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We present results for the isovector electromagnetic form factors of thenucleon computed on the CLS ensembles with $N_f=2+1$ flavors of$\mathcal{O}(a)$-improved Wilson fermions and an $\mathcal{O}(a)$-improvedvector current. The analysis includes ensembles with four lattice spacings andpion 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-statecontributions, we investigate several source-sink separations between 1.0 fmand 1.5 fm and apply the summation method as well as explicit two-state fits.The chiral interpolation is performed by applying covariant chiral perturbationtheory including vector mesons directly to our form factor data, thus avoidingan auxiliary parametrization of the $Q^2$ dependence. At the physical point, weobtain $\mu=4.71(11)_{\mathrm{stat}}(13)_{\mathrm{sys}}$ for the nucleonisovector magnetic moment, in good agreement with the experimental value and$\langler_\mathrm{M}^2\rangle~=~0.661(30)_{\mathrm{stat}}(11)_{\mathrm{sys}}\,~\mathrm{fm}^2$for the corresponding square-radius, again in good agreement with the valueinferred from the $ep$-scattering determination [Bernauer et~al., Phys. Rev.Lett., 105, 242001 (2010)] of the proton radius. Our estimate for the isovectorelectric charge radius, $\langle r_\mathrm{E}^2\rangle =0.800(25)_{\mathrm{stat}}(22)_{\mathrm{sys}}\,~\mathrm{fm}^2$, however, is inslight tension with the larger value inferred from the aforementioned$ep$-scattering data, while being in agreement with the value derived from the2018 CODATA average for the proton charge radius.

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