Scalar strangeness content of the nucleon and baryon sigma terms

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 ${\sigma }_{\pi N}=55(1)(4)\mathrm{MeV}$ and ${\sigma }_{sN}=27(27)(4)\mathrm{MeV}$, 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.

Figure 1

Octet baryon masses as a function of $M_{\pi }^2$ and $2M_K^2-M_{\pi }^2$ vs the BMW LQCD data [19]. The solid, dashed, and dot-dashed lines are obtained with the LECs from the three fits of Table 1. On the left and right panels, the strange-quark mass and the light-quark mass are fixed at their respective physical values.

Figure 2

Strangeness-nucleon sigma term determined from different studies. The blue and red bands are our NNLO and ${\mathrm{N}}^3\mathrm{LO}$ results, respectively.