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

J. Albacete; N. Armesto; J. G. Milhano; C. Salgado; U. Wiedemann

Paper

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

Abstract

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

on the nuclear size

and results in an exponential dependence on rapidity

. For the running coupling case, we re-derive analytical estimates for the

- and

-dependences of the saturation scale and test them numerically. The

-dependence of

vanishes

for large

and

. The

-dependence is reduced to

where we find numerically

. We study the behaviour of the gluon distribution at large transverse momentum, characterizing it by an anomalous dimension

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 (

) and running coupling (

) results. Our numerical findings show that both a scaling function depending only on the variable

and the perturbative double-leading-logarithmic expression, provide equally good descriptions of the numerical solutions for very small

-values below the so-called scaling window.