Nucleon structure with dynamical (2+1)-flavor domain wall fermions lattice QCD

We report isovector form factors and low moments of isovector structure functions of nucleon from the coarse RIKEN-BNL-Columbia (RBC) and UKQCD joint dynamical (2+1)-flavor domain-wall fermions (DWF) ensembles. The lattice cut off is estimated at (a^{-1}=1.7) GeV. The lattice volume is as large as 2.7 fm across. We carefully optimize the nucleon source/sink separation in time to about 1.4 fm. Unexpectedly large finite-size effect in the axial charge is found. The effect scales with a single variable, the product (m_\pi L) of the pion mass (m_\pi) and lattice spatial linear extent (L), and sets in at around (m_\pi L = 5). We also discuss momentum-transfer dependence of the vector, induced tensor, axial-vector and induced pesudo-scalar form factors. From structure functions, fully non-perturbatively renormalized iso-vector quark momentum fraction, (< x >_{u-d}), helicity fraction, (< x >_{\Delta u - \Delta d}), and transversity, (< 1 >_{\delta u - \delta d}), are reported, as well as an unrenormalized twist-3 coefficient, (d_1). The ratio of the momentum to helicity fractions, (< x >_{u-d}/< x >_{\Delta u - \Delta d}), does not depend on light quark mass and agree well with the experiment. Their respective absolute values, fully renormalized, shows interesting trending toward the respective experimental values at the lightest light quark mass.