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

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