quark sector. It is argued that HERA in eA mode would be able to discover a number of new phenomena including large gluon shadowing, large nonlinearities in parton evolution, small x color transparency in the vector meson production followed by color opacity at x ≤ .005, large probability of inclusive diffraction. Implications for the nucleus-nucleus collisions at LHC are discussed as well.
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The small shrinkage of the diffraction peak is used for studying the pomeron structure in the intermediate non-asymptotic energy region. Even in this region the cross sections are shown to be factorized and basically determined by a pole and by enhanced cuts. The total cross sections rise as (ln ln E)² and the interaction radius as ln ln E. The general character of inelastic processes is the same as in the strong coupling theory for the asymptotic region.
Regge behaviour in an asymptotically free field theory
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We consider the high energy behaviour at fixed momentum transfer of ϕ³ theory in six dimensional space-time, as the simplest example of an exactly renormalisable asymptotically free theory. We find that the damping in transverse momentum of the full theory is sufficiently strong to give rise to moving Regge pole singularities, in contrast to a fixed-point theory which would naturally lead to a fixed square-root branch point.
Self-consistent diffraction in the multiperipheral model (III)
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Asymptotic behaviour of the scattering amplitude at high energies

Abstract

Nuovo Cim.

Phys. Rev.

Progr. of Theor. Phys.