High-precision calculation of the strange nucleon electromagnetic form factors

We report a direct lattice QCD calculation of the strange nucleon electromagnetic form factors $G_E^s$ and $G_M^s$ in the kinematic range $0\le Q^2\lesssim 1.2{\mathrm{GeV}}^2$. For the first time, both $G_E^s$ and $G_M^s$ are shown to be nonzero with high significance. This work uses closer to physical lattice parameters than previous calculations, and achieves an unprecedented statistical precision by implementing a recently proposed variance reduction technique called hierarchical probing. We perform model-independent fits of the form factor shapes using the $z$-expansion and determine the strange electric and magnetic radii and magnetic moment. We compare our results to parity-violating electron-proton scattering data and to other theoretical studies.

Figure 1

Nonperturbative quark propagator contractions obtained from Eq. (1) by performing the path integral over the quark fields: connected (left) and disconnected (right).

Figure 2

The first 16 Hadamard vectors for hierarchical probing on a $4^3$ lattice; $\text{red}=+1$, $\text{black}=-1$.

Figure 3

Strange-quark and disconnected light-quark electric and magnetic form factors, with statistical error bars. The curves result from the $z$-expansion fits; the inner bands show the statistical uncertainty and the outer error bands show the combined statistical and systematic uncertainties (added in quadrature). The charge factors are not included.

Figure 4

Linear combination of form factors, $G_E^s+\eta G_M^s$, probed by forward-angle parity-violating elastic $ep$ scattering experiments [6, 7, 8, 10, 11, 12, 14, 15]. The coefficient $\eta$ depends on the scattering angle and $Q^2$; for the lattice data we use the approximation $\eta =A{Q}^2$, $A=0.94{\mathrm{GeV}}^{-2}$ [11]. In the low $Q^2$ region we also show the linear dependence on $Q^2$ resulting from the estimated charge radius and magnetic moment at the physical point.

Figure 5

Determinations of the strange magnetic moment: from direct lattice QCD calculations (this work and Ref. [18]; red circles), models and phenomenology [17, 48, 49, 50, 51, 52] (green squares), and from a recent global analysis of parity-violating elastic scattering data [53] (blue diamond).