More than 99% of the mass of the visible matter resides in hadrons which are bound states of quarks and gluons, collectively called partons. These are the fundamental constituents of Quantum Chromodynamics (QCD), the theory of the strong interactions. While QCD is a very elegant theory, it is highly non-linear and cannot be solved analytically, posing severe limitations on our knowledge for the structure of the hadrons. Lattice QCD is a powerful first-principle formulation that enables the study of hadrons numerically, which is done by defining the continuous equations on a discrete Euclidean four-dimensional lattice.
Hadron structure is among the frontiers of Nuclear and Particle Physics, with the 2015 Nuclear Science Advisory Committee’s Long-Range plan for Nuclear Physics identifying a future electron-ion collider (EIC) as the highest priority for new facility construction. In 2019, the National Academies of Sciences, Engineering, and Medicine (NAS) released an assessment report which strongly endorses the science case for an EIC. The NAS report identified three high-priority science questions to understand hadron structure:
- How does the mass of the nucleon arise?
- How does the spin of the nucleon arise?
- What are the emergent properties of dense systems of gluons?
In this talk I will discuss progress in Lattice QCD related to aspects of the above questions, with focus on the mass and spin decomposition. I will show results for the proton, which provides an ideal system for studying QCD dynamics. I will discuss the strengths of lattice calculations, but also identify the challenges associated with elimination of systematic uncertainties.