The production of $\phi$ mesons in the reaction $e~{+}p \rightarrow e~{+} \phi p$ ($\phi \rightarrow K~{+}K~{-}$), for $7 < Q~2 < 25$ GeV$~2$ and for virtual photon-proton centre of mass energies ($W$) in the range 42-134 GeV, has been studied with the ZEUS detector at HERA. When compared to lower energy data at similar $Q~2$, the results show that the $\gamma~*p \rightarrow \phid p$ cross section rises strongly with $W$. This behaviour is similar to that previously found for the $\gamma~*p \rightarrow \rho~0 p$ cross section. This strong dependence cannot be explained by production through soft pomeron exchange. It is, however, consistent with perturbative QCD expectations, where it reflects the rise of the gluon momentum density in the proton at small $x$. The ratio of $\sigma (\phi) / \sigma (\rho~0)$, which has previously been determined by ZEUS to be 0.065 $\pm$ 0.013 (stat.) in photoproduction at a mean $W$ of 70 GeV, is measured to be 0.18 $\pm $ 0.05 (stat.) $\pm$ 0.03 (syst.) at a mean $Q~2$ of 12.3 GeV$~2$ and mean $W$ of $\approx$ 100 GeV and is thus approaching at large $Q~2$ the value of 2/9 predicted from the quark charges of the vector mesons and a flavour independent production mechanism.
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Additional 32 PCT Systematic error.
Additional 32 PCT Systematic error.
Diffractive scattering of $\gamma~* p \to X + N$, where $N$ is either a proton or a nucleonic system with $M_N<4$GeV has been measured in deep inelastic scattering (DIS) at HERA. The cross section was determined by a novel method as a function of the $\gamma~* p$ c.m. energy $W$ between 60 and 245GeV and of the mass $M_X$ of the system $X$ up to 15GeV at average $Q~2$ values of 14 and 31GeV$~2$. The diffractive cross section $d\sigma~{diff} /dM_X$ is, within errors, found to rise linearly with $W$. Parameterizing the $W$ dependence by the form $d\sigma~{diff}/dM_X \propto (W~2)~{(2\overline{\mbox{$\alpha_{_{I\hspace{-0.2em}P}}$}} -2)}$ the DIS data yield for the pomeron trajectory $\overline{\mbox{$\alpha_{_{I\hspace{-0.2em}P}}$}} = 1.23 \pm 0.02(stat) \pm 0.04 (syst)$ averaged over $t$ in the measured kinematic range assuming the longitudinal photon contribution to be zero. This value for the pomeron trajectory is substantially larger than $\overline{\mbox{$\alpha_{_{I\hspace{-0.2em}P}}$}}$ extracted from soft interactions. The value of $\overline{\mbox{$\alpha_{_{I\hspace{-0.2em}P}}$}}$ measured in this analysis suggests that a substantial part of the diffractive DIS cross section originates from processes which can be described by perturbative QCD. From the measured diffractive cross sections the diffractive structure function of the proton $F~{D(3)}_2(\beta,Q~2, \mbox{$x_{_{I\hspace{-0.2em}P}}$})$ has been determined, where $\beta$ is the momentum fraction of the struck quark in the pomeron. The form $F~{D(3)}_2 = constant \cdot (1/ \mbox{$x_{_{I\hspace{-0.2em}P}}$})~a$ gives a good fit to the data in all $\beta$ and $Q~2$ intervals with $a = 1.46 \pm 0.04 (stat) \pm
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