We report on a measurement of Spin Density Matrix Elements (SDMEs) in hard exclusive $$\omega $$ ω meson muoproduction on the proton at COMPASS using 160 GeV/c polarised $$ \mu ^{+}$$ μ + and $$ \mu ^{-}$$ μ - beams impinging on a liquid hydrogen target. The measurement covers the range 5.0 GeV/$$c^2$$ c 2 $$< W<$$ < W < 17.0 GeV/$$c^2$$ c 2 , with the average kinematics $$\langle Q^{2} \rangle =$$ ⟨ Q 2 ⟩ = 2.1 (GeV/c)$$^2$$ 2 , $$\langle W \rangle = 7.6$$ ⟨ W ⟩ = 7.6  GeV/$$c^2$$ c 2 , and $$\langle p^{2}_{\mathrm{T}} \rangle = 0.16$$ ⟨ p T 2 ⟩ = 0.16  (GeV/c)$$^2$$ 2 . Here, $$Q^2$$ Q 2 denotes the virtuality of the exchanged photon, W the mass of the final hadronic system and $$p_T$$ p T the transverse momentum of the $$\omega $$ ω 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 sizeable contribution of unnatural-parity-exchange (UPE) transitions that decreases with increasing W. The results provide important input for modelling Generalised Parton Distributions (GPDs). In particular, they may allow to evaluate in a model-dependent way the contribution of UPE transitions and assess the role of parton helicity-flip GPDs in exclusive $$\omega $$ ω production.

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