1999/02/22 by Rim Dib, Justin Khoury, C. S. Lam
Physics and Astronomy · #Amplitude #Eikonal equation #Feynman diagram #Formalism (music) #HERA #High-Energy Particle Collisions Research #Mathematical physics #Particle physics #Particle physics theoretical and experimental studies #Parton #Physics #Pomeron #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Quantum mechanics #Resummation #Scattering #Scattering amplitude #hep-ph
paper · pdf · doi:10.1103/physrevd.60.036001
published as Phys.Rev.D60:036001,1999 · 41 pages in revtex preprint format, with 10 figures
arxiv created 1999/02/22 · openalex publication_date 1999/07/01 · arxiv updated 2014/11/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The problem of restoring the Froissart bound to the Balitski\ifmmode \checki\else \vi\fi-Fad'\in-Kuraev-Lipatov (BFKL) 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 energy-growth exponent on virtuality Q2 for \ensuremathγ*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.