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Soft and Hard Pomeron in the Structure Function of the Proton at Low x and Low Q^2

We study inclusive electroproduction on the proton at low $x$ and low $Q^2$ using a soft and a hard Pomeron. The contribution of the soft Pomeron is based on the Stochastic Vacuum Model, in which a nonperturbative dipole-dipole cross section can be calculated by means of a gauge invariant gluon field strength correlator. To model the hard Pomeron exchange we phenomenologically extend the leading order evolution of a power-behaved structure function, $F_2 \propto x^{- λ}$, proposed by López and Ynduráin. This extension allows to consider both the case $Q^2 = 0$ and the region of higher $Q^2$ on the basis of the same parametrization. A good simultaneous fit to the data on $F_2$ and on the cross section $σ_{γp}$ of real photoproduction is obtained for $λ=0.37$. With four parameters we achieve a $χ^2/\textrm{d.o.f.} = 0.98$ for 222 data points. In addition, we use our model of the inclusive $γ^{\ast} p$ interaction to compute the longitudinal structure function $F_L$.