$t$-Channel Unitarity Construction of Small-x Kernels

We present the BFKL equation as a reggeon Bethe-Salpeter equation and discuss the use of reggeon diagrams to obtain 2-2 and 2-4 reggeon interactions at $O(g^4)$. We then outline the dispersion theory basis of multiparticle $j$-plane analysis and describe how a gauge theory can be studied by combining Ward identity constraints with the group structure of reggeon interactions. The derivation of gluon reggeization, the $O(g^2)$ BFKL kernel, and $O(g^4)$ corrections, is described within this formalism. We give an explicit expression for the $O(g^4)$ forward ``parton'' kernel in terms of logarithms and evaluate the eigenvalues. A separately infra-red finite component with a holomorphically factorizable spectrum is shown to be present and conjectured to be a new leading-order partial-wave amplitude. A comparison is made with Kirschner's discussion of $O(g^4)$ contributions from the multi-Regge effective action.

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