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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 largespatial volumes (exceeding $(10\ \mathrm{fm})^3$). The second PACS10 gaugeconfigurations are generated by the PACS Collaboration with the sixstout-smeared $O(a)$ improved Wilson quark action and Iwasaki gauge action atthe second gauge coupling $\beta=2.00$ corresponding to the lattice spacing of$a=0.063$ fm. We determine the isovector electric, magnetic and axial radii andmagnetic moment from the corresponding form factors, as well as theaxial-vector coupling $g_A$. Combining our previous results for the coarserlattice spacing [E. Shintani et al., Phys. Rev. D99 (2019) 014510; Phys. Rev.D102 (2020) 019902 (erattum)], the finite lattice spacing effects on theisovector radii, magnetic moment and axial-vector coupling are investigatedusing the difference between the two results. It was found that the effect on$g_A$ is kept smaller than the statistical error of 2% while the effect on theisovector radii was observed as a possible discretization error of about 10%,regardless of the channel. We also report the partially conserved axial vectorcurrent (PCAC) relation using a set of nucleon three-point correlationfunctions in order to verify the effect by $O(a)$-improvement of theaxial-vector current.

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