Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2010-08-03
Physics
High Energy Physics
High Energy Physics - Phenomenology
11 pages, 2 figures
Scientific paper
The universal traveling wave solution to the Balitsky-Kovchegov equation with running coupling (and other equations in the same universality class) is extended to subleading orders at large rapidity and small dipole size $r$. The large rapidity expansion of the logarithm of the saturation scale $Q_s(Y)$ is derived from that traveling wave solution. In addition to the two already known leading terms in $Y^{1/2}$ and $Y^{1/6}$, which are determined only by the LL BFKL kernel, the three following terms in $Y^0$, $Y^{-1/6}$ and $Y^{-1/3}$ are obtained. They are universal and sensitive to NLL BFKL effects. Initial condition dependence and NNLL BFKL effects would both start to appear only at the next order, which is in $Y^{-1/2}$. In the light of these results, the impact of the precise implementation of the running coupling in gluon saturation is discussed, \emph{i.e.} parent dipole size prescription \emph{vs.} Balitsky's prescription, and also the effect of the full NLL corrections, not yet implemented in numerical simulations.
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