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(3) x 24 quenched lattice with Wilson fermion. The quark loops are calculated with Z(2) noise vectors and unbiased subtractions, and multiple nucleon sources are employed to reduce the statistical errors. We obtain 5 sigma signals for < x > for the u, d, and s quarks, but < x(2)> i 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 mu = 2 GeV is < x >(s+(s) over bar) = 0.027 +/- 0.006 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 0.88 +/- 0.07. This is about twice as large as the phenomenologically fitted < x >(s+($) over bar)/< x >((u) over bar)+< x >((d) over bar) from experiments where (u) over bar and (d) over bar include both the connected and disconnected insertion parts. We discuss the source and implication of this difference.