Spin density matrix elements in exclusive $$\rho ^0$$ ρ 0 meson muoproduction

We report on a measurement of Spin Density Matrix Elements (SDMEs) in hard exclusive $$\rho ^0$$ ρ 0 meson muoproduction at COMPASS using 160 GeV/ c polarised $$ \mu ^{+}$$ μ + and $$ \mu ^{-}$$ μ - beams impinging on a liquid hydrogen target. The measurement covers the kinematic range 5.0 GeV/ $$c^2$$ c 2 $$< W<$$ < W < 17.0 GeV/ $$c^2$$ c 2 , 1.0 (GeV/ c ) $$^2$$ 2 $$< Q^2<$$ < Q 2 < 10.0 (GeV/ c ) $$^2$$ 2 and 0.01 (GeV/ c ) $$^2$$ 2 $$< p_{\textrm{T}}^2<$$ < p T 2 < 0.5 (GeV/ c ) $$^2$$ 2 . Here, W denotes the mass of the final hadronic system, $$Q^2$$ Q 2 the virtuality of the exchanged photon, and $$p_{\textrm{T}}$$ p T the transverse momentum of the $$\rho ^0$$ ρ 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 ( $$\gamma ^*_T \rightarrow V^{ }_L$$ γ T ∗ → 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 $$\rho ^0$$ ρ 0 production.