Spectrum of theOg4Scale-Invariant Lipatov Kernel

An infrared scale-invariant approximation to the $O\left(g^4\right)$ Lipatov kernel has been determined by $t$-channel unitarity. The forward kernel responsible for parton evolution is evaluated and its eigenvalue spectrum determined. It can be written as a sum of two terms. The first term is proportional to the square of the $O\left(g^2\right)$ kernel. The second term is a new kinematic form whose spectrum shares many properties of the leading-order kernel. The full kernel gives a reduction $(\sim 68{\alpha }_s^2/{\pi }^2)$ in the power growth of parton distributions at small $x$.