principle, corrections to the BFKL answer can be calculated, thus making single scale high energy scattering systematically calculable in QCD.

There has been a long program\[14,45-47\], led by the work of V. Fadin and L. Lipatov, to calculate the next-to-leading corrections to BFKL evolution and it now appears that program may be coming to completion. When the work is finished one should get the next correction to $\alpha_P$ as well as next-to-leading resummations for anomalous dimension and coefficient functions. If one writes

$$\alpha_P = {4 N_c\over \pi} \ell n 2 \alpha(Q)[1-c \alpha(Q)]\eqno(6.1)$$

then there is the suggestion  $c$  may be near 3, a very large correction, although there is some work yet to be done before one can accept this number with confidence\[14\].

For the anomalous dimension matrix one writes

$$\gamma_n = \sum_{i=1}^\infty \gamma_{n i}^{(0)}\left[{\alpha N_c\over
\pi(n-1)}\right]^i + \alpha \sum_{i=1}^\infty \gamma_{n i}^{(1)}\left[{\alpha
N_c\over \pi(n-1)}\right]^i + \cdot \cdot \cdot\eqno(6.2)$$

where the first series represents the leading order (BFKL) answer. We should soon know the second series, the constants $\gamma_{n i}^{(1)}$ along with similar terms for the coefficient functions. When the BFKL corrections are known at next-to-leading order we should reap several benefits. (i) A better understanding of the importance of BFKL 