On the Determination of Small x Shadowing Corrections at HERA

The recent $F_2$ data can be described using the DGLAP evolution equations with an appropriate choice of input distributions and the choice of the starting scale for the $Q^2$ evolution. We demonstrate in this paper that we cannot conclude that there are no significant shadowing corrections at HERA kinematic region using $F_2$ data only. In this paper we calculate the shadowing corrections to the longitudinal structure function $F_L(x,Q^2)$ and to the charm component of the proton structure function $F_2^c(x,Q^2)$ at HERA kinematic region using an eikonal approach. We demonstrate that the shadowing corrections to these observables are very large and that the charm production is strongly modified at small-$x$. Our results agree with the recent few H1 data.