The feature of parton densities inside the nucleon at low Q 2 plays an essential role in particle physics. To calculate these densities there are different types of models, among which the chiral quark model (χ QM) is the famous one. In this model, baryons are made from the ground states of constituent quarks, which are initially bare and finally surrounded by pseudo-scalar mesonic clouds. Here, in addition to mesonic clouds, we also take into account the gluonic clouds. The required bare quarks are obtained using the solution of the Dirac equation under a squared radial potential. The wavefunctions which are primarily in momentum space can be converted to a distribution in the x-Bjorken space by two different methods. Using the modified χ QM, we extract the parton distributions inside the proton at low Q 2 values and compare them with some experimental and phenomenological groups. The distributions can be evolved to high-energy scales, using the DGLAP evolution equations. The results are in good agreement with available experimental data and some phenomenological groups.

We extract the polarized parton distribution functions (PPDFs) of proton. To this end we do a global analysis on recent and up-to-dated experimental data of polarized nucleon and deuteron structure functions at the NLO accuracy of perturbative QCD. We use the Jacobi polynomials expansion technique to do the required analyses. To achieve a more realistic estimation of the PPDFs and observable uncertainties we employ the Hessian error propagation. Following that we apply a theoretical approach which is based on imposing Lorentz structure in the parton model to investigate the transverse momentum dependence of these PPDFs. In this approach, the transverse momentum dependent (TMD) polarized parton distributions, which are also called the helicity distributions, are related to the integrated ones. This relation is indicating the priority and importance of data analysis for PPDFs. The results show a convenient general treatment expected for TMD densities which are in fact resulted from data analysis and fitting processes of integrated PPDFs in an adequate and a proper way.

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Abstract. We investigate the transverse momentum dependent (TMD) quark and gluon distribution functions in the modified chiral quark model (χQM ). Calculations of the TMD quark and gluon densities, using the modified χQM are done for the first time in this article. For this propose we first formulate the TMD interactions that occur in the χQM at low Q 2 scale (Q 2 = 0.35 GeV 2 ) and then obtain the TMD parton distributions inside the proton, considering the interactions. To this end, we need to compute the TMD bare quark distributions. These TMD bare densities are calculated, using the solution of Dirac equation with a squared radial symmetry potential . It is shown that our results consist appropriate behavior which are expecting for the TMD parton distributions.

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