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Lattice QCD for Precision Nucleon Matrix Elements

Precision measurements on nucleons provide constraints on the Standard Model and can also discern the signatures predicted for particles beyond the Standard Model. Knowing the Standard Model inputs to nucleon matrix elements will be necessary to constrain the couplings of dark matter candidates such as the neutralino, to relate the neutron electric dipole moment to the CP-violating theta parameter, or to search for new TeV-scale particles though non-$V-A$ interactions in neutron beta decay. However, these matrix elements derive from the properties of quantum chromodynamics (QCD) at low energies, where the coupling is strong and thus perturbative treatments fail. Using lattice gauge theory, we can nonperturbatively calculate the QCD path integral on a supercomputer. In this proceeding, I will review a few representative areas in which lattice QCD can contribute to understanding the structure inside nucleon and how they can contribute to the search for beyond-the-Standard Model physics, with discussions of the difficulties and prospects for future development.