Isovector electromagnetic form factors of the nucleon from lattice QCD and the proton radius puzzle

Abstract

We present results for the isovector electromagnetic form factors of the nucleon computed on the CLS ensembles with $N_f=2+1$ flavors of $\mathcal{O}(a)$-improved Wilson fermions and an $\mathcal{O}(a)$-improved vector current. The analysis includes ensembles with four lattice spacings and pion masses ranging from 130 MeV up to 350 MeV and mainly targets the low-$Q^2$ region. In order to remove any bias from unsuppressed excited-state contributions, we investigate several source-sink separations between 1.0 fm and 1.5 fm and apply the summation method as well as explicit two-state fits. The chiral interpolation is performed by applying covariant chiral perturbation theory including vector mesons directly to our form factor data, thus avoiding an auxiliary parametrization of the $Q^2$ dependence. At the physical point, we obtain $\mu =4.71(11{)}_{\mathrm{stat}}(13{)}_{\mathrm{sys}}$ for the nucleon isovector magnetic moment, in good agreement with the experimental value and $⟨r_{\mathrm{M}}^2⟩=0.661(30{)}_{\mathrm{stat}}(11{)}_{\mathrm{sys}}{\mathrm{fm}}^2$ for the corresponding square-radius, again in good agreement with the value inferred from the $ep$-scattering determination [Bernauer et~al., Phys. Rev. Lett., 105, 242001 (2010)] of the proton radius. Our estimate for the isovector electric charge radius, $⟨r_{\mathrm{E}}^2⟩=0.800(25{)}_{\mathrm{stat}}(22{)}_{\mathrm{sys}}{\mathrm{fm}}^2$, however, is in slight tension with the larger value inferred from the aforementioned $ep$-scattering data, while being in agreement with the value derived from the 2018 CODATA average for the proton charge radius.

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• Gravitational form factors of the proton from lattice QCD
• FLAG Review 2024
• The Present and Future of QCD
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• Dispersion-theoretical analysis of the electromagnetic form factors of the nucleon: Past, present and future
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• Electromagnetic form factors of the nucleon from $N_f=2+1$ lattice QCD
• $N\pi$-state contamination in lattice calculations of the nucleon electromagnetic form factors
• Pauli radius of the proton
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• Differential Cross Section Predictions for PRad-II from Dispersion Theory
• Isoscalar electromagnetic form factors of the nucleon in $N_{\mathrm{f}}=2+1$ lattice QCD
• Electromagnetic form factors of the proton and neutron from $N_f=2+1$ lattice QCD
• Proton and neutron electromagnetic radii and magnetic moments from lattice QCD
• Theory of QED radiative corrections to neutrino scattering at accelerator energies
• Proton and neutron electromagnetic radii and magnetic moments from $N_f=2+1$ lattice QCD