Abstract
We present the nucleon form factors and root-mean-square (RMS) radii measured on a ${(10.8\text{ }\text{ }\mathrm{fm})}^{4}$ lattice at the physical point. We compute the form factors at small momentum transfer region in ${q}^{2}\ensuremath{\le}0.102\text{ }\text{ }{\mathrm{GeV}}^{2}$ 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, and those RMS radii are consistent with the experimental values. 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
For the deep understanding of the nucleon and nucleus structures, a precise determination of structure functions is an essential ingredient
We present the nucleon form factors and root-mean-square (RMS) radii measured on a ð10.8 fmÞ4 lattice at the physical point
The measurement of the atomic spectroscopy [1] has agreed with the value from the ep scattering, while a recent measurement of the regular hydrogen spectroscopy [3] agrees with the value from the muonic hydrogen spectroscopy
Summary
For the deep understanding of the nucleon and nucleus structures, a precise determination of structure functions is an essential ingredient. An unknown effect for the proton charge radius has been revealed as a significant discrepancy between different approaches [1] in the ep scattering [1] process and the muonic hydrogen spectroscopy [2], in which 5.6-σ deviation appears as the so-called “proton radius puzzle.”. The measurement of the atomic spectroscopy [1] has agreed with the value from the ep scattering, while a recent measurement of the regular hydrogen spectroscopy [3] agrees with the value from the muonic hydrogen spectroscopy. Under such a confusing circumstance, the theoretical estimation is demanded as an independent test
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