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

Abstract

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, $F_2\propto x^{-\lambda }$, 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 ${\sigma }_{\gamma p}$ of real photoproduction is obtained for $\lambda =0.37$. With four parameters we achieve a ${\chi }^2/\text{d.o.f.}=0.98$ for 222 data points. In addition, we use our model of the inclusive ${\gamma }^{\ast }p$ interaction to compute the longitudinal structure function $F_L$.

Comments: 18 pages, Latex, 6 PS-figures, Regge-exchange neglected, more details concerning the soft Pomeron included, section on the longitudinal structure function added, all conclusions unchanged, final version to appear in Eur. Phys. J. C