$πN σ$ Term and Quark Spin Content of the Nucleon

Details $πN σ$ Term and Quark Spin Content of the Nucleon $πN σ$ Term and Quark Spin Content of the Nucleon

1994-12-12

arxiv.org/abs/hep-lat/9412059v1

Nucl.Phys.Proc.Suppl. 42 (1995) 322-324

Physics

High Energy Physics

High Energy Physics - Lattice

contribution to Lattice '94; 3 page uuencoded ps file

Scientific paper

10.1016/0920-5632(95)00239-6

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 $.

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