Unitarized Diffractive Scattering in QCD and Application to Virtual Photon Total Cross Sections

TL;DR

This paper develops a unitarized QCD framework for diffractive scattering that restores the Froissart bound, using nonabelian cut diagrams to efficiently include subleading contributions, and applies it to virtual photon cross sections at HERA.

Contribution

It introduces a novel method using nonabelian cut diagrams to incorporate subleading logs in QCD scattering amplitudes, ensuring unitarity and Froissart bound compliance.

Findings

Phase shifts up to three loops calculated.

Energy-growth exponent for virtual photon cross section shows slowdown.

Formalism explains energy dependence observed at HERA.

Abstract

The problem of restoring Froissart bound to the BFKL-Pomeron is studied in an extended leading-log approximation of QCD. We consider 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 nonabelian cut diagrams introduced elsewhere. They can be considered as colour filters used to isolate the multi-Reggeon contributions that supply these subleading-log terms. 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 energy-growth exponent on virtuality $Q^2$ for $\gamma^*P$ total cross section observed at 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.