Measurement of the spin-density matrix elements in exclusive electroproduction of $\rho^0$ mesons at HERA

Exclusive electroproduction of \(\rho^0\) mesons has been measured using the ZEUS detector at HERA in two \(Q^2\) ranges, \(0.25 < Q^2 < 0.85\) GeV\(^2\) and \(3< Q^2 < 30\) GeV\(^2\). The low-\(Q^2\) data span the range \(20 < W < 90\) GeV; the high-\(Q^2\) data cover the \(40 < W < 120\) GeV interval. Both samples extend up to four-momentum transfers of \(|t|=0.6\) GeV\(^2\). The distribution in the azimuthal angle between the positron scattering plane and the \(\rho^0\) production plane shows a small but significant violation of s-channel helicity conservation, corresponding to the production of longitudinally polarised (i.e. helicity zero) \(\rho^0\) mesons from transverse photons. Measurements of the 15 combinations of spin-density matrix elements which completely define the angular distributions are presented and discussed.