On the origin of the rise of $F_2$ at small $x$

Abstract

We show that, provided that the non-perturbative input is regular at the right of the $\omega =0$ singularity of the dominant DGLAP anomalous dimension, the rise of $F_2$ at small $x,$ experimentally measured by the averaged observable $\lambda =<(\partial ln{F}_2)/(\partial ln1/x)>,$ is input-independent in the perturbative $Q^2$ regime at small $x$. $(\partial lnxF)/(\partial ln{Q}^2)$ appears to be more input-dependent in the same range. The GRV-type parametrisations verify these properties. Other models, namely the BFKL kernel(QCD dipoles), DGLAP(hard pomeron singularity) give different predictions for $\lambda$. At moderate $Q^2,$ there is a possibility of distinguishing these different perturbative QCD predictions in the near future.

Comments: 14 pages, latex +eps. files, 3 figures