Geometric scaling and QCD evolution

Abstract

We study the impact of the QCD DGLAP evolution on the geometric scaling of the gluon distributions which is expected to hold at small x within the saturation models. To this aim we solve the DGLAP evolution equations with the initial conditions provided along the critical line Q^2=Q_s^2(x) where Q_s^2(x) = Q_0^2 x^{-λ}and satisfying geometric scaling. Both fixed and running coupling cases are studied. We show that in the fixed coupling case the geometric scaling at low x is stable against the DGLAP evolution for sufficiently large values of the parameter λand in the double logarithmic approximation of the DGLAP evolution this happens for λ> 4N_cα_s/π. In the running coupling case geometric scaling is found to be approximately preserved at very small x. The residual geometric scaling violation in this case can be approximately factored out and the corresponding form-factor controlling this violation is found.

23 pages, 8 figures, new figures with illustration of the geometric scaling, additional references added

References in corpus (10)

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• Saturation and Universality in QCD at small x
• Effective field theory for the small-x evolution
• Diffusion into infra-red and unitarization of the BFKL pomeron
• Parton densities and dipole cross-sections at small x in large nuclei
• Impact parameter dependent S-matrix for dipole-proton scattering from diffractive meson electroproduction
• Nuclear Structure Functions and Heavy Flavour Leptoproduction Off the Nucleus at Small x in Perturbative QCD
• Scaling phenomena from non-linear evolution in high energy DIS
• Parton densities and saturation scale from non-linear evolution in DIS on nuclei
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• Ultrahigh energy neutrinos and non-linear QCD dynamics
• Rapidity dependence of particle production in ultrarelativistic nuclear collisions
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• Saturation in inclusive production beyond leading logarithm accuracy
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• Nonlinear correction to the longitudinal structure function at small x
• Geometric Scaling and QCD Dynamics in DIS
• Physics of ultrahigh energy neutrinos
• Quantitative Study of Geometrical Scaling in Charm Production at HERA
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