Double $Q^2$-rescaling model and the nuclear effect of the parton distribution functions

In order to overcome the shortcoming of nonconservation of nuclear momentum existing in the original $Q^2$-rescaling model(O$Q^2$RM) and avoid introducing nuclear shadowing factor, we proposed a double $Q^2$-rescaling model(D$Q^2$RM) for the parton distributions of the bound nucleon. Using the experimental data of lepton-nucleus deep inelastic scattering(DIS) and the condition of the nuclear momentum conservation, the $Q^2$-rescaling parameters of various partons for Sn, Fe, Ca and C nuclei are determined. The rescaling parameters of valence quark distributions are larger than unity and graduauly increases with atomic number A, on the contrary, the rescaling parameters of sea quark distributions and gluon distributions are smaller than unity, and slowly decreases with A. By using this model, the experimental data of the DIS process, the nuclear Drell-Yan process and $J/\psi$ photoproduction process are consistently and quite satisfactorily explained. Key words --- parton distribution functions, Nuclear effect, Double $Q^2$-rescaling model