Extraction of first transverse moments of Sivers and $g_{1T}^{\perp}$ parton distribution functions from polarized semi-inclusive deep inelastic scattering data of the COMPASS experiment

COMPASS is a high-energy physics experiment located in the North-area of SPS (M2-beamline) at CERN. One of its main physics goals is the exploration of the transverse spin structure of the nucleon by measuring nucleon spin (in)dependent azimuthal asymmetries in semi-inclusive DIS and, recently, also in Drell-Yan processes. Within QCD parton model approach, these asymmetries are related to the specific convolutions of certain transverse-momentum-dependent (TMD) \textit{twist-2} and \textit{higher twist} parton distribution functions (PDFs) and fragmentation functions (FFs). The TMD PDFs play a fundamental role describing the parton-longitudinal and -transverse momenta distributions and their correlations with nucleon and quark spins. In 2010 COMPASS measured the complete set of SIDIS transverse-spin-dependent asymmetries (TSAs), using a longitudinally polarized muon beam striking a transversely polarized $NH_3$ target. Particular attention was given to the study of hadron transverse momentum $P_T$-weighted Sivers asymmetry which is used to extract first transverse moments of Sivers TMD PDF. In this work, the extraction of the first transverse moments of Sivers TMD PDF for $u$ and $d$ quarks is verified using reprocessed 2010 proton COMPASS data. The same formalism is then applied for the extraction of the $A_{LT}^{\cos(\phi_{h}-\phi_{S})}$ $P_T$-weighted asymmetries and the related first transverse moment of the $g_{1T}^{\perp}$ PDF. This leading-twist distribution describes the correlation between the longitudinal polarization of a quark inside the nucleon and the transverse spin of a nucleon. The first moment of the $g_{1T}^{\perp}$ PDF for $u$ and $d$ quarks is evaluated for the first time.