  The scalar strangeness content of the nucleon, characterized by the so-called
strangeness-nucleon sigma term, is of fundamental importance in understanding
its sea-quark flavor structure. We report a determination of the octet baryon
sigma terms via the Feynman-Hellmann theorem by analyzing the latest
high-statistics $n_f=2+1$ lattice QCD simulations with covariant baryon chiral
perturbation theory up to next-to-next-to-next-to-leading order. In particular,
we predict $\sigma_{\pi N}=55(1)(4)$ MeV and $\sigma_{sN}=27(27)(4)$ MeV, while
the first error is statistical and the second systematic due to different
lattice scales. The predicted $\sigma_{sN}$ is consistent with the latest LQCD
results and the results based on the next-to-next-to-leading order chiral
perturbation theory. Several key factors in determining the sigma terms are
systematically taken into account and clarified for the first time, including
the effects of lattice scale setting, systematic uncertainties originating from
chiral expansion truncations, and constraint of strong-interaction isospin
breaking effects.
