πNσterm,s¯sin the nucleon, and the 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 $〈N\left|\overline{s}s\right|N〉$. The disconnected insertion part of ${\sigma }_{\pi N}$ is found to be 1.8±0.1 times larger than the connected insertion contribution. The $q^2$ dependence of ${\sigma }_{\pi N}\left(q^2\right)$ is about the same as $G_E\left(q^2\right)$ of the proton so that ${\sigma }_{\pi N}\left(2\mathrm{}{m}_{\pi }^2\right)-{\sigma }_{\pi N}\mathrm{}\left(0\right)=6.6\mathrm{}\pm 0.6$ MeV. The ratio $y=\frac{〈N\left|\overline{s}s\right|N〉}{〈N|\overline{u}u+\overline{d}d|N〉}=0.36\mathrm{}\pm 0.03$. Both results favor a ${\sigma }_{\pi N}\sim 53$ MeV, slightly larger than our direct calculation of ${\sigma }_{\pi N}=49.7\mathrm{}\pm 2.6$ MeV. We also compute $F_s$ and $D_s$ and find that the agreement with those from the octet baryon mass splittings crucially depends on the inclusion of the large disconnected insertion. Finally, we give our result for the $\mathrm{KN}\sigma$ term.