Origin of difference between ū and d̄ partons in the nucleon

Using the Euclidean path-integral formulation for the hadronic tensor, we show that the large difference between ū and d̄ does not come from the disconnected quark-loop insertion. Rather, it can come from the connected (quark line) insertion involving quarks propagating backwards in time. We study the influence of the backward time propagator in the axial-vector and scalar matrix elements in lattice gauge calculations and give an estimate of the violation of the Gottfried sum rule.