Spin density matrix elements in exclusive $$\omega $$ ω meson muoproduction

We report on a measurement of Spin Density Matrix Elements (SDMEs) in hard exclusive $$\omega $$ meson muoproduction on the proton at COMPASS using 160 GeV/c polarised $$ \mu ^{+}$$ and $$ \mu ^{-}$$ beams impinging on a liquid hydrogen target. The measurement covers the range 5.0 GeV/ $$c^2$$ $$< W<$$ 17.0 GeV/ $$c^2$$ , with the average kinematics $$\langle Q^{2} \rangle =$$ 2.1 (GeV/c) $$^2$$ , $$\langle W \rangle = 7.6$$  GeV/ $$c^2$$ , and $$\langle p^{2}_{\mathrm{T}} \rangle = 0.16$$  (GeV/c) $$^2$$ . Here, $$Q^2$$ denotes the virtuality of the exchanged photon, W the mass of the final hadronic system and $$p_T$$ the transverse momentum of the $$\omega $$ 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 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 $$\omega $$ production.