The Spectrum of the O(g^4) scale-invariant Lipatov Kernel

Abstract

The scale-invariant $O(g^4)$ Lipatov kernel has been determined by t-channel unitarity. The forward kernel responsible for parton evolution is evaluated and its eigenvalue spectrum determined. In addition to a logarithmic modification of the $O(g^2)$ kernel a distinct new kinematic component appears. This component is infra-red finite without regularization and has the holomorphic factorization property necessary for conformal invariance. It gives a reduction (of ~$\sim 65\alpha_s^2/\pi^2\sim 0.15$) in the power growth of parton distributions at small-x.