Lattice Calculation of Nucleon Structure

A program to study nucleon structure from lattice Quantum Chromodynamics (QCD) with chi- ral fermions at the physical pion mass and in the continuum and innite volume limits is proposed. We would like to undertake the task of computing quark propagators of the overlap fermion and the gauge field tensor for the quark and glue observables in the nucleon on an ensemble of dynamical fermion gauge configurations with the 2+1- flavor domain-wall fermion (DWF) action on five lattice spacings and five volumes that include five large volume ones (spatial sizes from 4.8 fm to 9.6 fm) at the physical pion mass. Combining results from all 9 lattices covering lattice spacings from 0.06 fm to 0.2 fm, different volumes and pion masses ranging from 300 MeV down to physical pion mass at 139 MeV, we will perform large volume and continuum extrapolations for observables at the physical pion mass to be compared with existing experiments and to make predictions for those which will be measured in future experiments and calculated phenomenologically. We plan to concentrate our studies on the nucleon structure. We propose to continue our calculation of the glue and quarks spin and orbital angular momentum contributions to the nucleon spin so that we will have a complete decomposition of the nucleon spin. We will also continue to work on the N, strange and charm terms with additional large lattices at the physical pion mass to have more more precise and definitive global fitting to control the systematic errors, including the excited-states contamination, to finalize the calculation of these quantities to be compared with future experiments and to make a definite prediction for the Higgs coupling to the nucleon which is needed for dark matter search experiments. We propose to initiate a lattice calculation of the CP-violating neutron electric dipole moment (NEDM) from the QCD term. This is a challenging calculation as it is known to be quite noisy for small quark masses. Our preliminary results with the Cluster Decomposition Error Reduction (CDER) algorithm, shows that we can get 5 results at m = 330 MeV. Using a chiral fermion like the overlap fermion has an advantage: the chiral symmetry warrants that the NEDM is zero at zero quark mass. Given this anchor, it will help reduce the errors at the physical pion mass. We will extend our earlier calculation of the charmness, strangeness, and ..N term to include more lattices at the physical pion mass and different lattice spacings to better control the systematic errors due to continuum and infinite volume extrapolation and the excited-states contamination. To address the proton charge radius puzzle between the muonic hydrogen and the electron- proton scattering, we propose to use the overlap fermion to calculate the proton charge radius. Since the overlap fermion has smaller O(a2) errors compared to many other fermions, it should have similarly smaller O(q2a2) errors in the form factors with finite q2. This will allow better control of the q2 extrapolation with the z-expansion to obtain the charge radius. We will also calculate the isovector axial form factors gA(q2). Since the charge and axial radii are sensitive to the lattice volume, we propose to calculate them on three sets of otherwise identical lattices, except with lattice sizes ranging from 4.8 fm to 9.6 fm to assess the volum effect. An additional two lattices at smaller lattice spacings will be calculated for continuum extrapolation.