Moments of nucleon’s parton distribution for the sea and valence quarks from lattice QCD

We extend the study of lowest moments, ⟨x⟩ and ⟨x^2⟩, of the parton distribution function of the nucleon to include those of the sea quarks; this entails a disconnected insertion calculation in lattice QCD. This is carried out on a 16^324 quenched lattice with Wilson fermion. The quark loops are calculated with Z₂ noise vectors and unbiased subtractions, and multiple nucleon sources are employed to reduce the statistical errors. We obtain 5 signals for ⟨x⟩ for the u, d, and s quarks, but ⟨x^2⟩ is consistent with zero within errors. We provide results for both the connected and disconnected insertions. The perturbatively renormalized ⟨x⟩ for the strange quark at =2 GeV is ⟨x⟩ₒ+ₒ=0. 0270. 006 which is consistent with the experimental result. The ratio of ⟨x⟩ for s vs u/d in the disconnected insertion with quark loops is calculated to be 0. 880. 07. This is about twice as large as the phenomenologically fitted ⟨x⟩ₒ+ₒ⟨x{⟩ₔ+⟨x⟩₃} from experiments where u and d include both the connected and disconnected insertion parts. We discuss the source and implication of this difference.