Two nucleons on the lattice: Progress and challenges

Lattice QCD offers us the promise of quantitatively understanding and predicting the structure and interactions of nucleons directly from the quark and gluon degrees of freedom. With this foundation, we could then build a theory of nuclear structure and reactions with theoretical uncertainties that are fully rooted in the Standard Model of particle physics. In particular, lattice QCD can be used to determine key quantities and processes that are difficult to determine with experimental measurements and phenomenology alone. For example, lattice QCD can be used to determine the neutron-neutron to proton-proton-electron-electron amplitude that would arise from prospective lepton number violating interactions that could give rise to neutrinoless double beta decay of nuclei. Despite this promise, which members of the lattice QCD community have been diligently working towards for almost two decades, we have not yet observed lattice QCD calculations of two-nucleon interactions performed with a pion mass sufficiently light that we can make rigorous contact with the two- and three-nucleon effective theories that are routinely used to compute properties and reactions of light and medium mass nuclei. I will review the current status of lattice QCD calculations for two-nucleon (two-baryon) systems, as well as the challenges the calculations face and progress we are making to overcome these challenges.