Scalar strange content of the nucleon from lattice QCD

Abstract

The scalar strange-quark matrix element of the nucleon is computed with lattice QCD. A mixed-action scheme is used with domain-wall valence fermions computed on the staggered MILC sea-quark configurations. The matrix element is determined by making use of the Feynman-Hellmann theorem which relates this strange matrix element to the change in the nucleon mass with respect to the strange-quark mass. The final result of this calculation is ${m}_{s}⟨N|\overline{s}s|N⟩=48\ifmmode\pm\else\textpm\fi{}10\ifmmode\pm\else\textpm\fi{}15\text{ }\text{ }\mathrm{MeV}$ and, correspondingly, ${f}_{s}={m}_{s}⟨N|\overline{s}s|N⟩/{m}_{N}=0.051\ifmmode\pm\else\textpm\fi{}0.011\ifmmode\pm\else\textpm\fi{}0.016$. Given the lack of a quantitative comparison of this phenomenologically important quantity determined from various lattice QCD calculations, we take the opportunity to present such an average. The resulting conservative determination is ${f}_{s}=0.043\ifmmode\pm\else\textpm\fi{}0.011$.