Europe’s preeminent particle-physics organization will need global help to fund the project, which is expected to cost at least €21 billion and would be a follow-up to the lab’s famed Large Hadron Collider. The new machine would collide electrons with their antimatter partners, positrons, by the middle of the century. The design—to be built in an underground tunnel near CERN’s location in Geneva, Switzerland—will enable physicists to study the properties of the Higgs boson and, later, to host an even more powerful machine that will collide protons well into the second half of the century. The approval is not yet...