EVOLUTION PATHS FOR SMALL-X STRUCTURE FUNCTIONS

We compare the solutions of the "one-loop" (summing alpha-S(n) ln(n) Q2) and "all-loop" (including also alpha-S(n) ln(n) x) evolution equations for small-x structure functions. In the semi-classical approximation one can define evolution paths in the (ln x, ln Q2)-plane, which are helpful in understanding many, features of the solutions. We compute the asymptotic form of the mean path and the dispersion of paths for both the one-loop and all-loop cases, and compare the results with those of Monte Carlo simulations. We also use the Monte Carlo simulations to study the infrared stability of small-x evolution. Our results explain why the one-loop and all-loop solutions are similar, over a wide range of x and Q2, especially when the input structure function at low Q2 is a rapidly increasing function of 1/x.