Pion parton distribution functions with the nonrelativistic constituent quark model

Abstract: We calculate the valence quark distribution functions of the $\pi$ meson using the non-relativistic chiral constituent quark model. The $\pi$ wave function is obtained by solving the two-body Schr\"odinger equation within the framework of constituent quark model. We transform the $\pi$ wave function from the rest frame to the light cone or infinite momentum frame based on the Lorentz boost. The valence quark distributions at the initial evolution scale are obtained. The QCD evolution are given with the DGLAP equations with parton-parton recombination corrections. With tuning the valence up (down) quark mass to 70 MeV, the calculated valence up quark distributions at $Q^2=20$ GeV$^2$ are in good agreement with the E615 experimental data. The structure functions $\rm{F}_2^\pi(x,Q^2)$ of pion are also calculated which consist with the H1 experimental data. The proposed mechanisms here could be also used to study other hadrons.