Expanding running coupling effects in the hard Pomeron

We study QCD hard processes at scales of order ${\mathbf{k}}^{2}\ensuremath{\gg}{\ensuremath{\Lambda}}^{2}$ in the limit in which the beta-function coefficient b is taken to be small, but ${\overline{\ensuremath{\alpha}}}_{s}({\mathbf{k}}^{2})$ is kept fixed. The (nonperturbative) Pomeron is exponentially suppressed in this limit, making it possible to define purely perturbative high-energy Green's functions. The hard Pomeron exponent acquires diffusion and running coupling corrections which can be expanded in the b parameter and turn out to be dependent on the effective coupling $b{\overline{\ensuremath{\alpha}}}_{s}^{2}Y,$ where Y is rapidity of the process. We provide a general setup for this b expansion and we calculate the first few terms both analytically and numerically.