Gauge Theory High-Energy Behavior from J-Plane Unitarity

Abstract

In a non-abelian gauge theory the $t$-channel multiparticle unitarity equations continued in the complex j-plane can be systematically expanded around $j=1$. The combination of Ward identity constraints with unitarity is sufficient to produce directly many results obtained by Regge limit leading-log and next-to-leading log momentum space calculations. The $O(g^2)$ BFKL kernel is completely determined. $O(g^4)$ contributions to the kernel are also determined, including the leading contribution of a new partial-wave amplitude - previously identified as a separate forward component with a holomorphically factorizable spectrum. For this amplitude the only scale ambiguity is the overall normalization and it is anticipated to be a new conformally invariant kernel. The results suggest that all conformally invariant reggeon interactions are determined by $t$-channel unitarity.