Calculation of the derivative of nucleon form factors in Nf = 2 + 1 lattice QCD at Mπ = 138 MeV on a (5.5 fm)3 volume

We present a direct calculation for the first derivative of the isovector nucleon form factors with respect to the momentum transfer q2 using the lower moments of the nucleon 3-point function in the coordinate space. Our numerical simulations are performed using the Nf = 2 + 1 nonperturbatively O(a)-improved Wilson quark action and Iwasaki gauge action near the physical point, corresponding to the pion mass Mπ = 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 q2 extrapolation to the zero momentum point. These results are compared with the ones determined by the standard method, where the q2 extrapolations of the corresponding form factors are carried out by fitting models. We find that the new results from the momentum derivative method are obtained with a larger statistical error than the standard method, but with a smaller systematic error associated with the data analysis. Within the total error range of the statistical and systematic errors combined, the two results are in good agreement. On the other hand, two variations of the momentum derivative of the induced pseudoscalar form factor at the zero momentum point show some discrepancy. It seems to be caused by a finite volume effect, since a similar trend is not observed on a large volume, but seen on a small volume in our pilot calculations at a heavier pion mass of Mπ = 510 MeV. Furthermore, we discuss an equivalence between the momentum derivative method and the similar approach with the point splitting vector current.