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We report on a measurement of Spin Density Matrix Elements (SDMEs) in hard exclusive$$\rho ^0$$${\rho }^0$meson muoproduction at COMPASS using 160 GeV/cpolarised$$ \mu ^{+}$$${\mu }^{+}$and$$ \mu ^{-}$$${\mu }^{-}$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_{\text{T}}^2<$0.5 (GeV/c)$$^2$$${}^2$. Here,Wdenotes the mass of the final hadronic system,$$Q^2$$$Q^2$the virtuality of the exchanged photon, and$$p_{\textrm{T}}$$$p_{\text{T}}$the transverse momentum of the$$\rho ^0$$${\rho }^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 ($$\gamma ^*_T \rightarrow V^{ }_L$$${\gamma }_T^{\ast }\to V_L^{}$) indicate a violation ofs-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$$\rho ^0$$${\rho }^0$production.

 

A bstract A comprehensive set of azimuthal single-spin and double-spin asymmetries in semi-inclusive leptoproduction of pions, charged kaons, protons, and antiprotons from transversely polarized protons is presented. These asymmetries include the previously published HERMES results on Collins and Sivers asymmetries, the analysis of which has been extended to include protons and antiprotons and also to an extraction in a three-dimensional kinematic binning and enlarged phase space. They are complemented by corresponding results for the remaining four single-spin and four double-spin asymmetries allowed in the one-photon-exchange approximation of the semi-inclusive deep-inelastic scattering process for target-polarization orientation perpendicular to the direction of the incoming lepton beam. Among those results, significant non-vanishing cos ( ϕ−ϕ S ) modulations provide evidence for a sizable worm-gear (II) distribution, $$ {g}_{1\mathrm{T}}^q\left(x,{\mathrm{p}}_T^2\right) $$ g 1 T q x p T 2 . Most of the other modulations are found to be consistent with zero with the notable exception of large sin ( ϕ S ) modulations for charged pions and K + .