Analytic Multi - Regge Theory and the Pomeron in Qcd : Ii . Gauge Theory

The high-energy Regge behavior of gauge theories is studied via the formalism of Analytic Multi-Regge Theory. Perturbative results for spontaneously-broken theories are first organised into reggeon diagrams. Unbroken gauge theories are studied via a reggeon diagram infra-red analysis of symmetry restoration. Massless fermions play a crucial role and the case of QCD involves the Super-Critical Pomeron as an essential intermediate stage. An introductory review of the build up of transverse momentum diagrams and reggeon diagrams from leading log calculations in gauge theories is presented first. It is then shown that the results closely reproduce the general structure for multi-regge amplitudes derived in Part I of the article, allowing the construction of general reggeon diagrams for spontaneously-broken theories. Next it is argued that, with a transverse-momentum cutoff , unbroken gauge theories can be reached through an infra-red limiting process which successively decouples fundamental representation Higgs fields. The first infra-red limit studied is the restoration of SU (2) gauge symmetry. The analysis is dominated by the exponentiation of divergences imposed by Reggeon Uni-tarity and the contribution of massless quarks to reggeon interactions. Massless quarks also produce " triangle anomaly " transverse-momentum divergences which do not expo-nentiate but instead are absorbed into a reggeon condensate-which can be viewed as a " generalised winding-number condensate ". The result is a reggeon spectrum consistent with confinement and chiral symmetry breaking, but there is no Pomeron. The analysis is valid when the gauge coupling does not grow in the infra-red region, that is when a sufficient number of massless quarks is present. An analogy is drawn between the confinement produced by the reggeon condensate and that produced by regularisation of the fermion sea, in the presence of the anomaly, in the two-dimensional Schwinger model. When the analysis is extended to the case of QCD with the gauge symmetry restored to SU (2), the Reggeon condensate can be identified with the Pomeron conden-sate of Super-Critical Pomeron theory. In this case, the condensate converts an SU (2) singlet reggeised gluon to a Pomeron Regge pole-which becomes an SU (3) singlet when the full gauge symmetry is restored. The condensate disappears as SU (3) symmetry is recovered and, in general this limit gives the Critical Pomeron at a particular value of the transverse cutoff. If the maximal number of fermions consistent with asymptotic freedom is present no transverse momentum cutoff is required. For SU (N) gauge theory it is …