Low $Q^2$ proton structure function, using gluon and pseudoscalar meson clouds in the constituent quark framework

The idea of the meson cloud approach in the chiral quark model has been extended to include gluon cloud in order to achieve the parton densities in the nucleon, based on the constitute quark framework. The splitting function of the quark to the quark-meson and quark-gluon at low $Q^2$ value are used to obtain parton densities in the constituent quark. The phenomenological constituent model is employed to extract the parton distributions in the proton at low $Q^2$ value. Since we have access to the parton densities at low $Q^2$, we are able to obtain $F_{2}(x,Q^2)$ structure function at low $Q^2$ value. The result is in good agreement with available experimental data and some theoretical models. To confirm the validity of our calculations, the fraction of total momentum of proton which is carried by gluon at high $Q^2$ and also the Gottfried sum rule are computed. The results are in good agreement with what are expected.