Transverse spin azimuthal asymmetries in SIDIS at COMPASS: Multidimensional analysis

One of the important objectives of the COMPASS experiment (CERN, SPS north area) is the exploration of transverse spin structure of nucleon via study of spin (in)dependent azimuthal asymmetries with semi-inclusive deep inelastic scattering (SIDIS) processes and recently also with Drell-Yan (DY) reactions. In the past twelve years series of measurements were made in COMPASS, using 160 GeV/c longitudinally polarized muon beam and polarized $^6LiD$ and $NH_3$ targets. Drell-Yan measurements with high energy (190 GeV/c) pion beam and transversely polarized $NH_3$ target started in 2014 with a pilot-run have been followed by 140 days of data taking in 2015. The 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 and are widely used in theoretical analyses and global data fits. In addition, future first ever polarized DY-data from COMPASS compared with SIDIS results will open a new chapter probing general principles of QCD TMD-formalism. In this review main focus is given to the very recent results obtained by the COMPASS collaboration from first ever multi-dimensional extraction of SIDIS transverse spin asymmetries.