$\pi N \sigma$ Term and Quark Spin Content of the Nucleon

TL;DR

This paper presents lattice QCD calculations of the $ N$ sigma term and quark spin content of the nucleon, providing insights into sea quark contributions and nucleon structure.

Contribution

It introduces a stochastic $Z_2$ noise algorithm for disconnected insertions and reports new lattice results for the sigma term and quark spin contributions.

Findings

 N sigma term is approximately 39 MeV.

Strange quark condensate in the nucleon is large, about 1.16.

Quark spin contributions are .78 for u, .42 for d, and .13 for s quarks.

Abstract

We report results of our calculation on the $\pi N\sigma$ term and quark spin content of the nucleon on the quenched $16^3 \times 24$ lattice at $\beta = 6.0$. The disconnected insertions which involve contributions from the sea quarks are calculated with the stochastic $Z_2$ noise algorithm. As a physical test of the algorithm, we show that the forward matrix elements of the vector and pseudoscalar currents for the disconnected insertions are indeed consistent with the known results of zero. We tried the Wuppertal smeared source and found it to be more noisy than the point source. With unrenormalized $m_q=4.42(17)$MeV, we find the $\pi N\sigma$ term to be $39.2\pm 5.2$ MeV. The strange quark condensate in the nucleon is large, i.e. $\langle N|\bar{s}s|N\rangle = 1.16 \pm 0.54$. For the quark spin content, we find $\Delta u =0.78\pm 0.07$, $\Delta d =-0.42\pm 0.07$, and $\Delta s = -0.13\pm 0.06$. The flavor-singlet axial charge $g_A^1 = \Delta \Sigma =0.22\pm 0.09 $.