Scale Invariant $O(g^4)$ Lipatov Kernels at Non-Zero Momentum Transfer

We summarize recent work on the evaluation of the scale invariant next-to-leading order Lipatov kernel, constructed via transverse momentum diagrams. At zero momentum transfer the square of the leading-order kernel appears together with an additional component, now identified as a new partial-wave amplitude, having a separate, holomorphically factorizable, spectrum. We present a simplified expression for the full kernel at non-zero momentum transfer and give a complete analysis of its infrared properties. We also construct a non-forward extension of the new amplitude which is infra-red finite and satifies Ward identity constraints. We conjecture that this new kernel has the conformal invariance properties corresponding to the holomorphic factorization of the forward spectrum.