Spin density matrix elements in exclusive $\omega$ 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 µ${}^{+}$ and µ${}^{-}$ 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 $⟨$Q${}^2$$⟩$ = 2.1 (GeV/c)${}^2$, $⟨$W$⟩$ = 7.6 GeV/c${}^2$, and $⟨$p${}_T^2$$⟩$ = 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^{\ast }$$\to$ 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.