Extraction of the first transverse moments of Sivers and $g^{\perp}_{1T}$ PDFs from COMPASS SIDIS data

According to QCD the quark structure of the nucleon spin within the $\textit{twist-2}$ approximation is parameterized by eight transverse-momentum-dependent (TMD) parton distribution functions (PDFs). The PDFs describe the distributions of longitudinal and transverse momenta of partons and their correlations with nucleon and quark polarizations and can be accessed through measurement of spin (in)dependent azimuthal asymmetries in semi-inclusive DIS (SIDIS). The COMPASS experiment at CERN, as part of its programme, addresses the exploration of the spin structure of the nucleon by measuring spin (in)dependent azimuthal asymmetries in SIDIS. Using the high-statistics data collected by the COMPASS Collaboration in 2010 with naturally polarized $\mu^{+}$-beam and a transversely polarized proton ($NH_{3}$) target the first transverse moments of the Sivers PDF $f_{1T}^{\perp}$ for $\textit{u}$ and $\textit{d}$ quarks were obtained from the $P_{T}$-weighted Sivers asymmetries $A_{UT}^{\sin(\phi_{h} - \phi_{s})}$. Then, using the same formalism, the first moments of the $g_{1T}^{\perp}$ PDF were extracted for the $P_{T}$-weighted double spin asymmetries $A_{LT}^{\cos(\phi_{h} - \phi_{s})}$. The latter results have not yet been released by the collaboration and are not for public use at this stage.