Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2004-08-19
Phys.Rev. D71 (2005) 014003
Physics
High Energy Physics
High Energy Physics - Phenomenology
LaTeX, 29 pages, 7 eps figures; discussion on DLL enlarged and comparison with sub-leading terms in the rapidity behaviour of
Scientific paper
10.1103/PhysRevD.71.014003
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 $Y$, $Q^2_s(Y) = Q^2_s(Y_0) \exp{[ \bar\alpha_s d (Y-Y_0) ]}$. For the running coupling case, we re-derive analytical estimates for the $A$- and $Y$-dependences of the saturation scale and test them numerically. The $A$-dependence of $Q_s$ vanishes $\propto 1/ \sqrt{Y}$ for large $A$ and $Y$. The $Y$-dependence is reduced to $Q_s^2(Y) \propto \exp{(\Delta^\prime\sqrt{Y+X})}$ where we find numerically $\Delta^\prime\simeq 3.2$. We study the behaviour 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 ($\gamma \simeq 0.65$) and running coupling ($\gamma \sim 0.85$) results. Our numerical findings show that both a scaling function depending only on the variable $r Q_s$ 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.
Albacete Javier L.
Armesto Nestor
Milhano Jose Guilherme
Salgado Carlos A.
Wiedemann Urs Achim
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