The Scalar Strange Content of the Nucleon from Lattice QCD

TL;DR

The paper determines the scalar strange content of the nucleon using a mixed-action lattice QCD approach and the Feynman–Hellmann theorem, yielding $m_s \langle N| \bar{s} s | N \rangle = 49 \pm 10 \pm 15$ MeV and $f_s = 0.053 \pm 0.011 \pm 0.016$ for their calculation, with a conservative lattice average of $f_s = 0.043 \pm 0.011$. The method directly relates the strange content to the derivative of the nucleon mass with respect to $m_s$, $m_s \langle N| \bar{s} s | N \rangle = m_s \frac{\partial m_N}{\partial m_s}$, and benefits from reduced noise in ground-state extraction compared to direct matrix-element methods. Cross-lattice comparisons yield consistent results, supporting a smaller strange content than once expected and enabling estimates of heavy-quark matrix elements via the pion-nucleon sigma term, $\sigma_{\pi N}$. The findings have implications for dark-matter direct-detection predictions and for the understanding of strange-quark contributions to nucleon structure, providing a quantified lattice-based benchmark and a framework for future refinements with more light-quark mass points and continuum extrapolation.

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 | s-bar s| N > = 49 +-10 +- 15 MeV and, correspondingly f_s = m_s < N | s-bar s |N > / m_N = 0.051 +- 0.011 +- 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 +- 0.011.

Figures (8)

• Figure 1: Pion mass effective mass plots on the $b\approx0.125$ fm ensembles.
• Figure 2: Pion mass effective mass plots on the $b\approx0.09$ fm ensembles.
• Figure 3: Proton mass and representative effective mass plots on the $b\approx0.125$ fm ensembles.
• Figure 4: Proton mass and representative effective mass plots on the $b\approx0.09$ fm ensembles.
• Figure 5: Nucleon mass versus the strange-quark mass on the $b\approx0.125$ fm and $b\approx0.09$ fm ensembles. The vertical dashed lines represent the 68% confidence interval for the determination of $bm_s^\textrm{phy}$ on the $b\approx0.125$ fm and $b\approx0.09$ fm ensembles. The conversion to $r_1$ units is performed as in Eq. (\ref{['eq:mssbars_mev']}) using $\frac{1}{2}(\frac{r_1}{b}^{(1)} + \frac{r_1}{b}^{(2)})$ for each pair of ensembles.