Numerical analysis of the Balitsky-Kovchegov equation with running coupling: Dependence of the saturation scale on nuclear size and rapidity

We study the effects of including a running coupling constant in high-density QCD evolution. For fixed coupling constant, QCD evolution preserves the initial dependence of the saturation momentum Q(s) on the nuclear size A and results in an exponential dependence on rapidity Y, Q(s)(2)(Y)=Q(s)(2)(Y-0)exp[(alpha) over bar (s)d(Y-Y-0)]. For the running coupling case, we rederive analytical estimates for the A and Y dependences of the saturation scale and test them numerically. The A dependence of Q(s) vanishes proportional to1/rootY for large A and Y. The Y dependence is reduced to Q(s)(2)(Y)proportional toexp(Delta'rootY+X), where we find numerically Delta'similar or equal to3.2. We study the behavior of the gluon distribution at large transverse momentum, characterizing it by an anomalous dimension 1-gamma, which we define in a fixed region of small dipole sizes. In contrast to previous analytical work, we find a marked difference between the fixed coupling (gammasimilar or equal to0.65) and running coupling (gammasimilar to0.85) results. Our numerical findings show that both a scaling function depending only on the variable rQ(s) and the perturbative double-leading-logarithmic expression provide equally good descriptions of the numerical solutions for very small r values below the so-called scaling window.