Spin, TMDs and DVCS at COMPASS

The main objective of the COMPASS muon physics program is the study of the nucleon spin. COMPASS has accumulated data during 5 years using the CERN SPS 160 GeV polarized muon beam and a longitudinally or transversely polarized deuteron ($^{6}$LiD) or proton (NH$_{3}$) target. We present here results obtained on the gluon helicity from double spin asymmetries of cross-sections for two different channel, open charm production and high transverse momentum hadron pairs, both proceeding through the photon–gluon fusion process. Results show a gluon helicity compatible with zero in the measured range, $x$~0.1, constraining the total integral of $\Delta G$ below ~0.3 in absolute value. The consequence for the total nucleon spin decomposition is shown. The longitudinal spin structure functions of the proton $g_{1^{p}}$ and of the deuteron $g_{1^{d}}$ were measured in parallel as well as the quark helicities for the various flavours. On the transversity side, the results obtained with a proton target for the Collins and Sivers asymmetries are presented for positive and negative hadrons as a function of several variables: $x, z$ and $p_{T}$. The Collins asymmetry, sensitive to the transverse spin structure $h_{1}(x)$, shows a large signal at high $x$ for both hadron charges. The Sivers asymmetry shows a positive signal for positively charged hadrons, smaller than observed by HERMES, however in a slightly different kinematic range. Finally, we briefly present plans for the future COMPASS-II experiment which include two new topics: Exclusive reactions DVCS and DVMP using a muon beam and a hydrogen target in view of a transverse imaging of the nucleon, as well as polarized Drell-Yan measurements using a pion beam and a polarized NH$_{3}$ target to study transverse momentum dependent distributions.