Nucleon form factors with2+1flavor dynamical domain-wall fermions

We report our numerical lattice QCD calculations of the isovector nucleon form factors for the vector and axial-vector currents: the vector, induced tensor, axial-vector, and induced pseudoscalar form factors. The calculation is carried out with the gauge configurations generated with $N_f=2+1$ dynamical domain-wall fermions and Iwasaki gauge actions at $\beta =2.13$, corresponding to a cutoff $a^{-1}=1.73\mathrm{GeV}$, and a spatial volume of $(2.7\mathrm{fm}{)}^3$. The up and down-quark masses are varied so the pion mass lies between 0.33 and 0.67 GeV while the strange quark mass is about 12% heavier than the physical one. We calculate the form factors in the range of momentum transfers, $0.2<q^2<0.75{\mathrm{GeV}}^2$. The vector and induced tensor form factors are well described by the conventional dipole forms and result in significant underestimation of the Dirac and Pauli mean-squared radii and the anomalous magnetic moment compared to the respective experimental values. We show that the axial-vector form factor is significantly affected by the finite spatial volume of the lattice. In particular in the axial charge, $g_A/g_V$, the finite-volume effect scales with a single dimensionless quantity, $m_{\pi }L$, the product of the calculated pion mass and the spatial lattice extent. Our results indicate that for this quantity, $m_{\pi }L>6$ is required to ensure that finite-volume effects are below 1%.