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

Abstract

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 $16^3\times 24$ 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 $<x>$ 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 $\mu =2$ GeV is $<x{>}_{s+\bar{s}}=0.027\pm 0.006$ 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 $0.88\pm 0.07$. This is about twice as large as the phenomenologically fitted $\frac{<x{>}_{s+\bar{s}}}{<x{>}_{\bar{u}}+<x{>}_{\bar{d}}}$ 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.

50 Pages 58 Figures

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