Strange Electromagnetic Form Factors of the Nucleon with $N_f=2+1$ $\mathcal{O}(a)$-Improved Wilson Fermions

We present results for the strange contribution to the electromagnetic form factors of the nucleon computed on the coordinated lattice simulation ensembles with $N_f=2+1$ flavors of $\mathcal{O}(a)$-improved Wilson fermions and an $\mathcal{O}(a)$-improved vector current. Several source-sink separations are investigated in order to estimate the excited-state contamination. We calculate the form factors on six ensembles with lattice spacings in the range of $a=0.049–0.086\mathrm{fm}$ and pion masses in the range of $m_{\pi }=200–360\mathrm{MeV}$, which allows for a controlled chiral and continuum extrapolation. In the computation of the quark-disconnected contributions, we employ hierarchical probing as a variance-reduction technique.

Figure 1

Disconnected three-point function with a vector current inserted in the strange loop (red dot). For the range of momenta at the source and current insertion, we use ${\overrightarrow{n}}_{p/q}^2\le 6$, while at the sink, we restrict the range to ${\overrightarrow{n}}_{p^{\prime }}^2\le 2$ (${\overrightarrow{n}}_{p/q/p^{\prime }}^2$ denote the units of squared lattice momenta).

Figure 2

Results for the effective form factors on ensemble N200 determined via Eq. (13) at $Q^2=0.156{\mathrm{GeV}}^2$ compared to the estimate derived from the summation method (horizontal band).

Figure 3

Chiral and continuum extrapolation of the electric and magnetic radius and magnetic moment, using the standard method of Table 2. The vertical line denotes the physical kaon mass in the isospin limit [38].

Figure 4

Comparison of our final values for the radii and magnetic moments with LHPC [42], ETMC [43], and $\chi \mathrm{QCD}$ [34, 35], where the dark and light blue bands describe the statistical error and the total error, including systematics, respectively.

Figure 5

Comparison of our standard fit, based on the $z$ expansion up to $k=1$, to the analysis of existing experimental data [7]. The dark and light blue bands describe the statistical error and the total error, including systematics, respectively.