Transverse spin azimuthal asymmetries at COMPASS: SIDIS Multi-D analysis & Drell-Yan

COMPASS is a high-energy physics experiment operating on the M2 beam line at the SPS at CERN. Using high energy muon and hadron beams the experiment covers broad range of physics aspects in the field of the hadron structure and spectroscopy. One of the important objectives of the COMPASS experiment is the exploration of transverse spin structure of the nucleon via study of spin (in)dependent azimuthal asymmetries with semi-inclusive deep inelastic scattering (SIDIS) processes and starting from 2014 also with Drell-Yan (DY) reactions. Experimental results obtained by COMPASS for azimuthal effects in SIDIS play an important role in the general understanding of the three-dimensional nature of the nucleon. Giving access to the entire "twist-2" set of transverse momentum dependent (TMD) parton distribution functions (PDFs) and fragmentation functions (FFs) COMPASS data trigger constant theoretical interest and are being widely used in phenomenological analyses and global data fits. In particular, recent unique x-$Q^{2}$-z-pT multidimensional results for transverse spin asymmetries recently obtained by COMPASS will serve as a direct and unprecedented input for TMD $Q^{2}$-evolution related studies, one of the hottest topics in the field of spin-physics. In addition, measurement of the Sivers and all other azimuthal effects in polarized Drell-Yan at COMPASS will reveal another side of the spin-puzzle providing a link between SIDIS and Drell-Yan branches. This will be a unique possibility to test universality and key-features of TMD PDFs using essentially the same experimental setup and exploring the same kinematic domain. In this review main focus will be given to the very recent results obtained by the collaboration for multi-dimensional transverse spin asymmetries and to the physics aspects of COMPASS polarized Drell-Yan program.