Low-$Q^{2}$ nucleon structure from an infrared-saturated evolution scheme

Abstract The low-$Q^2$ nucleon structure is given with a simple nonperturbative input of three valence quarks and an all-order infrared-saturated evolution scheme, showing some consistencies with the experimental data. The resonance peaks in the experimental data of $F_2$ structure function are found to be modulated by the valence quark distributions. With little sea quark distributions at low $Q^2$, the valence-quark bump is clearly shown in the structure function. The three valence quark distributions at the hadronic scale is found to be the dominant origin of the PDFs at the hard scales. The high-twist corrections are needed to explain the sizeable discrepancy between the theory and the experimental measurements at low $Q^2$. The infrared-saturated evolution scheme is a powerful tool for connecting the nucleon structures in the nonperturbative and perturbative regions.