The visible universe is primarily composed of protons and neutrons which bind together to form nuclei and account for over 99% of the mass of all visible matter. However, nuclei as we know them would not exist without an intriguing strongly interacting particle called the pion, which plays a key role as the carrier of the strong nuclear force over distance scales greater than the size of the proton. Experimental research, coupled with significant advances in theory, have revealed that strongly interacting particles such as protons, neutrons, and pions are composed of elementary particles called quarks and gluons whose interactions are described by quantum chromodynamics (QCD). QCD is therefore responsible for the formation of atomic nuclei and as such, almost all visible matter in the universe. 

With this INCITE project, researchers are carrying out lattice QCD calculations of the 3D structures of the pion and kaon, which are the Nambu-Goldstone bosons in strong interactions. Using a lattice QCD Lagrangian that preserves chiral symmetry, the team aims to determine the electromagnetic form factors at high momentum transfer, transverse momentum-dependent (TMD) wave functions, and parton distribution functions. These calculations are aimed at providing comparisons and predictions for experimental programs such as the Jefferson Lab (JLab) 12 GeV upgrade and the future Electron-Ion Collider (EIC). The results will deepen the understanding of the strong interaction and confinement, and provide comprehensive 3D imaging of the pion and kaon. The team will also use their findings to extract the Collins-Soper kernel for TMD evolution, which is a crucial input for the global analysis of proton TMDs from the JLab and EIC experiments.