Nucleon form factors and root-mean-square radii on a (10.8 fm${)}^4$ lattice at the physical point

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 $t_{\mathrm{sep}}$ 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 $t_{\mathrm{sep}}$ 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.

Comments: 24 pages, 27 figures, published version. Erratum is appended to original version. We corrected the normalization factors in our analysis code, and then recalculated the form factors with the correct normalization factors