Abstract
We present the nucleon form factors and root-mean-square (RMS) radii measured on a (10.8 fm$)^4$ lattice at the physical point. We compute the form factors at small momentum transfer region in $q^2\le 0.102$ GeV$^2$ with the standard plateau method choosing four source-sink separation times $t_{\rm sep}$ from 0.84 to 1.35 fm to examine the possible excited state contamination. We obtain the electric and magnetic form factors and their RMS radii for not only the isovector channel but also the proton and neutron ones without the disconnected diagram. We also obtain the axial-vector coupling and the axial radius from the axial-vector form factor. We find that these three form factors do not show large $t_{\rm sep}$ dependence in our lattice setup. On the other hand, the induced pseudoscalar and pseudoscalar form factors show the clear effects of the excited state contamination, which affect the generalized Goldberger-Treiman relation.
Highlights
In our analysis we employed different normalization factors from Eqs. (20)–(23) in the paper to evaluate the electric, magnetic, axial-vector, induced pseudoscalar, and pseudoscalar form factors in the nonzero q2
The horizontal band represents the fit result of GvEðq2Þ at tsep=a 1⁄4 12, 14, 16 for each q2
The results for the proton channel are obtained without the disconnected diagram
Summary
2. tsep dependence of the isovector electric form factor GvEðq2Þ with five lowest momentum transfers. The horizontal band represents the fit result of GvEðq2Þ at tsep=a 1⁄4 12, 14, 16 for each q2. 5. Electric RMS radius hr2Ei for the isovector (left) and proton (right) obtained by linear, dipole, quadratic and z-expansion fits for the combined data. The results for the proton channel are obtained without the disconnected diagram. Results for the electric RMS charge radius hr2Ei in the isovector, proton and neutron channels.
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