Spin density matrix elements in exclusive $\rho ^0$ meson muoproduction
We report on a measurement of Spin Density Matrix Elements (SDMEs) in hard exclusive $\rho ^0$ meson muoproduction at COMPASS using 160 GeV/c polarised μ + and μ – beams impinging on a liquid hydrogen target. The measurement covers the kinematic range 5.0 GeV/c 2 < W < 17.0 GeV/c 2 , 1.0 (GeV/c) 2 < $\mathrm{Q}$ 2 < 10.0 (GeV/c) 2 and 0.01 (GeV/c) 2 < $p_{\textrm{T}}^2$ < 0.5 (GeV/c) 2 . Here, W denotes the mass of the final hadronic system, $\mathrm{Q}$ 2 the virtuality of the exchanged photon, and $p_{\textrm{T}}$ the transverse momentum of the $\rho ^0$ meson with respect to the virtual-photon direction. The measured non-zero SDMEs for the transitions of transversely polarised virtual photons to longitudinally polarised vector mesons ($\gamma ^*_T \rightarrow V^{ }_L$) indicate a violation of s-channel helicity conservation. Additionally, we observe a dominant contribution of natural-parity-exchange transitions and a very small contribution of unnatural-parity-exchange transitions, which is compatible with zero within experimental uncertainties. The results provide important input for modelling Generalised Parton Distributions (GPDs). In particular, they may allow one to evaluate in a model-dependent way the role of parton helicity-flip GPDs in exclusive $\rho ^0$ production.