Systematic Analysis of Scaling Properties in Deep Inelastic Scattering
  Using the ``Quality Factor'' (QF) method, we analyse the scaling properties of deep-inelastic processes at HERA and fixed target experiments for x<0.01. We look for scaling formulae of the form sigma(tau), where tau(log Q^2, Y) is a scaling variable suggested by the asymptotic properties of QCD evolution equations with rapidity Y. We consider four cases: ``Fixed Coupling'', corresponding to the original geometric scaling proposal and motivated by the asymptotic properties of the Balitsky-Kovchegov (BK) equation with fixed QCD coupling constant, two versions ``Running Coupling I,II'' of the scaling suggested by the BK equation with running coupling, and ``Diffusive Scaling'' suggested by the QCD evolution equation with Pomeron loops. The Quality Factors, quantifying the phenomenological validity of the candidate scaling variables, are fitted on the total and DVCS cross-section data from HERA and predictions are made for the elastic vector-meson and for the diffractive cross-sections at fixed small x_pom or beta. The first three scaling formulae have comparably good QF while the fourth one is disfavored. Adjusting initial conditions gives a significant improvement of the ``Running Coupling II'' scaling. 
Guillaume Beuf, Robi Peschanski, Christophe Royon and David Salek