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

TL;DR

This paper uses lattice QCD to calculate the moments of nucleon parton distribution functions, including sea quarks, providing results consistent with experiments and revealing differences in strange quark contributions.

Contribution

It extends lattice QCD calculations to include sea quark moments and provides the first such results with disconnected insertions for nucleon PDFs.

Findings

Calculated <x> for u, d, s quarks with 5σ significance.

Found <x^2> consistent with zero within errors.

Strange quark <x> at 2 GeV matches experimental data.

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 $\displaystyle\frac{< x>_{s+\bar{s}}}{< x>_{\bar{u}}+< x>_{\bar{d}}}$ 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.