Nucleon form factors in N_f=2+1 lattice QCD at the physical point : finite lattice spacing effect on the root-mean-square radii

We present results for the nucleon form factors: electric (G_E), magnetic (G_M), axial (F_A), induced pseudoscalar (F_P) and pseudoscalar (G_P) form factors, using the second PACS10 ensemble that is one of three sets of 2+1 flavor lattice QCD configurations at physical quark masses in large spatial volumes (exceeding (10 fm)^3). The second PACS10 gauge configurations are generated by the PACS Collaboration with the six stout-smeared O(a) improved Wilson quark action and Iwasaki gauge action at the second gauge coupling β=2.00 corresponding to the lattice spacing of a=0.063 fm. We determine the isovector electric, magnetic and axial radii and magnetic moment from the corresponding form factors, as well as the axial-vector coupling g_A. Combining our previous results for the coarser lattice spacing [E. Shintani et al., Phys. Rev. D99 (2019) 014510; Phys. Rev. D102 (2020) 019902 (erattum)], the finite lattice spacing effects on the isovector radii, magnetic moment and axial-vector coupling are investigated using the difference between the two results. It was found that the effect on g_A is kept smaller than the statistical error of 2 isovector radii was observed as a possible discretization error of about 10 regardless of the channel. We also report the partially conserved axial vector current (PCAC) relation using a set of nucleon three-point correlation functions in order to verify the effect by O(a)-improvement of the axial-vector current.