Unitarized diffractive scattering in QCD and its application to virtual photon total cross sections

Abstract

The problem of restoring the Froissart bound to the Balitskiǐ-Fadín-Kuraev-Lipatov ͑BFKL͒ Pomeron is studied in an extended leading-log approximation of QCD. We consider the parton-parton scattering amplitude and show that the sum of all Feynman-diagram contributions can be written in an eikonal form. In this form, dynamics is determined by the phase shift, and subleading-logs of all orders needed to restore the Froissart bound are automatically provided. The main technical difficulty is to find a way to extract these subleading contributions without having to compute each Feynman diagram beyond the leading order. We solve that problem by using non-Abelian cut diagrams introduced elsewhere. They can be considered as color filters used to isolate the multi-Reggeon contributions that supply these subleading-log terms. An illustration of the formalism is given for amplitudes and phase shifts up to three loops. For diffractive scattering, only phase shifts governed by one and two Reggeon exchanges are needed. They can be computed from the leading-log-Reggeon and the BFKL Pomeron amplitudes. In applications, we argue that the dependence of the energygrowth exponent on virtuality Q 2 for ␥*P total cross section observed at DESY HERA can be interpreted as the first sign of a slowdown of energy growth towards satisfying the Froissart bound. An attempt to understand these exponents with the present formalism is discussed. ͓S0556-2821͑99͒06513-3͔

High-energy forward scattering and the Pomeron: Simple pole versus unitarized models

“…The other school of thought starts from perturbative QCD, and assumes that unitarization changes the fierce rise observed at large Q 2 to something compatible with the Froissart bound. This approach suffers from the fact that, despite recent progress [4], no one has reliably unitarized a QCD cross section. However, it is clear that such a unitarization will involve the exchange of a very large number of gluons between the quarks.…”

Erratum: High-energy forward scattering and the Pomeron: Simple pole versus unitarized models [Phys. Rev. D61, 034019 (2000)]

“…This approach suffers from the fact that, despite recent progress [4], no one has reliably unitarized a QCD cross section. However, it is clear that such a unitarization will involve the exchange of a very large number of gluons between the quarks.…”

Coherent states in high-energy physics

“…The dash line gives a s 0.5 variation predicted by the leading-log BFKL Pomeron, and the solid line is the prediction of the unitary theory in Ref. [6].…”

“…The dotted line represents a dependence of s 0.08 obeyed by all hadronic total cross sections. The dash line gives a s 0.5 variation predicted by the leading-log BFKL Pomeron, and the solid line is the prediction of the unitary theory in Ref [6]…”