Moments of nucleon's parton distribution for the sea and calence quarks from lattice QCD

We extend the study of lowest moments, (x) and (x2), if 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 163×24 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 5σ signals for (x) for the u, d, and s quarks, but (x2) 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 μ=2 GeV is (x)s+s̅ =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+s̅ /(x)u̅ +(x)d̅ from experiments where u̅ and d̅ include both the connected and disconnected insertion parts. We discuss the source and implication of this difference.M. Deka, T. Streuer, T. Doi, S. J. Dong, T. Draper, K. F. Liu, N. Mathur, and A.W. Thoma