We propose to perform measurements of asymmetries of the Drell-Yan (DY) pairs production in collisions of non-polarized, longitudinally and transversally polarized protons and deuterons which provide an access to all leading twist collinear and TMD P
DFs of quarks and anti-quarks in nucleons. The measurements of asymmetries in production of J/Psi and direct photons will be performed as well simultaneously with DY using dedicated triggers. The set of these measurements will supply complete information for tests of the quark-parton model of nucleons at the QCD twist-two level with minimal systematic errors.
Search for azimuthal asymmetries in semi-inclusive production of charged hadrons by 160 GeV muons on the longitudinally polarized deuterium target, has been performed using the 2002- 2004 COMPASS data. The observed asymmetries integrated over the kin
ematical variables do not depend on the azimuthal angle of produced hadrons and are consistent with the ratio $g_1^d(x)/f_1^d(x)$. The asymmetries are parameterized taking into account possible contributions from different parton distribution functions and parton fragmentation functions depending on the transverse spin of quarks.They can be modulated (either/or/and) with $sin(phi), sin(2phi), sin(3phi)$ and $cos(phi)$. The $x$-, $z$- and $p_h^T$-dependencies of these amplitudes are studied.
