Lattice QCD Calculation of Nucleon Structure

This is a program to study nucleon structure from lattice Quantum Chromodynamics (QCD) with chiral fermions at the physical pion mass. The lattice gauge Monte Carlo calculation of Quantum Chromodynamics involves generating an ensemble of gauge background configurations with dynamical fermions and then calculating quark propagators on this background to form various two-point, three-point, and four-point correlation functions to study masses, decay constants, and nucleon structure through form factors and lepton-nucleon scattering cross sections. The realistic 3 flavor (u, d, and s quark) dynamical domain-wall fermion gauge configurations are generated by the RBC and UKQCD collaborations on lattices of different sizes and 5 lattice spacings at the physical pion mass point. The domain wall has very desirable chiral symmetry similar to QCD theory in the continuum. The specific quantities that we study include the gravitational form factors which can be obtained from the moments of the experimental generalized parton distribution (GPD) functions. This allows us to consider the decomposition of the proton spin and mass in terms of quarks and gluons. These will be probed at Jefferson Lab and the upcoming electron ion collider at Brookhaven National Lab. We also calculate the neutron electric dipole moment with the theta term. This addresses the charge-parity (CP) violation which may explain the excess of baryons in the Universe. This is being heavily pursued experimentally. We will also calculate the hadronic tensor to predict the neutrino- nucleon scattering cross section in the elastic, the resonance, and the shallow inelastic scattering region. These are needed input for the neutrino-nucleus scattering cross sections in order to help determine the neutrino flux in DUNE experiments. This will be a valuable theoretical advancement to serve the experimental program which needs precisely known neutrino flux in the energy range of 1 – 7 GeV in order to study neutrino oscillations, CP violations, etc.