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.
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