The Many Mysteries of CP Violation

The electroweak interactions in the quark sector break CP symmetry, and a heroic effort by theorists and experimentalist over decades has tested and established the CKM picture for understanding this phenomenon. But many mysteries of CP violation remain, presenting future grand challenges for both theory and experiment. Does the lepton sector also violate CP, as current data suggests? Theoretical arguments say that QCD should either violate CP or preserve it via a dynamical mechanism that also produces axion particles as dark matter: can we detect such axions in the laboratory? What we know so far about the Higgs boson, and about CP violation, cannot explain how matter came to dominate over antimatter in the early universe: what are we missing?