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{\large\bf\boldmath Proton dissociative and elastic electroproduction of 
$\rho$ mesons at HERA.
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{H1 Collaboration}\\                            
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{\small \em DESY, Hamburg, Germany}\\[6mm]
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The proton dissociative and elastic production of $\rho$ mesons is studied
with the H1 detector at HERA for a photon virtuality in the range $1 <
Q^2 < 60 {\rm\ GeV}^2$ and for a hadronic centre of mass energy in the
range $20 < W < 150 {\rm\ GeV}$.
The shape of the ($\pi\pi$) mass distribution in the $\rho$ resonance
region is measured as a function of $Q^2$.
The cross section is presented as a function of $Q^2$, $W$ and $t$ (the
four-momentum transfer squared to the proton) and the parameters of the
pomeron trajectory are extracted. Especially at large $Q^2$, the
$\gamma^\ast p$ cross section develops a stronger $W$ dependence than
expected from the behaviour of elastic and total hadron-hadron cross
sections.  Shrinkage of the diffractive peak is observed for $Q^2$ above a
few ${\rm GeV}^2$. An increase of the ratio of proton dissociative to
elastic cross sections is observed in the region of $Q^2 < 3 {\rm\
GeV}^2$.
Angular distributions are studied as a function of $t$ and $Q^2$ and the
full set of $\rho$ spin density matrix elements is determined. Evidence is
found for a helicity flip amplitude at the level of $8 \pm 3\%$ of the
non-flip amplitudes indicating a significant deviation from the prediction
of $s$-channel helicity conservation.

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