Nucleon form factors and structure functions with N_f=2+1 dynamical domain wall fermions

We report isovector form factors and low moments of structure functions of nucleon in numerical lattice quantum chromodynamics (QCD) from the on-going calculations by the RIKEN-BNL-Columbia (RBC) and UKQCD Collaborations with (2+1) dynamical flavors of domain-wall fermion (DWF) quarks. We calculate the matrix elements with four light quark masses, corresponding to pion mass values of m_\pi = 330-670 MeV, while the dynamical strange mass is fixed at a value close to physical, on (2.7 fm)^3 spatial volume. We found that our axial charge, g_A, at the lightest mass exhibits a large deviation from the heavier mass results. This deviation seems to be a finite-size effect as the g_A value scales with a single parameter, m_\pi L, the product of pion mass and linear spatial lattice size. The scaling is also seen in earlier 2-flavor dynamical DWF and Wilson quark calculations. Without this lightest point, the three heavier mass results show only very mild mass dependence and linearly extrapolate to g_A=1.16(6). We determined the four form factors, the vector (Dirac), induced tensor (Pauli), axial vector and induced pseudoscalar, at a few finite momentum transfer values as well. At the physical pion mass the form-factors root mean square radii determined from the momentum-transfer dependence %of the form factors are 20-30% smaller than the corresonding experiments. The ratio of the isovector quark momentum to helicity fractions, < x>_{u-d}/< x>_{\Delta u - \Delta d} is in agreement with experiment without much mass dependence including the lightest point. We obtain an estimate, 0.81(2), by a constant fit. Although the individual momentum and helicity fractions are yet to be renormalized, they show encouraging trend toward experiment.