Elastic electroproduction of $\rho^0$ and $J/\psi$ mesons at large Q$^2$ at HERA

The total cross sections for the elastic electroproduction of $\rh0$ and $J/\Psi$ mesons for $Q~2$ $>$ 8 GeV$~2$ and $\langle W \rangle \simeq 90$ GeV/c$~2$ are measured at HERA with the H1 detector. The measurements are for an integrated electron$-$proton luminosity of $\simeq$3pb$~{-1}$. The dependences of the total virtual photon$-$proton ($\gamma~* p$) cross sections on $Q~2$, $W$ and the momentum transfer squared to the proton ($t$), and, for the $\rho$, the dependence on the polar decay angle ($\cos \theta~*$), are presented. The $J/\Psi$ : $\rh0$ cross section ratio is determined. The results are discussed in the light of theoretical models and of the interplay of hard and soft physics processes.