We present a first QCD analysis of next-to-next-leading-order (NNLO) contributions of the spindependent parton distribution functions (PPDFs) in the nucleon and their uncertainties using the Jacobi polynomial approach. Having the NNLO contributions of the quark-quark and gluon-quark splitting functions in perturbative QCD (Nucl. Phys. B 889 (2014) 351-400), one can obtain the evolution of longitudinally polarized parton densities of hadrons up to NNLO accuracy of QCD. A very large sets of recent and up-to-date experimental data of spin structure functions of the proton g p 1 , neutron g n 1 , and deuteron g d 1 have been used in this analysis. The predictions for the NNLO calculations of the polarized parton distribution functions as well as the proton, neutron and deuteron polarized structure functions are compared with the corresponding results of the NLO approximation. We form a mutually consistent set of polarized PDFs due to the inclusion of the most available experimental data including the recently high-precision measurements from COMPASS16 experiments (Phys. Lett. B 753 (2016) 18-28). We have performed a careful estimation of the uncertainties using the most common and practical method, the Hessian method, for the polarized PDFs originating from the experimental errors. The proton, neutron and deuteron structure functions and also their first moments, Γ p,n,d , are in good agreement with the experimental data at small and large momentum fraction of x. We will discuss how our knowledge of spin-dependence structure functions can improve at small and large value of x by the recent COMPASS16 measurements at CERN, the PHENIX and STAR measurements at RHIC, and at the future proposed colliders such as Electron-Ion collider (EIC).

We use the valon model to calculate the transversity distribution functions , inside the Nucleon. Transversity distributions indicate the probability to find partons with spin aligned (anti-aligned) to the transversely polarized nucleon. The results are in good agreements with all available experimental data and also global fits.

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The spin dependent structure function, g ww 2 , is calculated in the valon model. A simple approach is given for the determination of the twist-3 part of theḡ 2 (x, Q 2 ) in Mellin space; thus, enabling us to obtain the full transverse structure function, g 2 (x, Q 2 ) for proton, neutron and the deuteron. In light of the new data, we have further calculated the transversely polarized structure function of g 3He 2 (x, Q 2 ). Our results are checked against the experimental data and nice agreements are observed.