SIDIS transverse spin azimuthal asymmetries at COMPASS: Multidimensional analysis

Exploration of transverse spin structure of the nucleon via study of the spin (in)dependent azimuthal asymmetries in semi-inclusive deep inelastic scattering (SIDIS) and Drell-Yan (DY) reactions is one of the main aspects of the broad physics program of the COMPASS experiment (CERN, Switzerland). In past decade COMPASS has collected a considerable amount of polarized deuteron and proton SIDIS data while 2014 and 2015 runs were dedicated to the Drell-Yan measurements. Results on SIDIS azimuthal effects provided so far by COMPASS play an important role in 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 are being widely used in phenomenological analyses and experimental data fits. Recent unique and first ever x-$Q^{2}$-z-pT multidimensional results for transverse spin asymmetries obtained by COMPASS serve as a direct and unprecedented input for one of the hottest topics in the field of spin-physics: the TMD $Q^{2}$-evolution related studies. In addition, extraction of the Sivers and all other azimuthal effects from first ever polarized Drell-Yan data collected recently by COMPASS will reveal another side of the spin-puzzle clarifying the link between SIDIS and Drell-Yan branches. This will be a unique possibility to test predicted universality and key-features of TMD PDFs using essentially the same experimental setup and exploring the same kinematical domain. In this review main focus will be given to the very recent results from COMPASS multi-dimensional analysis of transverse spin asymmetries and to the physics aspects of COMPASS polarized Drell-Yan program.