$\pi N\sigma$ Term , $\bar{s}s$ in Nucleon, and Scalar Form Factor --- a Lattice Study

Abstract

We report on a lattice QCD calculation of the $\pi N\sigma$ term, the scalar form factor, and $⟨N|\bar{s}s|N⟩$. The disconnected insertion part of $\text{sg}$ is found to be $1.8\pm 0.1$ times larger than the connected insertion contribution. The $q^2$ dependence of $\text{sg}(q^2)$ is about the same as $G_E(q^2)$ of the proton so that $\text{sg}(2m_{\pi }^2)-\text{sg}(0)=6.6\pm 0.6$ MeV. The ratio $y=\text{ss}/\text{ud}=0.36\pm 0.03$. Both results favor a $\text{sg}\sim 53$ MeV, slightly larger than our direct calculation of $\text{sg}=49.7\pm 2.6$ MeV. We also compute $F_s$ and $D_s$ and find that the agreement with those from the octect baryon mass splittings crucially depends on the inclusion of the large disconnected insertion. Finally, we give our result for the $KN\sigma$ term.

Comments: 7 pages in Latex, 5 postscript figures