Precision Nucleon Charges and Form Factors Using 2+1-flavor Lattice QCD

We present high statistics results for the isovector nucleon charges and form factors using seven ensembles of 2+1-flavor Wilson-clover fermions. The axial and pseudoscalar form factors obtained on each ensemble satisfy the PCAC relation once the lowest energy $N\pi$ excited state is included in the spectral decomposition of the correlation functions used for extracting the ground state matrix elements. Similarly, we find evidence that the $N\pi\pi $ excited state contributes to the correlation functions with the vector current, consistent with the vector meson dominance model. The resulting form factors are consistent with the Kelly parameterization of the experimental electric and magnetic data. Our final estimates for the isovector charges are $g_{A}^{u-d} = 1.31(06)(05)_{sys}$, $g_{S}^{u-d} = 1.06(10)(06)_{sys}$, and $g_{T}^{u-d} = 0.95(05)(02)_{sys}$, where the first error is the overall analysis uncertainty and the second is an additional combined systematic uncertainty. The form factors yield: (i) the axial charge radius squared, ${\langle r_A^2 \rangle}^{u-d}=0.428(53)(30)_{sys}\ {\rm fm}^2$, (ii) the induced pseudoscalar charge, $g_P^\ast=7.9(7)(9)_{sys}$, (iii) the pion-nucleon coupling $g_{\pi {\rm NN}} = 12.4(1.2)$, (iv) the electric charge radius squared, ${\langle r_E^2 \rangle}^{u-d} = 0.85(12)(19)_{sys} \ {\rm fm}^2$, (v) the magnetic charge radius squared, ${\langle r_M^2 \rangle}^{u-d} = 0.71(19)(23)_{\rm sys} \ {\rm fm}^2$, and (vi) the magnetic moment $\mu^{u-d} = 4.15(22)(10)_{\rm sys}$. All our results are consistent with phenomenological/experimental values but with larger errors. Lastly, we present a Pad\'e parameterization of the axial, electric and magnetic form factors over the range $0.04< Q^2 <1$ GeV${}^2$ for phenomenological studies.