Strangeness of nucleons from $N_f=2+1+1$ lattice QCD

Abstract

We present the strange electromagnetic form factors of the nucleon using lattice QCD simulations with degenerate light, a strange, and a charm quark in the sea with masses tuned to their physical values. For the first time, the strange electromagnetic form factors are computed at the continuum limit using only ensembles simulated with physical quark masses, eliminating the need for chiral extrapolations and their associated systematic uncertainty. We obtain the momentum transfer dependence of the form factors using the $z$-expansion and provide the strange electric and magnetic radii, as well as the strange magnetic moment. When combining our statistical errors and systematic uncertainties stemming from the momentum transfer dependence fit, our errors are an order of magnitude smaller than those associated with experimental determinations of the strange electromagnetic form factor.

Figures (5)

• Figure 1: Nucleon two-point function (top) and disconnected nucleon three-point function (bottom).
• Figure 2: Results for $G^s_E(Q^2)$ (top) and $G^s_M(Q^2)$ (bottom). The right-pointing green triangles, orange squares, downward-pointing blue triangles, and purple pentagons show the results of the cB211.072.64, cC211.060.80, cD211.054.96, and cE211.044.112 ensembles, respectively. The red band corresponds to the continuum limit obtained by fitting to the $z$-expansion.
• Figure 3: Values of $\langle r^2_E\rangle^s$, $\langle r^2_M\rangle^s$, and $\mu^s$ obtained as a result of fitting to $G_E^s(Q^2)$ and $G_M^s(Q^2)$ with different values of $Q^2_{\rm cut}$. The upward-pointing violet triangles denote results from the $z$-expansion fits, the green crosses denote the Galster-like fit results, and the downward-pointing green triangles denote the results from dipole fits. The red band, which runs through vertically, corresponds to the model-averaged value obtained using the AIC.
• Figure 4: Results for the strange electric and magnetic radii and the magnetic moment of the nucleon obtained within this work (red circles and vertical band). We compare to previous results by $\chi$QCD (left-pointing open triangles) Sufian:2016pex and the Mainz group (blue diamonds) Djukanovic:2019jtp.
• Figure 5: Ellipses showing $95\%$ confidence curves from different experimental data. The green ellipse is from Ref. Young:2006jc, the orange from Ref. Gonzalez-Jimenez:2014bia, the black from Ref. Liu:2007yi and the blue from Ref. Gonzalez-Jimenez:2011qkf. The red bands and the red ellipse in the inset are from the lattice QCD determination of the strange electromagnetic form factors presented in this work.