Renormalization group improved small-xequation
We propose and analyze an improved small-$x$ equation which incorporates exact leading and next-to-leading Balitski\ifmmode \breve{\imath}\else \u{\i}\fi{}-Fadin-Kuraev-Lipatov kernels on one hand and renormalization group constraints in the relevant collinear limits on the other. We work out in detail the recently proposed $\ensuremath{\omega}$ expansion of the solution, derive the Green's function factorization properties and discuss both the gluon anomalous dimension and the hard Pomeron. The resummed results are stable, nearly renormalization-scheme independent, and join smoothly with the fixed order perturbative regime. Two critical hard Pomeron exponents ${\ensuremath{\omega}}_{c}{(Q}^{2})$ and ${\ensuremath{\omega}}_{s}{(Q}^{2})$ are provided, which --- for reasonable strong-coupling extrapolations --- are argued to provide bounds on the Pomeron intercept ${\ensuremath{\omega}}_{P}.$