Calculation of derivative of nucleon form factors in $N_f = 2+1$ lattice QCD at $M_\pi = 138$ MeV on a (5.5 fm)$^3$ volume

Understand

We present a direct calculation for the first derivative of the isovector nucleon form factors with respect to the momentum transfer $q^2$ using the lower moments of the nucleon 3-point function in the coordinate space.

• Our numerical simulations are performed using the $N_f = 2 + 1$ nonperturbatively $O(a)$-improved Wilson quark action and Iwasaki gauge action near the physical point, corresponding to the pion mass $M_\pi =138$ MeV, on a (5.5 fm)$^4$ lattice at a single lattice spacing of $a = 0.085$ fm.
• In the momentum derivative approach, we can directly evaluate the mean square radii for the electric, magnetic, and axial-vector form factors, and also the magnetic moment without the $q^2$ extrapolation to the zero momentum point.
• These results are compared with the ones determined by the standard method, where the $q^2$ extrapolations of the corresponding form factors are carried out by fitting models.