Non-perturbative effect in the nucleon structure function and the   Gottfried sum
  We investigate the non-perturbative effect in the nucleon structure function and the Gottfried sum by using a non-perturbative quark propagator with lowest dimensional condensate contributions from the QCD vacuum. It is shown that the non-perturbative effect modifies the conventional quark-parton model formula of the nucleon structure function at finite $Q^2$ and suggests a non-trivial $Q^2$ dependence in the Gottfried sum. 
Jian-Jun Yang, Bo-Qiang Ma, Guang-Lie Li