Moments of Nucleon's Parton Distribution for the Sea and Valence Quarks from Lattice QCD

Details Moments of Nucleon's Parton Distribution for the Sea and Valence Quarks from Lattice QCD Moments of Nucleon's Parton Distribution for the Sea and Valence Quarks from Lattice QCD

2008-11-11

arxiv.org/abs/0811.1779v1

Phys.Rev.D79:094502,2009

Physics

High Energy Physics

High Energy Physics - Phenomenology

50 Pages 58 Figures

Scientific paper

10.1103/PhysRevD.79.094502

We extend the study of lowest moments, $$ and $$, 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 $16^3 \times 24$ 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 $$ for the $u,d,$ and $s$ quarks, but $$ is consistent with zero within errors. We provide results for both the connected and disconnected insertions. The perturbatively renormalized $$ for the strange quark at $\mu = 2$ GeV is $_{s+\bar{s}} = 0.027 \pm 0.006$ which is consistent with the experimental result. The ratio of $$ for $s$ vs. $u/d$ in the disconnected insertion with quark loops is calculated to be $0.88 \pm 0.07$. This is about twice as large as the phenomenologically fitted $\displaystyle\frac{< x>_{s+\bar{s}}}{< x>_{\bar{u}}+< x>_{\bar{d}}}$ from experiments where $\bar{u}$ and $\bar{d}$ include both the connected and disconnected insertion parts. We discuss the source and implication of this difference.

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