Lattice QCD for Nuclear Physics
Only ~4% of the mass-energy in the universe is in a form (visible) that we have been able to explore and control in the laboratory. Unraveling the origin and the nature of the visible matter in our universe defines the field of Nuclear Physics. While the ``Yukawa-Couplings'' in the Standard Model of Electroweak Interactions provide the masses of the quarks and leptons, it is the strong dynamics of the quarks and gluons that provide more than 90% of the mass of the visible matter. Further, it is the strong dynamics that hold nucleons together into nuclei, providing the building blocks of life in the universe.
The laws that dictate the interactions between quarks and gluons are quite simple to construct, based upon an invariance under local gauge-transformations in an abstract (color) group space. The synthesis of special-relativity and quantum mechanics into quantum field theory provides the framework with which to describe all processes involving quarks and gluons. As the quantum fluctuations increase strength of the strong interactions with decreasing energy, low-energy nuclear processes cannot be determined as perturbations about non-interacting quarks and gluons, and the probabilities for various processes must be determined numerically by direct evaluation of the path integral. The numerical technique called Lattice QCD, in which space-time is discretized into a grid on which the quantum fields are defined, is the only known way to perform such a rigorous evaluation with uncertainties that can be systematically removed by decreasing the lattice-spacing and increasing the lattice-volume. Lattice QCD involves the stochastic evaluation of a very high dimensional integral (the path integral over the value of the fields at each point in space-time) and requires the largest computational resources that are currently available.
The NPLQCD collaboration is making rapid progress toward computing nuclear processes with lattice QCD. The presently available computational resources are providing the largest obstacle in such calculations - a limitation that is being slowly eliminated as computational resources move toward the exascale. Currently, calculations are performed at pion masses that are somewhat larger than those of nature, at lattice spacings which are barely small enough and in lattice volumes that are barely large enough. However, calculations are now being performed that are impacting the theoretical and experimental programs, a trend that will increase rapidly during the next few years, where the quark masses will be at their physical values, lattice-spacing artifacts will be removed by extrapolation of multiple lattice-spacing calculations, and finite-volume effects will be removed by extrapolation from multiple-volume calculations - using the known theoretical forms for such extrapolations. At that point, nuclear processes will be calculated with quantified uncertainties.
