Elastic electroproduction of $$\rho$$ mesons at HERA

Abstract. The elastic electroproduction of $$\rho$$ mesons is studied at HERA with the H1 detector for a photon virtuality in the range \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$1 < Q^2 < 60 {\rm GeV^2}$\end{document} and for a hadronic centre of mass energy in the range \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$30 < W < 140$\end{document} GeV. The shape of the ($$\pi \pi$$) mass distribution in the $$\rho$$ resonance region is measured as a function of $$Q^2$$. The full set of $$\rho$$ spin density matrix elements is determined, and evidence is found for a helicity flip amplitude at the level of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$8 \pm 3\%$\end{document} of the non-flip amplitudes. Measurements are presented of the dependence of the cross section on $$Q^2$$, W and t (the four-momentum transfer squared to the proton). They suggest that, especially at large $$Q^2$$, the $$\gamma^*p$$ cross section develops a stronger W dependence than that expected from the behaviour of elastic and total hadron–hadron cross sections.